text:
\section{Introduction}

Within the last decade, we have seen a surge of interest in utilizing solid state dopants like rare earth ions in crystals~\cite{Casabone2018, PhysRevB.77.125111, Gobron:17, Mitsunaga:91}, nitrogen vacancy (NV) centers in nanodiamonds~\cite{Kaupp2016, Weber8513} and quantum dots in nanoscale semiconductors~\cite{PhysRevLett.119.143601} for quantum operations.
Experimentally, there has been significant progress leading to single photon sources~\cite{PhysRevLett.85.290}, quantum memories~\cite{PhysRevLett.110.250503}, individual addressing of ions~\cite{Kaupp2016}, observation of ultra slow group velocities of light~\cite{PhysRevLett.88.023602} and much more.
However, due to their complex structure and high density, all of these systems suffer from vast intrinsic inhomogeneous broadening~\cite{doi:10.1063/1.4913428, PhysRevLett.117.250504, PhysRevB.70.214116}.
The broadening is predominantly observed in the excited state since it interacts strongly with the surrounding crystal medium which leads to a shift in the transition frequencies.

\begin{figure}
\centering
\includegraphics[width=1.0\columnwidth]{F1.pdf}
\caption{Schematic representation of an idealized hole burning process using STIRAP.
(a) Absorption profile of the $\ket{1}\leftrightarrow\ket{2}$ transition.
(b) Spectral hole of width $\delta_\omega$ around the central frequency $\omega_\mathrm{target}$ after application of STIRAP.
(c) Isolated (qubit) structure inside the spectral hole.
(d) Level diagram and couplings commonly used in STIRAP. The dotted lines represent the excited state $\ket{2}$ for different ions and the inhomogeneous broadening is illustrated by the shaded region. The bold line represents the ions for which the pulses are resonant, i.e., for which $E_2 - E_1= \hbar\omega_\mathrm{target}$.
}
\label{fig:sketch}
\end{figure}

One well known method to combat this inhomogeneous broadening is to employ spectral hole burning~\cite{PhysRevB.47.14741, PhysRevB.50.18200}.
This is usually carried out by illuminating monochromatic (laser) light on the sample and sweeping the frequency across a range where the hole is desired.
This excites near resonant ions from the ground state to an excited state.
A subsequent decay to a different ground state, not coupled by the laser, then leads to a hole in the spectrum around the chosen frequencies.
This scheme is time consuming, operating on a time scale defined by the lifetime of the excited state.

In this paper, we propose to utilize stimulated Raman adiabatic passage (STIRAP)~\cite{doi:10.1063/1.458514, Goldner_1994} to create spectral holes and to establish isolated peaks in the inhomogeneously broadened absorption spectrum of the dopant ions in a crystal, as illustrated in Fig.~\ref{fig:sketch}(a-c).
STIRAP constitutes a highly efficient technique to transfer population between internal levels of an ion or a molecule without populating the intermediate levels of the Raman transition.
It is robust to variations in the applied laser fields, flexible in choosing the target level, and, as long as the adiabaticity condition is fulfilled, it yields high fidelities~\cite{RevModPhys.89.015006}.
STIRAP has been realized in a diverse range of settings from trapped ions~\cite{S_rensen_2006,PhysRevLett.115.053003}, to chiral molecules~\cite{PhysRevLett.71.3637} and even for quantum computations~\cite{PhysRevA.73.042321, PhysRevA.88.010303}.
For detailed reviews of this method see~\cite{Bergmann2015, RevModPhys.89.015006}.

We consider an ensemble of $\Lambda$ type systems [see Fig.~\ref{fig:sketch}(d)] with a broad, inhomogeneous distribution [see Fig.~\ref{fig:sketch}(a)] of the transition frequencies to the excited state $\ket{2}$.
In our scheme, spectral hole burning is achieved by adiabatically transferring the population from state $\ket{1}$ to state $\ket{3}$ for those ions with resonance frequencies around a predefined frequency $\omega_\mathrm{target}$.
Despite the robustness of STIRAP against parameter variations, the population transfer fidelity drops if the detuning [$\Delta$ in Fig.~\ref{fig:sketch}(d)] is too large.
We shall show that this defines a sharp cut-off at $\omega_\mathrm{target}\pm \delta_\omega/2$, yielding a spectral hole with well-defined edges where, as illustrated in Fig.~\ref{fig:sketch}(b), every ion has been transferred to $\ket{3}$.
The width $\delta_\omega$ of this spectral hole can be tuned by the pulse parameters and under ideal conditions one can engineer a spectral hole with a completely flat base.

