text:
\section*{Abstract} The majority of microfabricated ion traps in use for quantum information processing are of the 2D `surface-electrode' type or of the 3D `wafer' type. Surface-electrode traps greatly simplify fabrication and hold the promise of allowing trapped-ion quantum computers to scale via standard semiconductor industry fabrication techniques.  However, their geometry constrains them to having much lower trapping efficiency, depth, and harmonicity compared to 3D geometries.  Conversely 3D geometries offer superior trap performance but fabrication is more complex, limiting potential to scale. We describe new `trench' geometries that exist in the design space between these two paradigms.  They still allow for a simple, planar electrode layer but with much more favourable trapping properties.  We propose such traps could be 3D-printed over a 2D wafer with microfabricated components already integrated into it, thus retaining all the integration techniques and scaling advantages of surface-electrode traps. As a proof of principle we use 2-photon direct
laser writing lithography to print the required electrode structures with the proposed geometry.

\section{Introduction}

The surface-electrode ion trap (SET)~\cite{Chi05} was a major step forward for realizing the trapped ion quantum computer when it was first demonstrated in 2006~\cite{Sei06}.  The SET allows for the trap electrodes to be fabricated as a single layer on a wafer.  This has allowed for a diverse range of traps to be easily fabricated with rapid turnaround in relatively simple university cleanrooms as well as with commercial MEMS and CMOS processes~\cite{Blain_2021}. Underneath this top electrode layer can be many other functional layers containing all the required classical control elements, as shown schematically in Fig.~\ref{wafer}.  These include current-carrying wires for magnetic field-driven gates~\cite{Allcock13,Warring13}, photonic integrated circuits for laser delivery~\cite{Mehta2016, Ivory21, Mehta20}, superconducting nanowires~\cite{Slichter17, Todaro_2021} or avalanche photodiodes~\cite{Setzer_2021, Reens_2022} for photon detection, active CMOS electronics such as DACs for trap voltage generation~\cite{Stuart19}, and routing layers and thru-wafer vias~\cite{Guise15} to external connections.  Whilst the complete set of control elements required for QIP has yet to be integrated into a single  device, they have all been demonstrated separately and efforts to combine them are underway.

\begin{figure}[h]
\includegraphics[width=1\textwidth]{wafer4.pdf}
\centering
\caption{\label{wafer}Cross-section of a trap fabricated using our proposed method of 3D printing an electrodes onto a wafer containing electrode routing and some of the potential integrated ion control elements that have been demonstrated.}
\end{figure}

3D `wafer' traps on the other hand typically require thru-wafer machining~\cite{Wilpers12}, and usually alignment and stacking of multiple wafers, to achieve the desired geometries.  These processes generally preclude the CMOS-like monolithic approach to integrating functional elements, and instead relies on further serial assembly of bespoke and heterogeneous components that requires much new process development~\cite{Ernzer, AQTION, Translume, Day21}.  The recently developed approach of combining wafer stacking and SETs~\cite{Auchter22} potentially offers a solution to some of these issues.

Despite these fabrication disadvantages, wafer traps are still under active development because SETs have several major drawbacks~\cite{Blakestad09}, specifically:
\begin{itemize}
\item  Trapping potentials are less harmonic.  This causes any slight displacement of the trapping location due to stray charges or control voltage inaccuracies to shift the trap frequencies.  Without recalibration this will lead to errors in multi-qubit gates.  The increased cross-Kerr nonlinearity can also lead to gate errors due to spectator modes~\cite{Roos_2008, Nie_2009}.
\item  Trap depths are much lower~\cite{Chi05}, typically close to room temperature.  This makes loading ions less efficient and ion losses due to control field errors, stray charges, and background gas collisions are much more likely. Room temperature operation of more than a couple of ions in lighter ion species is effectively precluded due to short ion lifetimes.
\item Junctions between ion traps with favourable trapping strength and depth, and small pseudopotential barriers are harder to achieve than with a 3D geometry~\cite{Wesenberg2009}.
\item  As the ions reside in an open volume above a surface, they are poorly shielded from electric charges or crosstalk (photons, microwave control fields, or electric trapping fields) from other trapping zones on the SET.
\end{itemize}

In this paper we propose mitigating these issues by adding a 3D-printed dielectric structure onto the trap wafer before depositing the final metal electrode surface.  This allows us to retain the fabrication advantages of the SET whilst also retaining the advantageous trapping geometry of a 3D trap.  This requires finding trap geometries that meet these requirements.  In section~\ref{quantifying_trap_performance} we lay out how to quantify the performance of a given geometry.  In section~\ref{trench_trap_geometries} we propose several feasible geometries and simulate them.  Then finally, in section~\ref{3d_printing} we identify a suitable 3D printing process and print demonstration devices.

\section{\label{quantifying_trap_performance} Quantifying Trap Performance}

As alternatives to existing microfabricated trap designs, we explore several possible `trench' geometries, discussed in greater detail in the following section.  To assess the viability of these designs, we simulate them with COMSOL Multiphysics using the boundary element method (BEM). The Electrode software package~\cite{Electrode} is used for further post-processing of the electric fields extracted from the simulations.

In each trap simulation we set RF electrodes to unit voltage and DC electrodes to ground and calculate the electric field generated in the vicinity of the ion.  From these fields, we can calculate the pseudopotential of the trap, which is the effective potential seen by the ion~\cite{DEHMELT1968}.  By finding where this pseudopotential is at a minimum in the plane perpendicular to the trap axis, we locate the equilibrium position of the ion in two dimensions.  By also finding the saddle point of the pseudopotential (ie, the `escape point') and comparing the pseudopotential at this point to the pseudopotential at the center of the trap, we have a rough proxy for the depth of the trap (though in reality the situation is more complex due to the dynamical nature of a Paul trap).  At the ion's position, we fit the surrounding electric potential $V=V(r, \theta)$ to a cylindrical harmonic expansion

\begin{equation}
    V(r,\theta) = V_0\sum_{n=2}^\infty C_n \left(\frac{r}{r_0}\right)^n \cos(n\theta + \phi_n) + V_{off}
\end{equation}

\noindent where $r$ is distance from the trap center, $r_0$ is the minimum ion-electrode separation, $V_{off}$ is the potential at the ion, $\phi_n$ is the orientation of the $n$th-order multipole, and $C_n$ is the expansion coefficient associated with an $n$th-order multipole.  From these expansion coefficients, we define what we call the `quadrupole,' `hexapole,' and `octopole' strengths generated by our traps,
\begin{align*}
    \text{quadrupole}, C_2, \\
    \text{hexapole}, C_3' =& \frac{C_3}{C_2}, \\
    \text{octopole}, C_4' =& \frac{C_4}{C_2},
\end{align*}

\noindent which we illustrate schematically in Fig.~\ref{multipole}.

\begin{figure}[h]
\includegraphics[width=0.8\textwidth]{cyl_harm_exp.pdf}
\centering
\caption{\label{multipole}(a) A schematic cross-section of the potential generated by a SET, with the equilibrium position of the ion marked with a dot. (b) schematic cross-sections of the first three multipoles the potential in (a) can be expanded into, labelled with their respective expansion coefficients.}
\end{figure}

The quadrupole term gives the geometric efficiency of the trap.  Greater efficiency is desirable as it reduces the required RF voltage, and thus power dissipation as well as the possibility of voltage breakdown on the chip.  The hexapole and octupole terms give the leading order anharmonicities in the potential and are normalized to the quadrupole term as it is most useful to compare traps at the same ion secular frequency, not the same RF voltage.  Anharmonicities  increase cross-Kerr nonlinearity and introduce displacement-dependent frequency shifts in the ion's motion, increasing sensitivity of gate fidelity to the temperature of non-gate modes and the presence of stray electric fields.  Therefore, we seek designs which minimize higher-order multipole terms around the trap center.

In addition to trap depth and the multipole components of the trapping potential, we also calculate the open numerical aperture (NA) available for fluorescence collection and for laser beam access, as illustrated in Fig.~\ref{designs}.  A high NA (typically $\sim0.4$) is important for fast state readout on the ion.  For the novel designs discussed in Sec.~\ref{trench_trap_geometries}, we give an NA from above and from the substrate, as the ion detectors could be located in the substrate~\cite{Slichter17, Todaro_2021, Setzer_2021}, or placed above the trap.  For SETs the NA is trivially one, while our wafer traps, by their symmetry, have the same NA from both sides.  In all cases we consider a circular detector, but a modest improvement could be achieved with a rectangular detector.  These NA also gives us an idea of the range of angles available for laser beams perpendicular to the trap axis such that they can exit the trap without striking an electrode.

We scale all of our traps such that the closest electrode to the ion is 75\,$\mu$m away.  Because anomalous heating has a strong $\sim d^4$ dependence~\cite{King_1998, Turchette_2000}, the closest electrode will tend to dominate the heating rate.  For calculating trap depths we assume a $^{40}$Ca$^+$ ion trapped at a secular frequency of 4\,MHz by a 40\,MHz RF trap drive with no DC potentials applied.

\section{\label{trench_trap_geometries} Trench Trap Geometries}

3D printing offers great geometric versatility in trap design, since it can be used to produce arbitrary shapes.  In principle, we could 3D print electrodes with hyperbolic cross-sections.  Such electrodes would generate pure quadrupole potentials, with lower anharmonicities (as discussed in Sec.~\ref{quantifying_trap_performance}) than other geometries.  In practice however, our choices of geometry are limited by other fabrication and operation constraints, namely whether the geometry allows optical access to the ion for laser beam delivery and fluorescence detection and how easily the 3D-printed dielectric can be metalized (a problem discussed further in Sec.~\ref{3d_printing}).  These constraints naturally suggest what we refer to as a `trench' geometry, illustrated in Fig.~\ref{wafer}.  Trench geometries confine ions between two walls 3D printed on the surface of a wafer.  We explore several such `trench' geometries for microfabricated ion traps and compare their performance to SETs and wafer traps of similar dimensions.  Cross-sectional views of the geometries simulated are shown in Fig.~\ref{designs}.

The trap geometries we considered can be classified as either symmetric or anti-symmetric. Both sets of trap geometries are mirrored around a vertical plane along the trap axis, but in the anti-symmetric traps the role of RF and DC electrode is switched in the mirror half of the trap.  Obviously many asymmetric variations on these traps are possible, usually with properties somewhere between the symmetric or anti-symmetric ones.  We do not consider them here though as symmetries are generally desirable, and pragmatically we need to keep the parameter space of different traps to simulate tractable.

\begin{figure}[h]
\includegraphics[width=0.9\textwidth]{trap_designs.pdf}
\centering
\caption{\label{designs}Cross-sectional views of of the trap designs simulated.  The ions' location is shown as an orange dot and the trap axis is out of the page.  DC electrodes are blue, RF electrodes are red.  Numerical apertures are shown in lavender.}
\end{figure}

As shown in Fig.~\ref{designs}, all simulated traps aside from the SET are characterized by $\ge 3$ geometric parameters.  We select a subset of parameters (marked with Latin letters) to sweep while fixing the other parameters (marked with Greek letters).  For our trench traps, we also investigate how performance changes with the more relevant of the fixed parameters.  We do so by making multiple sweeps over the continuous parameters for different values of a fixed parameter.