In addition to coherent spectral hole burning, our protocol offers the possibility to \textit{unburn} a part of the hole by adding a second set of reversed pulses with different parameters, thereby preparing a group of emitters which absorb light within a narrow frequency interval inside the wider spectral hole, as illustrated in Fig.~\ref{fig:sketch}(c).
Such a reversed STIRAP (rSTIRAP) protocol can be used to isolate well-defined ions which may serve as qubits within a broad ensemble.
In principle, this can be done at multiple frequency locations to create several qubits which, if geometrically located close to each other, experience dipole-dipole interactions that can facilitate the implementation of controlled NOT (cNOT) gate~\cite{PhysRevA.69.022321}.
Such an architecture will ultimately pave the way towards scalable quantum computing schemes relying on inhomogeneously broadened ensembles of quantum systems~\cite{PhysRevA.75.012304,OHLSSON200271}.

The paper is organized as follows.
We start by presenting a generalized three-level model with a brief description of STIRAP in Sec.~\ref{S2}.
In Sec.~\ref{S3}, we discuss the hole burning protocol and study the parameters that determine the shape and width of the spectral hole.
Furthermore, we evaluate the influence of decoherence channels and off-resonant cross coupling on our scheme.
Then, in Sec.~\ref{S4}, we introduce and characterize a reversed STIRAP process (rSTIRAP) which returns the population to $\ket{1}$ for a selected frequency range.
Finally, we conclude with an outlook in Sec.~\ref{S5}.

\section{Physical system \label{S2}}
We consider a collection of three-level ions in a $\Lambda$ configuration [Fig.~\ref{fig:sketch}(d)] which suffer from intrinsic inhomogeneous broadening as shown by the schematic representation of the absorption spectra on its $\ket{1}\leftrightarrow \ket{2}$ transition in Fig.~\ref{fig:sketch}(a).
This can be any inhomogeneous system, as for example, NV centers in nanodiamonds or a given species of rare earth ion doped in a host crystal like Eu$^{3+}$ ions in Y$_2$O$_3$~\cite{Casabone2018} or Y$_2$SiO$_5$~\cite{Gobron:17} and Nd$^{3+}$ ions in YVO$_4$~\cite{PhysRevB.77.125111}.

\subsection{Three-level model}
The two transitions $\ket{1}\leftrightarrow \ket{2}$ and $\ket{2}\leftrightarrow \ket{3}$ are driven with (time dependent) Rabi frequencies $\Omega_{12}(t)$ and $\Omega_{23}(t)$.
We drive the $\ket{1}\leftrightarrow \ket{2}$ transition with frequency $\omega_\mathrm{target}$ (around which the spectral hole is desired) and assume the two photon resonance condition, which fixes the driving frequency on the $\ket{2}\leftrightarrow \ket{3}$ transition.
Due to the inhomogeneous broadening, each ion perceives a different detuning
$\Delta_i = \omega_\mathrm{target} - \omega_{12}^{(i)}$, where $\omega_{12}^{(i)}$ is the resonance frequency on the $\ket{1}\leftrightarrow \ket{2}$ transition of the $i^{th}$ ion .
For simplicity of notation we will omit the index on $\Delta_i$ below.
Assuming the ions to be non interacting, they each evolve independently according to a Hamiltonian ($\hbar= 1$)
\begin{align}
H &= \frac{\Omega_{12}(t)}{2}\Big(\ket{1}\bra{2} + \ket{2}\bra{1} \Big) + \frac{\Omega_{23}(t)}{2}\Big(\ket{2}\bra{3} + \ket{3}\bra{2} \Big) \nonumber \\ &\qquad + \Delta \ket{2}\bra{2} .
\label{E1}
\end{align}
In realistic settings, the excited state $\ket{2}$ has a finite lifetime and the ensemble suffers from dephasing due to crystal imperfections and stray magnetic fields.
To assess the effects of such mechanisms on our proposal, we describe the evolution of our system by a Lindblad master equation,
\begin{align}
\dot{\rho} &= -i[H,\rho] + \gamma_{21}\mathcal{D} \big[\ket{1}\bra{2}\big]\rho + \gamma_{23}\mathcal{D} \big[\ket{3}\bra{2}\big]\rho
\nonumber \\ & \qquad + \Gamma\mathcal{D}\big[\ket{2}\bra{2}-\ket{1}\bra{1}-\ket{3}\bra{3}\big]\rho,
\label{E2}
\end{align}
where we apply the superoperator $\mathcal{D}[\hat{\mathcal{O}}]\rho = \hat{\mathcal{O}}\rho\hat{\mathcal{O}}^{\dagger} - \frac{1}{2}\{\hat{\mathcal{O}}^{\dagger}\hat{\mathcal{O}}, \rho\}$ to describe spontaneous decay with rates $\gamma_{21}$ and $\gamma_{23}$ on the two optical transitions, and dephasing at a rate $\Gamma$ of the excited state relative to the two ground states.