\subsection{Simple Trench}

The first trap geometry we consider is the `simple trench'.  In this design, the two outermost electrodes of the SET are extended vertically to above the height of the ion.  The symmetric simple trench is primarily characterized by four dimensions, DC and RF electrode widths $c$ and $d$, trench wall height $\beta$, and trench wall thickness $\alpha$.  This last dimension does not strongly affect the potential seen by the ion, since the ion is shielded from all but the inner surfaces of the trench.  Because of this, a fixed value $\alpha = 100$\,$\mu$m, comparable to values used in our test fabrications (see section~\ref{3d_printing}), is used in all trench trap simulations.

We simulate a set of symmetric simple trench traps at a fixed ion height, allowing $c$ and $d$ to vary for discrete values of $\beta$.  Unlike the symmetric design, the anti-symmetric simple trench can be characterized with just two parameters, plane electrode width $e$ and trench wall height $f$.  (We find that ion height in the anti-symmetric trench depends mainly on $e$, as shown in Fig.~\ref{simple_trench}(f).  In fact, past $f\approx200$\,$\mu$m, ion height shows no dependency on $f$ noticeable beyond numerical noise.)  The full simulation results for our symmetric and anti-symmetric simple trench traps are shown in Fig.~\ref{simple_trench}.

\begin{figure}[h]
\includegraphics[width=1.0\textwidth]{data_trench_sym_anti_marked.pdf}
\centering
\caption{\label{simple_trench}Simulated parameters of SET traps vs the symmetric and anti-symmetric `simple trench' geometry. (a) Trap depth at a fixed radial frequency. (b) The quadrupole component ($C_2$) of the trapping potential at the ion.  (c) The hexapole component ($C_3'$) of the trapping potential.  (d) The octopole component ($C_4'$) of the trapping potential.  (e) Electrode dimensions at a constant ion-electrode separation for the symmetric simple trench trap.  (f) Electrode dimensions at a constant ion-electrode separation for the anti-symmetric simple trench trap. (g,h) NA above and below the ion.  Parameters are plotted against a generic geometric variable $w$, which is related to an electrode dimension of each trap as shown in the legend.  Simulation results are shown with markers.  The representative SET, wafer, and simple trench traps whose characteristics are summarized in Table \ref{tab:trap-summary} are highlighted with larger markers.  Simulation points are connected with dashed lines only as a guide to eye.}
\end{figure}

\subsection{Stacked Trench}

The simple trench geometry discussed above is closer to the ideal quadrupole geometry than a surface trap, but the flexibility of this geometry is limited by the fact that each wall can only contain one electrode.  As an alternative, we consider what we call the `stacked trench' geometry.  By allowing multiple electrodes to make up the trench wall, we can produce arrangements that more closely match the boundary conditions of a quadrupole, though the fact that the trench must remain open on the top prevents any trench geometry from being fully rotationally symmetrical.

The symmetric stacked trench trap can be characterized by four parameters: trench height $\epsilon$, trench width $\mu$, RF electrode height $g$, and the height of the RF electrode off of the ground plane $h$.  The anti-symmetric stacked trench trap can be characterized by three parameters: trench height $\xi$, bottom electrode height $j$, and trench width $i$.

These traps have two regimes for which ion-electrode separation is  75\,$\mu$m.  In the first regime, the ion is 75\,$\mu$m from the ground plane and the trench walls are further away, while in the second regime, the ion is 75\,$\mu$m  from the trench walls.  We consider both regimes in the antisymmetric case, but only the second in the symmetric case, since performance in the other regime was notably worse.

\begin{figure}[h]
\includegraphics[width=1.0\textwidth]{data_stacked_sym_marked.pdf}
\centering
\caption{\label{sym_stacked_trench}Simulated parameters of SET traps and wafer traps vs the symmetric `stacked trench' geometry. (a) Trap depth at a fixed radial frequency. (b) The quadrupole component ($C_2$) of the trapping potential at the ion.  (c) The hexapole component ($C_3'$) of the trapping potential.  (d) The octopole component ($C_4'$) of the trapping potential.  (e) The hexapole component of the trapping potential, excluding the SET data to make the other series more clear.  (f) Electrode dimensions at a constant ion-electrode separation for the symmetric stacked trench trap. (g,h) NA above and below the ion.   Parameters are plotted against a generic geometric variable $w$, which is related to an electrode dimension of each trap as shown in the legend.  Simulation results are shown with markers.  The representative wafer and symmetric stacked trench traps whose characteristics are summarized in Table \ref{tab:trap-summary} are highlighted with larger markers.  Simulation points are connected with dashed lines only as a guide to eye.}
\end{figure}

\begin{figure}[h]
\includegraphics[width=1.0\textwidth]{data_stacked_anti_marked.pdf}
\centering
\caption{\label{anti_stacked_trench}Simulated parameters of SET traps and wafer traps vs the anti-symmetric `stacked trench' geometry. (a) Trap depth at a fixed radial frequency. (b) The quadrupole component ($C_2$) of the trapping potential at the ion.  (c) The hexapole component ($C_3'$) of the trapping potential.  (d) The octopole component ($C_4'$) of the trapping potential.  (e) The hexapole component of the trapping potential, excluding the SET data to make the other series more clear.  (f) Electrode dimensions at a constant ion-electrode separation for the anti-symmetric stacked trench trap. (g,h) NA above and below the ion.   Parameters are plotted against a generic geometric variable $w$, which is related to an electrode dimension of each trap as shown in the legend.  Simulation results are shown with markers.  The representative wafer and anti-symmetric stacked trench traps whose characteristics are summarized in Table \ref{tab:trap-summary} are highlighted with larger markers.  Simulation points are connected with dashed lines only as a guide to eye.}
\end{figure}

\subsection{Comparison Geometries - SET and Wafer Traps}

As a point of comparison, we simulate common varieties of microfabricated trap: the SET and the wafer trap.  We first simulate the symmetric and anti-symmetric SET (also known as 5-wire and 4-wire SETs respectively).  One nice feature of SETs is that under the assumption of an infinitely large trap with no gaps between electrodes, simple closed-form expressions for the potential are available~\cite{House2008}.  While we use these closed-form expressions to calculate the parameters shown in Figs.~\ref{simple_trench}-\ref{anti_stacked_trench}, we also simulate our SETs in COMSOL as a way of benchmarking our BEM simulations.  We compare the multipole expansions, trap heights, and trap depths of BEM-generated and analytic potentials for the symmetric SET.  For most of the free parameter range, agreement across these parameters is within 2\%.  In the range where $a \ll b$ (see Fig.~\ref{designs}), divergence approaches 10\% due to the fact that the 1\,$\mu$m electrode spacing present in all BEM simulations is no longer negligible~\cite{Schmied_2010}.  For a fixed ion height there is one free parameter in the symmetric SET and no free parameters in the anti-symmetric one.

To compare our proposed trench designs against the most prominent set of current 3D microfabricated designs, we also simulate symmetric and anti-symmetric wafer traps, illustrated in the bottom row of Fig.~\ref{designs}.  A wafer thickness of $\lambda=50$\,$\mu$m of our simulated traps is comparable to those of designs implemented in the lab~\cite{Jost2010,Kienzler2015}.  The depth $\tau=1$\,mm of the wafers is selected to be much larger than wafer thickness and spacing so that the exact depth is unimportant.   Therefore, both designs have only one free parameter, the spacing $k$ between wafers in a stack.  This parameter is swept over while holding the ion-electrode distance constant.

\subsection{Summary}

Having generated the data shown above, we want to compare the simple and stacked trench trap designs with established SET and wafer trap designs and assess their relative merits.  For easy comparison between these four sets of simulated geometries, we select a `representative' trap from each category.  These traps in some qualitative way optimize the balance between trap depth and quadrupole strength/purity.  This selection is somewhat subjective, and optimum parameters may vary by application, but they are unlikely to differ greatly from what we have chosen here.  A table of values for there representative traps are shown in Table~\ref{tab:trap-summary}, and the associated dimensions given in Table~\ref{tab:trap-dims-summary}.

\begin{table}
\centering
\begin{tabular}{|c|c c|c c|c c|c c|}
\hline
& \multicolumn{2}{|c|}{SET} & \multicolumn{2}{|c|}{Simple} & \multicolumn{2}{|c|}{Stacked} & \multicolumn{2}{|c|}{Wafer}  \\
\hline
           & Sym & Anti & Sym & Anti & Sym & Anti & Sym & Anti  \\
\hline
\hline
Depth (eV)         & 0.06 & 0.07 & 0.08 & 0.23 & 0.33 & 0.22 & 0.16 & 0.39 \\
\hline
Quadrupole ($C_2$) & 0.17 & 0.17 & 0.18 & 0.24 & 0.31 & 0.40 & 0.35 & 0.39 \\
\hline
Hexapole ($C_3'$)  & 1.0 & 1.0 & 0.86 & 0.62 & 0.020 & 0.008 & 0.000 & 0.001 \\
\hline
Octopole ($C_4')$  & 0.75 & 0.75 & 0.55 & 0.36 & 0.024 & 0.407 & 0.344 & 0.007 \\
\hline
\end{tabular}
\newline
\caption{Summary of results for trap parameter calculations for the SET, simple trench trap (`Simple'), stacked trench trap (`Stacked'), and wafer trap. Values shown correspond to a set of geometric parameters selected to balance trap depth and quadrupole strength/purity.}
\label{tab:trap-summary}
\end{table}

\begin{table}
\centering
\begin{tabular}{|c|c|l|}
\hline
\multicolumn{2}{|c|}{Trap} & Dimensions ($\mu$m) \\
\hline
\hline
\multirow{2}{*}{SET} & Sym  & $a=161.2$, $b=59$ \\
                     & Anti & $\phi=75$\\
\hline
Simple & Sym  & $d=77.3$, $c=210$, $\beta=600$ \\
                      Trench  & Anti & $e=135.2$, $f=525$ \\
\hline
Stacked & Sym  & $g=140$, $h=80$, $\epsilon=300$ \\
                        Trench & Anti & $i=150$, $j=160$ \\
\hline
\multirow{2}{*}{Wafer} & Sym  & $k=50$ \\
                       & Anti & $k=53$ \\
\hline
\end{tabular}
\newline
\caption{The dimensions (in microns) of the traps whose parameters are summarized in Table \ref{tab:trap-summary}.}
\label{tab:trap-dims-summary}
\end{table}

From Table~\ref{tab:trap-summary}, we predict that all our trench geometries will outperform SETs.  For the symmetric simple trench trap, the improvement is practically negligible though. The antisymmetric simple trench is a significant improvement over the SET, offering $\sim$3$\times$ the depth, $\sim$40\% higher quadrupole strength, and $\sim$40\% lower hexapole strength.  Despite this it is still notably inferior to the wafer traps. The stacked trench traps on the other hand can have very comparable performance to wafer traps, with similar depth, quadrupole strength, and octopole terms.  The hexapole term for our representative trap is still larger than in wafer traps (where it can be zero by symmetry), but the factor $\sim50$ improvement over SETs will still lead to drastic improvement in trap performance.  Further improvement can be gained at the cost of lower NA optical access by making the walls higher.  As some point though manufacturing tolerances and curvature from stray fields will set a practical limit for either design.

\section{\label{3d_printing} 3D Printing}

Our chosen fabrication process for realizing these trench geometries is 2-photon direct laser write (DLW)
3D printing. The electrode structure is printed directly onto a functional trap wafer using a dielectric material.  The printing process uses a focused laser to polymerize this photosensitive material to generate solid structures~\cite{Pearre2019}. This can then be metallized to create conductive electrode surfaces.

Whilst not explored here, we note that the simple trench traps could be fabricated using UV-LIGA (Ultraviolet - Lithographie, Galvanoformung, Abformung). This process is already widely used to make electrodes for SETs~\cite{Arr13} and so would be straightforward to adopt.  UV-LIGA  is a fabrication process where metal is electroplated inside a photoresist mold patterned using UV lithography. As discussed above, the performance advantage of these designs over SETs is fairly modest compared to the stacked trench traps.  The stacked trench geometries could also be built using conventional MEMS techniques.  However, the 100s of $\mu$m vertical heights required are likely challenging to achieve with oxide film deposition.\\

\subsection{Dielectric Material}

We propose using ormocer (\textbf{or}ganically \textbf{mo}dified \textbf{cer}amic), a silica-based material, as our printable dielectric material.  The high RF frequencies ($\sim$10-100\,MHz) and voltages ($\sim$10-1000\,V) applied to ion trap electrodes places stringent requirements on the electrical and thermal properties of any dielectrics used.  High dielectric strength is required to avoid breakdown.  High resistivity and low loss tangent avoid direct heating of the dielectric.  A low dielectric constant reduces parasitic capacitance, requiring less current to drive the electrodes, and thus lower Ohmic losses in the electrode metal.   Finally, a high thermal conductivity ensures any heating from losses is minimized.  Ormocer properties are somewhat formulation dependent, but in Table~\ref{tab:ormocer-characteristics} we give some representative values measured in the literature to give an idea of what can be achieved.

\begin{table}
\centering
\begin{tabular}{|c|c|}
\hline
Relative permittivity & 2.5~\cite{Froehlich02}, 2.7~\cite{Laine92}, 3.1~\cite{Johansson03}  \\
\hline
Loss tangent & 0.0035~\cite{Johansson03}, 0.00397~\cite{Laine92}, 0.004~\cite{Froehlich02},\\
\hline
Dielectric strength (V/cm) & $8.7\times10^5$~\cite{Laine92}  \\
\hline
Bulk resistivity ($\Omega\cdot\text{cm}$) & $4.5\times 10^{16}$~\cite{Laine92}  \\
\hline
Thermal conductivity (W/m$\cdot$K) & 2.3\cite{Laine92}   \\
\hline
\end{tabular}
\newline
\caption{Electrical and thermal properties of ormocer.}
\label{tab:ormocer-characteristics}
\end{table}

For room temperature operation, outgassing needs to be low to ensure ultra-high vacuum pressures can be reached and the material must be able to withstand $\sim$200\,$^\circ$C vacuum bakes.  Low outgassing is also desirable as it reduces the chance of contaminating metal electrode surfaces, which are known to play a role in anomalous heating~\cite{hite2013surface}.  The organic cross-linked structure of ormocer reduces outgassing and makes ormocer fit for vacuum processes~\cite{fraunhofer}, although quantitative outgassing data is so far lacking.  Ormocer is stable to $>300\,^{\circ}$C~\cite{fraunhofer}.  For cryogenic operation, vacuum compatibility is much less of an issue but the structure must be able to survive repeated temperature cycles without structural failure, something that will need testing in future work.

\subsection{Initial Fabrication}

\subsubsection{Print}
As an initial test, ormocer based trap structures were printed onto a borosilicate glass wafer and metalized with $\sim20$\,nm of sputtered gold.  SEM images of which are shown in Fig.~\ref{unmetalized-prints}.  The printed structures are  $200\,\mu$m high with $100\,\mu$m wide trenches in between them, giving a $50\,\mu$m ion-electrode distance.  This is a fairly typical value, with most microfabricated traps historically lying in the few-10s to few-100s\,$\mu$m range. These traps were fabricated via a two-photon direct laser write process. A custom printer was used, based on open source concepts from the Janelia's open source Modular In vivo Multiphoton Microscopy System (MIMMS) and the printer described in~\cite{Pearre2019}.

This printer was built to address specific needs in terms of print speed and full wafer scalability while retaining the necessary resolution. In the print process, an individual 2D field of view (FOV) is scanned using a galvo for $y$ axis steps paired with a fast resonant imaging mirror operating at 8\,kHz in the $x$ axis; allowing for printing at speeds up to $\sim$8000\,mm/s. A piezoelectric actuator is then used to sweep this FOV in the normal $z$ axis to form an individual metavoxel. Series of these are then stitched together across the entirety of the wafer via a controllable hexapod (Physik Instrumente) with sub-micron precision. We chose to break each "island" into 4 metavoxels with a $200\,\mu$m~$\times$~$200\,\mu$m FOV. Each individual island is printed in under a minute with a voxel resolution under $2\,\mu$m in the $xy$ print plane (142  $x$ and  512 $y$ voxels) and under $3\,\mu$m in $z$. Demonstrating that, whilst this is an inherently serial  process, the overall  processing  times at the required resolution are  tractable  for  much  larger traps than are currently in use.

A hybrid resist is used in this printing process, based on Ormocomp photoresist (Microchem). To this we add a photoinitator, 2.4.6-trimethylbenzoyl phosphine oxide (TPO) (Sigma), a stabilizing agent, 3,5-Di-tert-butyl-4-hydroxytoluene (BHT), and Fluorescein (Sigma) for in situ imaging during printing. A Chameleon Discovery laser, set to 780\,nm, 100\,fs pulse width, 80\,MHz Rep rate, and $\sim$100\,mW was used to initiate polymerization. Resolution and therefore surface roughness is a function of resin choice as well as the fundamental optics and scan mechanics of the printer. The current design takes advantage of the critical electrical dimensions of the trap being on a vertical surface which minimizes discretization concerns. In addition, a small amount of shrinkage during curing is inevitable. We minimize this by using the highest possible laser power before explosions occur. We do not see delamination from the substrate or noticeable distortion of the structures under SEM imaging.

\begin{figure}[h]
\includegraphics[width=0.95\textwidth]{Aug21prints_marked_v1.pdf}
\centering
\caption{\label{unmetalized-prints}SEM images of gold coated ormocer trap structures printed on glass. In this structure, many trenches have been connected up with X-junctions, as is envisaged in a large `QCCD' processor~\cite{Blakestad09}. (a) An overhead view of a grid of symmetric stacked trenches showing segmentation of the top DC electrodes.  (b) An oblique view of the same grid.  (c) A close up view of an intersection of trenches.  (d) A false-color version of (c) showing DC electrodes in blue and RF electrodes in red.  (e) A close-up view of a DC electrode segment.}
\end{figure}

\begin{figure}[h]
\includegraphics[width=0.95\textwidth]{fab_process_v1.pdf}
\centering
\caption{\label{fab-process}Proposed integration of electrode metalization with printing process shown here on a short section of the larger trap shown in Fig~\ref{unmetalized-prints}.  (a) Silicon wafer with electrode routing and vias up to the surface is fabricated using standard CMOS process (metal shown copper coloured,  SiO$_2$ dielectric shown transparent).  (b) Aluminum is deposited and patterned to define gaps between electrodes.  (c) DLW used to print ormocer trap structures (blue).  (d) Gold is deposition from multiple angles to coat all surfaces of the print.  (e) Aluminium is etched to allow liftoff of the gold over the gaps between electrodes.  Insets shown the liftoff process in more detail.}
\end{figure}

\subsubsection{Metalization}

The next stage in our fabrication development is metalization.  Our trap structure is designed to be `self masking' - the isolation gaps between electrodes can be made deep enough (or with an undercut) such that directional deposition of metal onto the structure will not cause shorting between them. This metalization will connect the trap to vias already pre-fabricated on a planarized wafer using a standard CMOS process (see fig.~\ref{wafer}).  These vias must be off to the side of the printed structures as printing directly onto metal is difficult - the laser heats the metal causing violent disruption of the print.  On the substrate around the prints, isolation between electrodes will be achieved using a liftoff process.  We envisage using gold as our electrode metal as this is well established in ion trapping, and aluminium for the lifoff material.  The full process can be seen in Figure\,\ref{fab-process} and will be described in more detail in a forthcoming publication.

\subsubsection{Integrated Optics}

The final step to producing a working trap will be to integrate optics for laser delivery.  This is because trench designs do not offer the required optical access for free-space laser delivery.   Waveguides for light routing and grating couplers to focus beams onto the ions have now been demonstrated by several groups~\cite{Mehta2016, Ivory21, Mehta20}.  These demonstrations were using SETs, but one of the strengths of the traps proposed here is that the same technique can be used without modification. Other integrated features shown in Fig.~\ref{wafer}, whilst desirable, aren't an immediate requirement.

\section{Conclusion}

Additive 3D printing has the potential be a powerful enabling technology for trapped-ion quantum computing. It allows the combination of wafer-integrated ion control with the 3D structures required to obtain optimal trap performance. In order to realise this we have developed a novel trench geometry and shown it can be printed.  We lay out a roadmap to integrate the necessary electrical and optical routing to enable functional devices.

\section*{Acknowledgements}

We would like to acknowledge Aaron Casserly who suggested this collaboration, David Miller who assisted with process development, and Daniel Slichter who provided simulation code examples.\\

\FloatBarrier

\section*{Abstract} The majority of microfabricated ion traps in use for quantum information processing are of the 2D `surface-electrode' type or of the 3D `wafer' type. Surface-electrode traps greatly simplify fabrication and hold the promise of allowing trapped-ion quantum computers to scale via standard semiconductor industry fabrication techniques.  However, their geometry constrains them to having much lower trapping efficiency, depth, and harmonicity compared to 3D geometries.  Conversely 3D geometries offer superior trap performance but fabrication is more complex, limiting potential to scale. We describe new `trench' geometries that exist in the design space between these two paradigms.  They still allow for a simple, planar electrode layer but with much more favourable trapping properties.  We propose such traps could be 3D-printed over a 2D wafer with microfabricated components already integrated into it, thus retaining all the integration techniques and scaling advantages of surface-electrode traps. As a proof of principle we use 2-photon direct
laser writing lithography to print the required electrode structures with the proposed geometry.

\section{Introduction}

The surface-electrode ion trap (SET)~\cite{Chi05} was a major step forward for realizing the trapped ion quantum computer when it was first demonstrated in 2006~\cite{Sei06}.  The SET allows for the trap electrodes to be fabricated as a single layer on a wafer.  This has allowed for a diverse range of traps to be easily fabricated with rapid turnaround in relatively simple university cleanrooms as well as with commercial MEMS and CMOS processes~\cite{Blain_2021}. Underneath this top electrode layer can be many other functional layers containing all the required classical control elements, as shown schematically in Fig.~\ref{wafer}.  These include current-carrying wires for magnetic field-driven gates~\cite{Allcock13,Warring13}, photonic integrated circuits for laser delivery~\cite{Mehta2016, Ivory21, Mehta20}, superconducting nanowires~\cite{Slichter17, Todaro_2021} or avalanche photodiodes~\cite{Setzer_2021, Reens_2022} for photon detection, active CMOS electronics such as DACs for trap voltage generation~\cite{Stuart19}, and routing layers and thru-wafer vias~\cite{Guise15} to external connections.  Whilst the complete set of control elements required for QIP has yet to be integrated into a single  device, they have all been demonstrated separately and efforts to combine them are underway.

\begin{figure}[h]
\includegraphics[width=1\textwidth]{wafer4.pdf}
\centering
\caption{\label{wafer}Cross-section of a trap fabricated using our proposed method of 3D printing an electrodes onto a wafer containing electrode routing and some of the potential integrated ion control elements that have been demonstrated.}
\end{figure}

3D `wafer' traps on the other hand typically require thru-wafer machining~\cite{Wilpers12}, and usually alignment and stacking of multiple wafers, to achieve the desired geometries.  These processes generally preclude the CMOS-like monolithic approach to integrating functional elements, and instead relies on further serial assembly of bespoke and heterogeneous components that requires much new process development~\cite{Ernzer, AQTION, Translume, Day21}.  The recently developed approach of combining wafer stacking and SETs~\cite{Auchter22} potentially offers a solution to some of these issues.

Despite these fabrication disadvantages, wafer traps are still under active development because SETs have several major drawbacks~\cite{Blakestad09}, specifically:
\begin{itemize}
\item  Trapping potentials are less harmonic.  This causes any slight displacement of the trapping location due to stray charges or control voltage inaccuracies to shift the trap frequencies.  Without recalibration this will lead to errors in multi-qubit gates.  The increased cross-Kerr nonlinearity can also lead to gate errors due to spectator modes~\cite{Roos_2008, Nie_2009}.
\item  Trap depths are much lower~\cite{Chi05}, typically close to room temperature.  This makes loading ions less efficient and ion losses due to control field errors, stray charges, and background gas collisions are much more likely. Room temperature operation of more than a couple of ions in lighter ion species is effectively precluded due to short ion lifetimes.
\item Junctions between ion traps with favourable trapping strength and depth, and small pseudopotential barriers are harder to achieve than with a 3D geometry~\cite{Wesenberg2009}.
\item  As the ions reside in an open volume above a surface, they are poorly shielded from electric charges or crosstalk (photons, microwave control fields, or electric trapping fields) from other trapping zones on the SET.
\end{itemize}

In this paper we propose mitigating these issues by adding a 3D-printed dielectric structure onto the trap wafer before depositing the final metal electrode surface.  This allows us to retain the fabrication advantages of the SET whilst also retaining the advantageous trapping geometry of a 3D trap.  This requires finding trap geometries that meet these requirements.  In section~\ref{quantifying_trap_performance} we lay out how to quantify the performance of a given geometry.  In section~\ref{trench_trap_geometries} we propose several feasible geometries and simulate them.  Then finally, in section~\ref{3d_printing} we identify a suitable 3D printing process and print demonstration devices.

\section{\label{quantifying_trap_performance} Quantifying Trap Performance}

As alternatives to existing microfabricated trap designs, we explore several possible `trench' geometries, discussed in greater detail in the following section.  To assess the viability of these designs, we simulate them with COMSOL Multiphysics using the boundary element method (BEM). The Electrode software package~\cite{Electrode} is used for further post-processing of the electric fields extracted from the simulations.

In each trap simulation we set RF electrodes to unit voltage and DC electrodes to ground and calculate the electric field generated in the vicinity of the ion.  From these fields, we can calculate the pseudopotential of the trap, which is the effective potential seen by the ion~\cite{DEHMELT1968}.  By finding where this pseudopotential is at a minimum in the plane perpendicular to the trap axis, we locate the equilibrium position of the ion in two dimensions.  By also finding the saddle point of the pseudopotential (ie, the `escape point') and comparing the pseudopotential at this point to the pseudopotential at the center of the trap, we have a rough proxy for the depth of the trap (though in reality the situation is more complex due to the dynamical nature of a Paul trap).  At the ion's position, we fit the surrounding electric potential $V=V(r, \theta)$ to a cylindrical harmonic expansion

\begin{equation}
    V(r,\theta) = V_0\sum_{n=2}^\infty C_n \left(\frac{r}{r_0}\right)^n \cos(n\theta + \phi_n) + V_{off}
\end{equation}

\noindent where $r$ is distance from the trap center, $r_0$ is the minimum ion-electrode separation, $V_{off}$ is the potential at the ion, $\phi_n$ is the orientation of the $n$th-order multipole, and $C_n$ is the expansion coefficient associated with an $n$th-order multipole.  From these expansion coefficients, we define what we call the `quadrupole,' `hexapole,' and `octopole' strengths generated by our traps,
\begin{align*}
    \text{quadrupole}, C_2, \\
    \text{hexapole}, C_3' =& \frac{C_3}{C_2}, \\
    \text{octopole}, C_4' =& \frac{C_4}{C_2},
\end{align*}

\noindent which we illustrate schematically in Fig.~\ref{multipole}.

\begin{figure}[h]
\includegraphics[width=0.8\textwidth]{cyl_harm_exp.pdf}
\centering
\caption{\label{multipole}(a) A schematic cross-section of the potential generated by a SET, with the equilibrium position of the ion marked with a dot. (b) schematic cross-sections of the first three multipoles the potential in (a) can be expanded into, labelled with their respective expansion coefficients.}
\end{figure}

The quadrupole term gives the geometric efficiency of the trap.  Greater efficiency is desirable as it reduces the required RF voltage, and thus power dissipation as well as the possibility of voltage breakdown on the chip.  The hexapole and octupole terms give the leading order anharmonicities in the potential and are normalized to the quadrupole term as it is most useful to compare traps at the same ion secular frequency, not the same RF voltage.  Anharmonicities  increase cross-Kerr nonlinearity and introduce displacement-dependent frequency shifts in the ion's motion, increasing sensitivity of gate fidelity to the temperature of non-gate modes and the presence of stray electric fields.  Therefore, we seek designs which minimize higher-order multipole terms around the trap center.

In addition to trap depth and the multipole components of the trapping potential, we also calculate the open numerical aperture (NA) available for fluorescence collection and for laser beam access, as illustrated in Fig.~\ref{designs}.  A high NA (typically $\sim0.4$) is important for fast state readout on the ion.  For the novel designs discussed in Sec.~\ref{trench_trap_geometries}, we give an NA from above and from the substrate, as the ion detectors could be located in the substrate~\cite{Slichter17, Todaro_2021, Setzer_2021}, or placed above the trap.  For SETs the NA is trivially one, while our wafer traps, by their symmetry, have the same NA from both sides.  In all cases we consider a circular detector, but a modest improvement could be achieved with a rectangular detector.  These NA also gives us an idea of the range of angles available for laser beams perpendicular to the trap axis such that they can exit the trap without striking an electrode.

We scale all of our traps such that the closest electrode to the ion is 75\,$\mu$m away.  Because anomalous heating has a strong $\sim d^4$ dependence~\cite{King_1998, Turchette_2000}, the closest electrode will tend to dominate the heating rate.  For calculating trap depths we assume a $^{40}$Ca$^+$ ion trapped at a secular frequency of 4\,MHz by a 40\,MHz RF trap drive with no DC potentials applied.

\section{\label{trench_trap_geometries} Trench Trap Geometries}

3D printing offers great geometric versatility in trap design, since it can be used to produce arbitrary shapes.  In principle, we could 3D print electrodes with hyperbolic cross-sections.  Such electrodes would generate pure quadrupole potentials, with lower anharmonicities (as discussed in Sec.~\ref{quantifying_trap_performance}) than other geometries.  In practice however, our choices of geometry are limited by other fabrication and operation constraints, namely whether the geometry allows optical access to the ion for laser beam delivery and fluorescence detection and how easily the 3D-printed dielectric can be metalized (a problem discussed further in Sec.~\ref{3d_printing}).  These constraints naturally suggest what we refer to as a `trench' geometry, illustrated in Fig.~\ref{wafer}.  Trench geometries confine ions between two walls 3D printed on the surface of a wafer.  We explore several such `trench' geometries for microfabricated ion traps and compare their performance to SETs and wafer traps of similar dimensions.  Cross-sectional views of the geometries simulated are shown in Fig.~\ref{designs}.

The trap geometries we considered can be classified as either symmetric or anti-symmetric. Both sets of trap geometries are mirrored around a vertical plane along the trap axis, but in the anti-symmetric traps the role of RF and DC electrode is switched in the mirror half of the trap.  Obviously many asymmetric variations on these traps are possible, usually with properties somewhere between the symmetric or anti-symmetric ones.  We do not consider them here though as symmetries are generally desirable, and pragmatically we need to keep the parameter space of different traps to simulate tractable.

\begin{figure}[h]
\includegraphics[width=0.9\textwidth]{trap_designs.pdf}
\centering
\caption{\label{designs}Cross-sectional views of of the trap designs simulated.  The ions' location is shown as an orange dot and the trap axis is out of the page.  DC electrodes are blue, RF electrodes are red.  Numerical apertures are shown in lavender.}
\end{figure}

As shown in Fig.~\ref{designs}, all simulated traps aside from the SET are characterized by $\ge 3$ geometric parameters.  We select a subset of parameters (marked with Latin letters) to sweep while fixing the other parameters (marked with Greek letters).  For our trench traps, we also investigate how performance changes with the more relevant of the fixed parameters.  We do so by making multiple sweeps over the continuous parameters for different values of a fixed parameter.

\subsection{Simple Trench}

The first trap geometry we consider is the `simple trench'.  In this design, the two outermost electrodes of the SET are extended vertically to above the height of the ion.  The symmetric simple trench is primarily characterized by four dimensions, DC and RF electrode widths $c$ and $d$, trench wall height $\beta$, and trench wall thickness $\alpha$.  This last dimension does not strongly affect the potential seen by the ion, since the ion is shielded from all but the inner surfaces of the trench.  Because of this, a fixed value $\alpha = 100$\,$\mu$m, comparable to values used in our test fabrications (see section~\ref{3d_printing}), is used in all trench trap simulations.

We simulate a set of symmetric simple trench traps at a fixed ion height, allowing $c$ and $d$ to vary for discrete values of $\beta$.  Unlike the symmetric design, the anti-symmetric simple trench can be characterized with just two parameters, plane electrode width $e$ and trench wall height $f$.  (We find that ion height in the anti-symmetric trench depends mainly on $e$, as shown in Fig.~\ref{simple_trench}(f).  In fact, past $f\approx200$\,$\mu$m, ion height shows no dependency on $f$ noticeable beyond numerical noise.)  The full simulation results for our symmetric and anti-symmetric simple trench traps are shown in Fig.~\ref{simple_trench}.

\begin{figure}[h]
\includegraphics[width=1.0\textwidth]{data_trench_sym_anti_marked.pdf}
\centering
\caption{\label{simple_trench}Simulated parameters of SET traps vs the symmetric and anti-symmetric `simple trench' geometry. (a) Trap depth at a fixed radial frequency. (b) The quadrupole component ($C_2$) of the trapping potential at the ion.  (c) The hexapole component ($C_3'$) of the trapping potential.  (d) The octopole component ($C_4'$) of the trapping potential.  (e) Electrode dimensions at a constant ion-electrode separation for the symmetric simple trench trap.  (f) Electrode dimensions at a constant ion-electrode separation for the anti-symmetric simple trench trap. (g,h) NA above and below the ion.  Parameters are plotted against a generic geometric variable $w$, which is related to an electrode dimension of each trap as shown in the legend.  Simulation results are shown with markers.  The representative SET, wafer, and simple trench traps whose characteristics are summarized in Table \ref{tab:trap-summary} are highlighted with larger markers.  Simulation points are connected with dashed lines only as a guide to eye.}
\end{figure}

\subsection{Stacked Trench}

The simple trench geometry discussed above is closer to the ideal quadrupole geometry than a surface trap, but the flexibility of this geometry is limited by the fact that each wall can only contain one electrode.  As an alternative, we consider what we call the `stacked trench' geometry.  By allowing multiple electrodes to make up the trench wall, we can produce arrangements that more closely match the boundary conditions of a quadrupole, though the fact that the trench must remain open on the top prevents any trench geometry from being fully rotationally symmetrical.

The symmetric stacked trench trap can be characterized by four parameters: trench height $\epsilon$, trench width $\mu$, RF electrode height $g$, and the height of the RF electrode off of the ground plane $h$.  The anti-symmetric stacked trench trap can be characterized by three parameters: trench height $\xi$, bottom electrode height $j$, and trench width $i$.

These traps have two regimes for which ion-electrode separation is  75\,$\mu$m.  In the first regime, the ion is 75\,$\mu$m from the ground plane and the trench walls are further away, while in the second regime, the ion is 75\,$\mu$m  from the trench walls.  We consider both regimes in the antisymmetric case, but only the second in the symmetric case, since performance in the other regime was notably worse.

\begin{figure}[h]
\includegraphics[width=1.0\textwidth]{data_stacked_sym_marked.pdf}
\centering
\caption{\label{sym_stacked_trench}Simulated parameters of SET traps and wafer traps vs the symmetric `stacked trench' geometry. (a) Trap depth at a fixed radial frequency. (b) The quadrupole component ($C_2$) of the trapping potential at the ion.  (c) The hexapole component ($C_3'$) of the trapping potential.  (d) The octopole component ($C_4'$) of the trapping potential.  (e) The hexapole component of the trapping potential, excluding the SET data to make the other series more clear.  (f) Electrode dimensions at a constant ion-electrode separation for the symmetric stacked trench trap. (g,h) NA above and below the ion.   Parameters are plotted against a generic geometric variable $w$, which is related to an electrode dimension of each trap as shown in the legend.  Simulation results are shown with markers.  The representative wafer and symmetric stacked trench traps whose characteristics are summarized in Table \ref{tab:trap-summary} are highlighted with larger markers.  Simulation points are connected with dashed lines only as a guide to eye.}
\end{figure}

\begin{figure}[h]
\includegraphics[width=1.0\textwidth]{data_stacked_anti_marked.pdf}
\centering
\caption{\label{anti_stacked_trench}Simulated parameters of SET traps and wafer traps vs the anti-symmetric `stacked trench' geometry. (a) Trap depth at a fixed radial frequency. (b) The quadrupole component ($C_2$) of the trapping potential at the ion.  (c) The hexapole component ($C_3'$) of the trapping potential.  (d) The octopole component ($C_4'$) of the trapping potential.  (e) The hexapole component of the trapping potential, excluding the SET data to make the other series more clear.  (f) Electrode dimensions at a constant ion-electrode separation for the anti-symmetric stacked trench trap. (g,h) NA above and below the ion.   Parameters are plotted against a generic geometric variable $w$, which is related to an electrode dimension of each trap as shown in the legend.  Simulation results are shown with markers.  The representative wafer and anti-symmetric stacked trench traps whose characteristics are summarized in Table \ref{tab:trap-summary} are highlighted with larger markers.  Simulation points are connected with dashed lines only as a guide to eye.}
\end{figure}

\subsection{Comparison Geometries - SET and Wafer Traps}

As a point of comparison, we simulate common varieties of microfabricated trap: the SET and the wafer trap.  We first simulate the symmetric and anti-symmetric SET (also known as 5-wire and 4-wire SETs respectively).  One nice feature of SETs is that under the assumption of an infinitely large trap with no gaps between electrodes, simple closed-form expressions for the potential are available~\cite{House2008}.  While we use these closed-form expressions to calculate the parameters shown in Figs.~\ref{simple_trench}-\ref{anti_stacked_trench}, we also simulate our SETs in COMSOL as a way of benchmarking our BEM simulations.  We compare the multipole expansions, trap heights, and trap depths of BEM-generated and analytic potentials for the symmetric SET.  For most of the free parameter range, agreement across these parameters is within 2\%.  In the range where $a \ll b$ (see Fig.~\ref{designs}), divergence approaches 10\% due to the fact that the 1\,$\mu$m electrode spacing present in all BEM simulations is no longer negligible~\cite{Schmied_2010}.  For a fixed ion height there is one free parameter in the symmetric SET and no free parameters in the anti-symmetric one.

To compare our proposed trench designs against the most prominent set of current 3D microfabricated designs, we also simulate symmetric and anti-symmetric wafer traps, illustrated in the bottom row of Fig.~\ref{designs}.  A wafer thickness of $\lambda=50$\,$\mu$m of our simulated traps is comparable to those of designs implemented in the lab~\cite{Jost2010,Kienzler2015}.  The depth $\tau=1$\,mm of the wafers is selected to be much larger than wafer thickness and spacing so that the exact depth is unimportant.   Therefore, both designs have only one free parameter, the spacing $k$ between wafers in a stack.  This parameter is swept over while holding the ion-electrode distance constant.

\subsection{Summary}

Having generated the data shown above, we want to compare the simple and stacked trench trap designs with established SET and wafer trap designs and assess their relative merits.  For easy comparison between these four sets of simulated geometries, we select a `representative' trap from each category.  These traps in some qualitative way optimize the balance between trap depth and quadrupole strength/purity.  This selection is somewhat subjective, and optimum parameters may vary by application, but they are unlikely to differ greatly from what we have chosen here.  A table of values for there representative traps are shown in Table~\ref{tab:trap-summary}, and the associated dimensions given in Table~\ref{tab:trap-dims-summary}.

\begin{table}
\centering
\begin{tabular}{|c|c c|c c|c c|c c|}
\hline
& \multicolumn{2}{|c|}{SET} & \multicolumn{2}{|c|}{Simple} & \multicolumn{2}{|c|}{Stacked} & \multicolumn{2}{|c|}{Wafer}  \\
\hline
           & Sym & Anti & Sym & Anti & Sym & Anti & Sym & Anti  \\
\hline
\hline
Depth (eV)         & 0.06 & 0.07 & 0.08 & 0.23 & 0.33 & 0.22 & 0.16 & 0.39 \\
\hline
Quadrupole ($C_2$) & 0.17 & 0.17 & 0.18 & 0.24 & 0.31 & 0.40 & 0.35 & 0.39 \\
\hline
Hexapole ($C_3'$)  & 1.0 & 1.0 & 0.86 & 0.62 & 0.020 & 0.008 & 0.000 & 0.001 \\
\hline
Octopole ($C_4')$  & 0.75 & 0.75 & 0.55 & 0.36 & 0.024 & 0.407 & 0.344 & 0.007 \\
\hline
\end{tabular}
\newline
\caption{Summary of results for trap parameter calculations for the SET, simple trench trap (`Simple'), stacked trench trap (`Stacked'), and wafer trap. Values shown correspond to a set of geometric parameters selected to balance trap depth and quadrupole strength/purity.}
\label{tab:trap-summary}
\end{table}

\begin{table}
\centering
\begin{tabular}{|c|c|l|}
\hline
\multicolumn{2}{|c|}{Trap} & Dimensions ($\mu$m) \\
\hline
\hline
\multirow{2}{*}{SET} & Sym  & $a=161.2$, $b=59$ \\
                     & Anti & $\phi=75$\\
\hline
Simple & Sym  & $d=77.3$, $c=210$, $\beta=600$ \\
                      Trench  & Anti & $e=135.2$, $f=525$ \\
\hline
Stacked & Sym  & $g=140$, $h=80$, $\epsilon=300$ \\
                        Trench & Anti & $i=150$, $j=160$ \\
\hline
\multirow{2}{*}{Wafer} & Sym  & $k=50$ \\
                       & Anti & $k=53$ \\
\hline
\end{tabular}
\newline
\caption{The dimensions (in microns) of the traps whose parameters are summarized in Table \ref{tab:trap-summary}.}
\label{tab:trap-dims-summary}
\end{table}

From Table~\ref{tab:trap-summary}, we predict that all our trench geometries will outperform SETs.  For the symmetric simple trench trap, the improvement is practically negligible though. The antisymmetric simple trench is a significant improvement over the SET, offering $\sim$3$\times$ the depth, $\sim$40\% higher quadrupole strength, and $\sim$40\% lower hexapole strength.  Despite this it is still notably inferior to the wafer traps. The stacked trench traps on the other hand can have very comparable performance to wafer traps, with similar depth, quadrupole strength, and octopole terms.  The hexapole term for our representative trap is still larger than in wafer traps (where it can be zero by symmetry), but the factor $\sim50$ improvement over SETs will still lead to drastic improvement in trap performance.  Further improvement can be gained at the cost of lower NA optical access by making the walls higher.  As some point though manufacturing tolerances and curvature from stray fields will set a practical limit for either design.

\section{\label{3d_printing} 3D Printing}

Our chosen fabrication process for realizing these trench geometries is 2-photon direct laser write (DLW)
3D printing. The electrode structure is printed directly onto a functional trap wafer using a dielectric material.  The printing process uses a focused laser to polymerize this photosensitive material to generate solid structures~\cite{Pearre2019}. This can then be metallized to create conductive electrode surfaces.

Whilst not explored here, we note that the simple trench traps could be fabricated using UV-LIGA (Ultraviolet - Lithographie, Galvanoformung, Abformung). This process is already widely used to make electrodes for SETs~\cite{Arr13} and so would be straightforward to adopt.  UV-LIGA  is a fabrication process where metal is electroplated inside a photoresist mold patterned using UV lithography. As discussed above, the performance advantage of these designs over SETs is fairly modest compared to the stacked trench traps.  The stacked trench geometries could also be built using conventional MEMS techniques.  However, the 100s of $\mu$m vertical heights required are likely challenging to achieve with oxide film deposition.\\

\subsection{Dielectric Material}

We propose using ormocer (\textbf{or}ganically \textbf{mo}dified \textbf{cer}amic), a silica-based material, as our printable dielectric material.  The high RF frequencies ($\sim$10-100\,MHz) and voltages ($\sim$10-1000\,V) applied to ion trap electrodes places stringent requirements on the electrical and thermal properties of any dielectrics used.  High dielectric strength is required to avoid breakdown.  High resistivity and low loss tangent avoid direct heating of the dielectric.  A low dielectric constant reduces parasitic capacitance, requiring less current to drive the electrodes, and thus lower Ohmic losses in the electrode metal.   Finally, a high thermal conductivity ensures any heating from losses is minimized.  Ormocer properties are somewhat formulation dependent, but in Table~\ref{tab:ormocer-characteristics} we give some representative values measured in the literature to give an idea of what can be achieved.

\begin{table}
\centering
\begin{tabular}{|c|c|}
\hline
Relative permittivity & 2.5~\cite{Froehlich02}, 2.7~\cite{Laine92}, 3.1~\cite{Johansson03}  \\
\hline
Loss tangent & 0.0035~\cite{Johansson03}, 0.00397~\cite{Laine92}, 0.004~\cite{Froehlich02},\\
\hline
Dielectric strength (V/cm) & $8.7\times10^5$~\cite{Laine92}  \\
\hline
Bulk resistivity ($\Omega\cdot\text{cm}$) & $4.5\times 10^{16}$~\cite{Laine92}  \\
\hline
Thermal conductivity (W/m$\cdot$K) & 2.3\cite{Laine92}   \\
\hline
\end{tabular}
\newline
\caption{Electrical and thermal properties of ormocer.}
\label{tab:ormocer-characteristics}
\end{table}

For room temperature operation, outgassing needs to be low to ensure ultra-high vacuum pressures can be reached and the material must be able to withstand $\sim$200\,$^\circ$C vacuum bakes.  Low outgassing is also desirable as it reduces the chance of contaminating metal electrode surfaces, which are known to play a role in anomalous heating~\cite{hite2013surface}.  The organic cross-linked structure of ormocer reduces outgassing and makes ormocer fit for vacuum processes~\cite{fraunhofer}, although quantitative outgassing data is so far lacking.  Ormocer is stable to $>300\,^{\circ}$C~\cite{fraunhofer}.  For cryogenic operation, vacuum compatibility is much less of an issue but the structure must be able to survive repeated temperature cycles without structural failure, something that will need testing in future work.

\subsection{Initial Fabrication}

\subsubsection{Print}
As an initial test, ormocer based trap structures were printed onto a borosilicate glass wafer and metalized with $\sim20$\,nm of sputtered gold.  SEM images of which are shown in Fig.~\ref{unmetalized-prints}.  The printed structures are  $200\,\mu$m high with $100\,\mu$m wide trenches in between them, giving a $50\,\mu$m ion-electrode distance.  This is a fairly typical value, with most microfabricated traps historically lying in the few-10s to few-100s\,$\mu$m range. These traps were fabricated via a two-photon direct laser write process. A custom printer was used, based on open source concepts from the Janelia's open source Modular In vivo Multiphoton Microscopy System (MIMMS) and the printer described in~\cite{Pearre2019}.

This printer was built to address specific needs in terms of print speed and full wafer scalability while retaining the necessary resolution. In the print process, an individual 2D field of view (FOV) is scanned using a galvo for $y$ axis steps paired with a fast resonant imaging mirror operating at 8\,kHz in the $x$ axis; allowing for printing at speeds up to $\sim$8000\,mm/s. A piezoelectric actuator is then used to sweep this FOV in the normal $z$ axis to form an individual metavoxel. Series of these are then stitched together across the entirety of the wafer via a controllable hexapod (Physik Instrumente) with sub-micron precision. We chose to break each "island" into 4 metavoxels with a $200\,\mu$m~$\times$~$200\,\mu$m FOV. Each individual island is printed in under a minute with a voxel resolution under $2\,\mu$m in the $xy$ print plane (142  $x$ and  512 $y$ voxels) and under $3\,\mu$m in $z$. Demonstrating that, whilst this is an inherently serial  process, the overall  processing  times at the required resolution are  tractable  for  much  larger traps than are currently in use.

A hybrid resist is used in this printing process, based on Ormocomp photoresist (Microchem). To this we add a photoinitator, 2.4.6-trimethylbenzoyl phosphine oxide (TPO) (Sigma), a stabilizing agent, 3,5-Di-tert-butyl-4-hydroxytoluene (BHT), and Fluorescein (Sigma) for in situ imaging during printing. A Chameleon Discovery laser, set to 780\,nm, 100\,fs pulse width, 80\,MHz Rep rate, and $\sim$100\,mW was used to initiate polymerization. Resolution and therefore surface roughness is a function of resin choice as well as the fundamental optics and scan mechanics of the printer. The current design takes advantage of the critical electrical dimensions of the trap being on a vertical surface which minimizes discretization concerns. In addition, a small amount of shrinkage during curing is inevitable. We minimize this by using the highest possible laser power before explosions occur. We do not see delamination from the substrate or noticeable distortion of the structures under SEM imaging.

\begin{figure}[h]
\includegraphics[width=0.95\textwidth]{Aug21prints_marked_v1.pdf}
\centering
\caption{\label{unmetalized-prints}SEM images of gold coated ormocer trap structures printed on glass. In this structure, many trenches have been connected up with X-junctions, as is envisaged in a large `QCCD' processor~\cite{Blakestad09}. (a) An overhead view of a grid of symmetric stacked trenches showing segmentation of the top DC electrodes.  (b) An oblique view of the same grid.  (c) A close up view of an intersection of trenches.  (d) A false-color version of (c) showing DC electrodes in blue and RF electrodes in red.  (e) A close-up view of a DC electrode segment.}
\end{figure}

\begin{figure}[h]
\includegraphics[width=0.95\textwidth]{fab_process_v1.pdf}
\centering
\caption{\label{fab-process}Proposed integration of electrode metalization with printing process shown here on a short section of the larger trap shown in Fig~\ref{unmetalized-prints}.  (a) Silicon wafer with electrode routing and vias up to the surface is fabricated using standard CMOS process (metal shown copper coloured,  SiO$_2$ dielectric shown transparent).  (b) Aluminum is deposited and patterned to define gaps between electrodes.  (c) DLW used to print ormocer trap structures (blue).  (d) Gold is deposition from multiple angles to coat all surfaces of the print.  (e) Aluminium is etched to allow liftoff of the gold over the gaps between electrodes.  Insets shown the liftoff process in more detail.}
\end{figure}

\subsubsection{Metalization}

The next stage in our fabrication development is metalization.  Our trap structure is designed to be `self masking' - the isolation gaps between electrodes can be made deep enough (or with an undercut) such that directional deposition of metal onto the structure will not cause shorting between them. This metalization will connect the trap to vias already pre-fabricated on a planarized wafer using a standard CMOS process (see fig.~\ref{wafer}).  These vias must be off to the side of the printed structures as printing directly onto metal is difficult - the laser heats the metal causing violent disruption of the print.  On the substrate around the prints, isolation between electrodes will be achieved using a liftoff process.  We envisage using gold as our electrode metal as this is well established in ion trapping, and aluminium for the lifoff material.  The full process can be seen in Figure\,\ref{fab-process} and will be described in more detail in a forthcoming publication.

\subsubsection{Integrated Optics}

The final step to producing a working trap will be to integrate optics for laser delivery.  This is because trench designs do not offer the required optical access for free-space laser delivery.   Waveguides for light routing and grating couplers to focus beams onto the ions have now been demonstrated by several groups~\cite{Mehta2016, Ivory21, Mehta20}.  These demonstrations were using SETs, but one of the strengths of the traps proposed here is that the same technique can be used without modification. Other integrated features shown in Fig.~\ref{wafer}, whilst desirable, aren't an immediate requirement.

\section{Conclusion}

Additive 3D printing has the potential be a powerful enabling technology for trapped-ion quantum computing. It allows the combination of wafer-integrated ion control with the 3D structures required to obtain optimal trap performance. In order to realise this we have developed a novel trench geometry and shown it can be printed.  We lay out a roadmap to integrate the necessary electrical and optical routing to enable functional devices.

\section*{Acknowledgements}

We would like to acknowledge Aaron Casserly who suggested this collaboration, David Miller who assisted with process development, and Daniel Slichter who provided simulation code examples.\\

\FloatBarrier

redpajama_set_name: RedPajamaArXiv


text:
DPA Microphones Makes the Grade with Jeremiah Slovarp
Multi-talented audio engineer and producer teaches upcoming audio professionals benefits of company's d:vote™4099 Instrument Microphone
Multi-talented audio engineer and producerteaches upcoming audio professionals benefits of company's d:vote™4099 Instrument Microphone
BOZEMAN, MONTANA, DECEMBER 7, 2015 — Jeremiah Slovarp, a five-time Emmy-Award winner, began his career in the early 2000s as a location sound engineer on various films and commercials. Today, the active engineer and producer brings that knowledge with him to the classroom at Montana State University, his alma mater, where he teaches students at the School of Music tips and tricks for life in the audio industry. Among Slovarp's go-to instructional tools is DPA Microphones'd:vote™ 4099 InstrumentMicrophone.
"We teach classical musicians to play classical instruments in private lessons, in a one-on-one, teacher-to-student model," he explains. "That's very uncommon for most state schools, but we want our students to be able to go out and get a job. That's where I come in—I teach music technology classes, which provide students the opportunity to learn recording and sound engineering skills while also studying for their music careers."
Slovarp purchased a pair of the d:vote™ Instrument mics, along with the d:vote™ 4099 Classic Touring Kit, after watching a live demo of the microphone and witnessing how well it amplified the natural sound of an instrument. It wasn't long before he also purchased DPA's d:facto™ Vocal Microphone. Since then, he regularly uses the mics for his various projects, including his teaching stints, and also rents them out. Students in his classroom are able to work with a wide variety of microphones, with the d:vote™ Instrument mics among the higher-end options.
"The d:vote™ 4099 is such an easy tool to use, so it's always in demand on campus," adds Slovarp. "Also DPA's d:vote™ 4099 Classic Touring Kit and its various mounts are great. It's very easy for me to show the students a really effective way to mount microphones on a classical instrument. Musicians, students included, tend to be very protective of their instruments. They are concerned with how they're going to sound and where the mic will sit. The instrument mounts that DPA has developed and the possibilities those mounts have opened up for capturing sound in tight spaces, is incredible."
Two of Slovarp's courses that see especially heavily use of the d:vote™ Instrument mics are Recording I and Recording II, the first of which is taught on an intense bi-weekly schedule. Each Recording I class is eight hours long, and in that time the students must set up and mic a band for recording, track and record the band's performance and then pack it up. The students then have two weeks before the next class to produce an album at home or in a recording studio, before they hand it in for review.
"Being able to teach the students proper mic techniques with a high-quality microphone is very important, especially as we help transition them into the professional market," Slovarp continues. "The students appreciate the DPA brand and how easy and flexible its mics are to use. They always tell me they recognize how natural DPA sounds."
Slovarp recently took 36 members of the student choir to Italy to sing in old churches, bringing along the d:vote™ Instrument microphones. "We used two d:vote™ mics for our front and center microphones to get up close to the performers," Slovarp adds. "The mics performed beautifully, especially as I was able to turn up the gain on them and capture the choir singing loudly without the interference of any surrounding line noise."
In addition to his teaching work, Slovarp is president and founder of Peach Street Studios, a commercial recording facility, which also uses DPA for almost all of its musical recordings. He is also president of Jereco Studios, which provides sound for film and music applications. He produces and engineers post-production sound, live sound, music recording and location sound for regional and national events, and serves as the Montana Chair for the National Academy of Television Arts & Sciences. Slovarp has worked with several networks, including Animal Planet, Disney, HBO/Cinemax, the National Geographic Channel, Nickelodeon, PBS and The Discovery Channel, along with the animation studio Pixar.
ABOUT DPA MICROPHONES:
DPA Microphones is the leading Danish Professional Audio manufacturer of high-quality condenser microphone solutions for professional applications. DPA's ultimate goal is to always provide its customers with the absolute finest possible microphone solutions for all its markets, which include live sound, installation, recording, theatre and broadcast. When it comes to the design process, DPA takes no shortcuts. Nor does the company compromise on its manufacturing process, which is done at the DPA factory in Denmark. As a result, DPA's products are globally praised for their exceptional clarity and transparency, unparalleled specifications, supreme reliability and, above all, pure, uncolored and undistorted sound.
For more information on DPA Microphones, please visit www.dpamicrophones.com
DPA Microphones' 6000 Series Makes Waves in the Industry
DPA Microphones Features Its Sought After Broadcast Microphones at NAB 2016
DPA Microphones Makes Conference Audio Quality Its Main Focus For ISE 2016
A DPA! A DPA! My Kingdom For A DPA!
DPA Microphones Expands d:vote™ Instrument Microphones with New Line of Mounts
DPA Microphones Makes Believers out of Enrique Iglesias' Touring Sound Engineers Eddie "El Brujo" Caipo And Brad Divens

redpajama_set_name: RedPajamaCommonCrawl


text:
Nintendo Flips the Gender Script with "Captain Toad"
"Captain Toad" breaks the sexist mold with the game's two leads, Toadette and Toad, taking turns saving one another.
Isis Madrid
Nintendo is making amends for the millions of Mario players who grew up with the helpless-princess-in-a-tower-who-needs-saving trope. Their just-released "Captain Toad" Wii U game is breaking the sexist mold with the game's two leads, Toadette and Toad, taking turns saving one another.
"She has her eyes on the treasure, too! And she'll carry a big chunk of the adventure on her capable shoulders," says the Captain Toad website of its Toadette character.
This is huge for parents who want their children to grow up with a sense of gender equality. Moreover, the game places importance on the characters' wits and critical thinking, rather than physical strength or superpowers. Nintendo players seem to be responding well to the gaming company's progressive strides—players gave "Captain Toad" a score of 91/100, placing it in the Top Ten best-liked Wii U games of the year.


text:
Q: Relationship between three matrices I think this might be an odd question, and a little vague.  But here goes.
This is related to coordinate transformations.  Three matrices are given: $G_1 , G_2$, and $\Lambda$.  $G_1$ and $G_2$ are symmetric.  (They are metrics, actually.)  $\Lambda$ is the matrix in question.  The three matrices satisfy
$\Lambda^{-1} = G_1^{-1} \Lambda^T G_2$
Is there anything we can say about the properties of $\Lambda$, such as it is symmetric, or it is either symteric or anti-symmetric, or ...?
Thanks.

A: If you rewrite this as $$G_1 = \Lambda^T G_2 \Lambda\,,$$
this is just the change-of-basis formula for a symmetric bilinear form. That is, $\Lambda$ is the matrix that interpolates from the expression for the metric in one coordinate system to the expression in another coordinate system. As it stands, $\Lambda$ could be any invertible matrix.

redpajama_set_name: RedPajamaStackExchange


20 foreground recordings and 4 background recordings of Centropus leucogaster . Total recording duration 17:04.
Just next to the track, in dense bushes (species often heard in this area but tricky to see).
Single individual at Kakum NP, 20 meters away about 10 meters high in slender tree, moving slowly toward top of tree.
Dense and humid secondary bush.
Interval between two songs shortened.
Several birds calling together along the jeep track at Aboabo.


Photoshoots are now offsale. To buy a shoot please go to the kiosk on the day of the event.
Photoshoots are the perfect way to record the day you met one of your heroes. They're taken by professional photographers and printed to the highest quality which makes them perfect for framing and cherishing.
EM-Con makes it easy to book photoshoots – just check the list below. Once you've booked you just have to wait for the photoshoot ticket to be mailed to you and come along to EM-Con 2019 to have your shoot! You even get to collect your photo on the day.
Once you have purchased a photoshoot will get a printed ticket to be redeemed at the photo areas, this is for one per person any additional people buying into the photoshoot will also be given additional person tickets with the shoot written on the ticket. Schedules will be posted prior to the convention and on the day, proceed to the photo area prior to the scheduled time.
Photoshoots do not cover entry into the event; please ensure you have a valid ticket.
Photoshoot tickets are valid once, for either day.
Is there a deadline for buying tickets online?
The deadline for buying a photoshoot online is midnight on Tuesday 16th April 2019. After this you'll only be able to purchase a ticket on the day but we can't guarantee there'll be any available; for this reason we strongly advise buying in advance.
When are tickets mailed out?
Photoshoot tickets are sent out after the deadline of 16th April and before 21st April.
What time do photoshoots start?
Photoshoot sessions begin at 11am. We publish a precise schedule closer to the weekend of EM-Con.
Can another person join me in the photo?
Photoshoots are limited to the photoshoot ticket holder, but if you want to add more people you can pay to do. You can add a maxmimum of two extra people – meaning 3 people in total (you and two extras). The cost is 50% of the listed photoshoot price. For example; a £30 photoshoot is valid for one person. To add one person will cost £15. To add another will cost £15. The total for three people will be £60 in this example.
This can only be done on the day at the EM-Con Photo Kiosk on the upper concourse.
Where can I buy on the day?
While we recommend buying before the event, photoshoot tickets can be purchased from the EM-Con Photo Kiosk situated on the concourse in front of the main entry point. Please consult the map for directions.
Why does it say processing on my photoshoot purchase?
Can I save on postage?
The website is set up to add an admin and postage fee for every order you make. To avoid this we advise you to purchase all photoshoots you want in one go to ensure this fee is charged just once.
Do I get a digital copy?
Digital copies will be available online after the event. These will be charged at £5 per download.
Can I change my mind on a photoshoot?
Unfortunately not; once the purchase has been made we're unable to change your selection. One advantage of the Gold and Weekend VIP options is that you can change your chosen photoshoot.
Can I get a refund on a photoshoot?
Unfortunately not; once the purchase has been made we're unable to give a refund, so please make an informed decision when purchasing.
Has my ticket been sent yet?
Tickets are not sent until the deadline for buying photos has expired. For EM-Con 2019 this is 17th April.
What if I lose my photoshoot ticket?
EM-Con sends tickets using Royal Mail Signed For™ – once we send the entry or photoshoot ticket they are your responsibility. We will not replace tickets so please don't lose them!
All group shoots are sold subject to the availability of those guests being at the convention. If a guest cancels we will do our best to replace them We consider 2 guests to be a group.


This is a placeholder page for Alfreda Dameron, which means this person is not currently on this site. We do suggest using the tools below to find Alfreda Dameron.
You are visiting the placeholder page for Alfreda Dameron. This page is here because someone used our placeholder utility to look for Alfreda Dameron. We created this page automatically in hopes Alfreda Dameron would find it. If you are not Alfreda Dameron, but are an alumni of Granite Falls High School Granite Falls, NC, register on this site for free now.


text:
var express = require('express')
  , path    = require('path')
  , bodyParser = require('body-parser')
  , cons = require('consolidate');

// Creando la primera instancia de mi aplicacion
var app = express();

var debug = require('debug')('lab5-8');

// Configurando parametros de funcionamiento para express con respecto a la aplicacion

// Puerto de trabajo para la url
app.set('port', process.env.PORT || 3636);

// Motor de templates utilizando Consolidate y swig
app.engine('html', cons.swig);

// Tipo de templates que utilizaran; en nuestro caso `html`
app.set('view engine', 'html');

// Path o directorio donde se encuentran los templates
app.set('views', path.join(__dirname, 'views'));

// Encoding para las tramas HTTP
app.use(bodyParser.json());
app.use(bodyParser.urlencoded({
	extended : true
}));

// Sirviendo los estaticos de la aplicacion en nuestro caso los `assets`
app.use(express.static(path.join(__dirname, 'assets')));

// Quien resuelve y gestiona las url a través del controlador

var controllers = require('./controllers/routers');

app.use(controllers);

// En el caso en que la url no sea conocida o resuelta

app.get('*', function(req, res){
	res.status(405).send('Method not allowed');
});

var server = app.listen(app.get('port'), function(){
	debug('Express esta escuchando por el puerto' + server.address().port);
});

redpajama_set_name: RedPajamaGithub


text:
Q: preg_match works in regexbuddy, not in php Ok so I have this regex that I created and it works fine in RegexBuddy but not when I load it into php. Below is an example of it.
Using RegexBuddy I can get it to works with this:
\[code\](.*)\[/code\]

And checking the dot matches newline, I added the case insensitive, but it works that way as well.
Here is the php:
$q = "[code]
html code to display on screen
[/code]";

$pattern = '/\[code\](.*)\[/code\]/si';

$m = preg_match($pattern, $q, $code);

So you can see I am using [code][/code] and then once I can extract this I will run htmlentities() on it to display instead of render html code.

A: You're including the forward slash in the middle of your pattern (/code).  Either escape it or delimit your pattern with something else (I prefer !).

A: When transferring your regular expression from RegexBuddy to PHP, either generate a source code snippet on the Use tab, or click the Copy button on the toolbar at the top, and select to copy as a PHP preg string.  Then RegexBuddy will automatically add the delimiters and flags that PHP needs, without leaving anything unescaped.

A: It's because you didn't escape the closing marker /
Escaping the backslashes wouldn't hurt either:
$pattern = "/\\[code\\](.*)\\[\\/code\\]/si";

PHP lets you choose any characters as the RegEx delimiter, so I'll often use a character which isn't also used in the regex, like @.
$pattern = "@\\[code\\](.*)\\[/code\\]@si";

A: This worked:
$pattern = '/\[code\](.*)\[\/code\]/si';

A: You need to escape the forward slash in /code
$pattern = '/\[code\](.*)\[\/code\]/si';

Also, realize the matches are stored in $code, not $m
Edit: Beaten to it :p


text:
Science and lasers to protect frescoes: This is how Ennis researchers save beauty
Monitor murals from Huge complex in Saint Pivignate and the "The Trinity and the Saints" by Raphael and Perugino in Church of San Severo in Perugia with 3D laser scanning and fluorescence techniques, Study the composition of colors and materials used. This is what the researchers realized Enea from Frascati Research Center As part of a campaign to promote cultural heritage "Keep the beauty"Created by journalist Monica La Torre It is funded by the newspaper Umbria 24 And from Umbria region Supported byDepartment of Culture of the Municipality of Perugia and Faculty of Letters and PhilosophyUniversity of Perugia. Two prototype laser scanners were used at the two sites: one with three lasers capable of instantaneous detection of information regarding the structure and color of artwork, and another using an ultraviolet laser to study surface-forming materials and monitor from biological attacks.
"The work carried out allowed the study of the materials and colors from which the frescoes were made, and the identification of a year zero in relation to the monitoring of works whose present health we now know and which we will be able to monitor continually in the coming years" Massimiliano Guarneri Researcher in the Enea Diagnostic and Metrology Laboratory and coordinator of the team in which colleagues participated Luisa Canev, Valeria Spuccino, Massimo Francucci, Massimiliano Ciafi and Marco Pestelli. The first data collected led to the creation of Two mobile apps made by Oniride, which supports the visitor in reading the frescoes and is also used on the interactive totem of San Bevignate. Guarneri concludes that "one of the goals set was to make the frescoes dynamic, and to make the complex visible, even to the higher parts of it, that otherwise would have been impossible to notice." "The project is of particular importance due to the fact that the municipal administration of the capital of Umbrian will be the pioneer of the European network of Templar sites: from this perspective, the intervention in Saint-Pivignate acquires a central and transnational importance," emphasized the "creator of the "Save the Beauty" project, Monica La Torre, On the occasion of the reopening of the Church of San Severo after restoration." Contacts have already begun with the Faculty of Engineering of the University of Perugian to compare the various surveys already conducted on the site, travel in this direction and open a season for further research and in-depth analysis. All this, it is hoped, will contribute in a fundamental way to the preservation of the huge complex, in keeping with the non-profit nature of the foundation of the project", concludes La Torre. Raphael painted the fresco in the church of San Severo in the years 1505-08, but left it unfinished. After The artist died of Urbino in 1520, his master Pietro Perugino, now elderly, completed this only work left for him in the city.
See also Thirty years after his death, he studied for the philosopher Gemonat at the only school that bears his name
Previous The Faculty of Political Science of the University of Milan celebrates its fiftieth anniversary – the facts of events
Next 3 minutes to conquer the public with science – Corriere.it
Study of adolescent chimpanzees as emotional as humans
"For the love of ants and all" –


Selecting the right people for the organization?
IT, and other technical skills are in short supply. And unlike prior years, this problem is no longer one of "hiring top people" or "recruiting better than your competition." Now we need to source and locate operations around the world to find the skills we need. You must expand your sourcing and recruiting to a global level. Locate work where you can best find talent. And build talent networks which attract people around the world" (Josh Bersin Dec 19 2013).
There is always a challenge to find the right person for the job, which fits as per the organization's need and further to achieve its goals and mission. Around the world companies are struggling with the aging workforce and less loyal employees. Globalization has increased the demand for skilled workforce. The selecting right candidate for the job requires a particular expertise in determining several factors to hire and retain the most qualified incumbent possible.
The task of selecting the right person consists of several processes; such as: job planning, recruitment, compensation, benefits, selection and development. The three broad steps of HRM are: finding, developing and maintaining an effective workforce (Daft 333).
These steps can be explained through the following figure below.
The first step consists of prediction by HRM, in which he identifies the need of the new employee, based on the availability of the vacancies in the company. The second step consists of contacting candidates through various available sources. Third step is a selection process, those persons were selected which can prove to be potential contributors to the organization. And final step is to welcome the new employee (Daft 332).
By definition we can state that human resource planning is the process of forecasting the current and future needs of human resource in the organization in order to achieve its goals. It basically serves as a bridge between the human resource management and overall strategic plan of an organization. By predicting human resource needs, the organization can prepare itself to face challenges for effectively (Daft 333).
It is the process through which organization publicized for the job opening available with them, in order to attract the suitable candidates. Now days it is also referred as talent acquisition.


Step into the 2019 Mitsubishi Outlander Sport. It features a continuously variable transmission, 4-wheel drive, and a 2 liter 4 cylinder engine. Mitsubishi prioritized fit and finish as evidenced by: a tachometer, a trip computer, an outside temperature display, heated door mirrors, remote keyless entry, cruise control, and much more. Audio features include an AM/FM radio, steering wheel mounted audio controls, and 4 speakers, providing excellent sound throughout the cabin. Mitsubishi ensures the safety and security of its passengers with equipment such as: dual front impact airbags with occupant sensing airbag, head curtain airbags, traction control, brake assist, anti-whiplash front head restraints, a security system, and 4 wheel disc brakes with ABS. Electronic stability control ensures solid grip atop the road surface, no matter how challenging the driving conditions. Our sales reps are knowledgeable and professional. They'll work with you to find the right vehicle at a price you can afford. Stop in and take a test drive!


text:
Airgain Reports Positive Net Income for Q4 and 2016
By Brad Graves
Airgain Inc. — which makes wireless antennas for household, office and industrial devices — reported net income of $1.1 million on sales of $12.6 million during its fourth quarter, which ended on Dec. 31.
In the same quarter one year ago, the company reported a net loss of $660,000 on revenue of $9.3 million.
Airgain (Nasdaq: AIRG) completed an initial public offering in August and a follow-on offering at the end of the year.
For the year, the company reported net income of $2.2 million on revenue of $43.4 million. During 2015, the company had a net loss of $2.7 million on sales of $27.8 million.
Airgain Inc. Reports Fourth Quarter and Yearly Results
Airgain's Action Breaks San Diego's 15-Month IPO Drought
Airgain Inc. Names Waadt Director of Investor Relations
Airgain Announces Follow-on Offering
Airgain Inc. Announces Follow-on Offering
Franklin Wireless Posts Improved Second-Quarter Revenue, Profit
Franklin Wireless Corp. Reports Q2 Net Income of $525,000
Qualcomm Reports Solid Quarterly Numbers


At Collateral Recovery Team our primary objective is to protect our clients from burdensome claims and to stay in compliance with all laws and regulations. We follow the CFPB guidelines in everything we do.
Our company partnered with the highest quality LPR provider in the country. Focused on compliance and results MVtrac has become the leader in LPR technology in North America.
Clearplan has made our company more efficient. This software has increase our recovery rate and reduced the time it take for vehicles to be located and secured. We could not work without this amazing software.
Our C.A.R.S. Certified repossession agents and office staff create a knowledgeable and reliable staff for our lenders. Everyone is trained to follow CFPB guidelines on an annual basis.
Collateral Recovery Team LLC is a professional and highly experienced repossession company that repossess all types of collateral for lenders across the country. We only hire the most experienced and professional recovery agents available. We have many agents with 20+ years' experience in the repossession and towing industry. Our repossession agents number one priority is to ensure they mitigate any losses or claims for our clients. All of our agents follow the guidelines set forth by the Consumer Financial Protection Bureau (CFPB). Collateral Recovery Team boast a combine 250 years' experience in the towing and repossession business. As a client you can rest assured that your collateral will be treated with the utmost care and your customer will be treated fair and respectful.
We also pride ourselves in using the latest technology in our industry. We use every online portal available to accept and manage repossession orders. We also have one of the largest LPR scanning operations in the state. We scan 10s of thousands of license plates a day with the use of 20 MVtrac License Plate Recognition (LPR) systems. This creates a tremendous advantage when vehicles are not where they are supposed to be. We have historical scans on nearly 70% of the cases we receive.
If you are looking for a reliable and stable partner in this volatile industry contact us today. See why we have earned a reputation as one of the most successful repossession companies in the great state of Texas.
Don't worry, we will take care of you.


YVF2 variable frequency motors - Product Details - ZHEJIANG FANGLI ELECTRIC MOTOR CO.,LTD.
YVF2 series variable frequency adjustable-speed converter-fed three phase induction motor is a kind of special motor which driven by frequency converter, rotating speed of the YVF2 series motors can be regulated steplessly by frequency converter, thus enable energy saving and automatic control of the motors. YVF2 series motors are fitted with ventilation fan which provide better cooling effect to ensure motors running at various speed YVF2 series motors are suitable for transmissions by which speed一regulation is needed, are widely used in light industries, metallurgy industries, textile industries, chemical industries, machine tool industries etc. while fitted with highly accurate sensor, the motors can achieve highly accurate operation of closed loop. To be convenient for users, dimensions and rated output of YVF2 series motors are same as those of Y2 series motors, also in conformity with IEC60072一 1:1991.


text:
Gang Feng
Post-replication DNA mismatch repair plays crucial roles in mutation avoidance and maintenance of chromosome stability in both prokaryotes and eukaryotes. In humans, deficiency in this repair system causes the formation of cancers. The biochemistry of the repair system has been best studied in a model bacterium Escherichia coli. In this thesis, regulation of expression of mutS, mutL and mutH genes, whose products mediate methyl-directed mismatch (MDM) repair in E. coli, is investigated. One-step affinity purification schemes were developed to purify E. coli MutS, MutL and MutH proteins fused to His-6-affinity tag. His-6-MutS exhibited the same mismatch binding activity and specificity as the native MutS protein. Purified His-6-MutS, -MutL and -MutH proteins were used to develop quantitative Western blotting assays for amounts of MutS, MutL and MutH proteins under various conditions. It was found that the three proteins were present in relatively low amounts in exponentially growing cells and MutS and MutH diminished in stationary-phase cells. Further studies indicated that the drop in the amounts of MutS and MutH proteins in stationary-phase cells was mediated through RpoS, a key global regulator of stationary-phase transition. In both exponential- and stationary-phase cells, MutS amount was also negatively regulated by Hfq (HF-1) global regulator, which is required for RpoS translation, through an RpoS-independent mechanism. b-galactosidase assays of mutS-ÐlacZ operon and gene fusions suggested that hfq regulates mutS posttranscriptionally, and RNase T2 protection assays revealed that Hfq destabilizes mutS transcripts in exponentially growing cells. To study the relation between regulation of MDM repair and mutagenesis, amounts of MutS, MutL and MutH were measured in starved cells undergoing adaptive mutagenesis. It was found that MutS amount dropped drastically, MutH amount dropped slightly, whereas MutL amount remained essentially constant in starved cells. Overexpression of MutL did not reverse the drop in the amounts of MutS or MutH protein. These results ruled out several explanations for a phenomenon in which overexpression of MutL, but not MutS, reversed adaptive mutagenesis. The findings further suggested that functional MutL is limiting during adaptive mutagenesis. The implications of regulation of the MDM repair are discussed in the context of mutagenesis, pathogenesis and tumorogenesis.
Search pubmed for papers by G Feng and ME Winkler
Regulation of The Expression of MutS, MutL, and MutH Mismatch Repair Genes in Escherichia coli K-12