\begin{figure*}
\centering
\includegraphics[width=\textwidth]{F2.png}
\caption{STIRAP protocol.
(a) Rabi frequencies during the protocol with the delay $\tau$ indicated.
(b) Spectrum of the Hamiltonian for positive detuning $\Delta$ during the protocol.
(c) Final population $\mathcal{P}_3$ in state $\ket{3}$ as a function of the detuning $\Delta$ and pulse delay $\tau$. The chosen (optimal) time delay $\tau= \sqrt{2}\sigma$, used in the rest of the article is indicated with a green dot-dashed line. Results are shown for $\Omega_{\max} = 10\sigma^{-1}$ and $\gamma_{21}= \gamma_{23} = \Gamma = 0$.
}
\label{F2}
\end{figure*}

\subsection{STIRAP scheme}

The Hamiltonian~\eqref{E1} has one zero eigenvalue ($\varepsilon_0=0$), with corresponding eigenstate
\begin{equation}
\ket{D} = \cos \theta \ket{1} - \sin\theta\ket{3}.
\label{E3}
\end{equation}
The other eigenvalues are
\begin{equation}
\label{eq:bright_energies}
\varepsilon_\pm = \frac{1}{2} \left(\Delta \pm \sqrt{\Delta^2 + \Omega^2_0} \right)
\end{equation}
and their corresponding eigenstates are
\begin{align}
\label{E4p}
\ket{+} &= \sin\theta \sin\phi\ket{1} + \cos\phi\ket{2} + \cos\theta \sin\phi\ket{3} ,
\\
\label{E4m}
\ket{-} &= \sin\theta \cos\phi\ket{1} - \sin\phi\ket{2} + \cos\theta \cos\phi\ket{3} ,
\end{align}
where
\begin{align}
\tan \theta&= \frac{\Omega_{12}}{\Omega_{23}},
\qquad
\tan 2\phi= \frac{\Omega_0}{\Delta},
\end{align}
with
\begin{equation}
\Omega_0=\sqrt{\Omega^2_{12} + \Omega^2_{23}}.
\end{equation}

Clearly, $\ket{D}$ is a non radiative dark state since it involves only the ground states $\ket{1}$ and $\ket{3}$ with a mixing angle $\theta$, which depends on the two Rabi frequencies.
The idea in STIRAP is to adiabatically follow this dark state while varying $\theta$ between
$\theta= 0$ ($\Omega_{23}\gg\Omega_{12}$, $\ket{D}=\ket{1}$) and
$\theta= \pi/2$ ($\Omega_{23}\ll\Omega_{12}$, $\ket{D}=-\ket{3}$).
This will effectively transfer all the populations from $\ket{1}$ to $\ket{3}$.
The introduction of a time delay $\tau > 0$ between the pulses ensures that the $\Omega_{23}$ pulse arrives before the $\Omega_{12}$ pulse.
This constitutes the core mechanism in STIRAP --- the first pulse opens an energy gap in the spectrum, allowing an adiabatic transfer when the second pulse arrives.

The basic requirement is thus that the two pulses overlap while the mixing angle $\theta$ is varied.
However, as long as the adiabaticity condition is satisfied (see below), the exact shape of the pulses is immaterial.
Hence, for simplicity, we shall consider Gaussian pulses with identical strengths $\Omega_{\max}$ and widths $\sigma$, as shown in Fig.~\ref{F2}(a),
\begin{align}
\label{eq:Omega12}
\Omega_{12}(t) &= \Omega_{\max} \exp \left( - \frac{(t-\tau/2)^2}{2 \sigma^2} \right) ,
\\
\label{eq:Omega23}
\Omega_{23}(t) &= \Omega_{\max} \exp \left( - \frac{(t+\tau/2)^2}{2 \sigma^2} \right) .
\end{align}

\begin{figure*}
\centering
\includegraphics[width=\textwidth]{F3new2.png}
\caption{ Spectral hole burning.
(a) $\mathcal{P}_3$ as a function of pulse delay and detuning.
The blue, dot-dashed line corresponds to $\pm \Delta_\mathrm{edge}$ defined in Eq.~\eqref{AE1}.
The bold, green line corresponds to $\pm \Omega_0^2 / 16\dot{\theta}$.
(b) Spectral hole profile ($\mathcal{P}_3$) as a function of $\Delta$ for selected values of $\Omega_{\max}$.
(c) $\mathcal{P}_3$ as a function of $\Omega_{\max}$ and detuning normalized to $\Delta_\mathrm{edge}$.}
\label{F3}
\end{figure*}

\subsection{Adiabaticity and optimal time delay}

In order to ensure an adiabatic transfer, the local adiabaticity condition must hold throughout the entire process.
Namely,
\begin{equation}
| \varepsilon_0 - \varepsilon_\pm | \gg | \braket{\pm}{\dot{D}} | ,
\label{E5}
\end{equation}
which in the absence of single photon detuning ($\Delta=0$) becomes
$\Omega_0 \gg |\dot{\theta}|$~\cite{RevModPhys.89.015006}.
This condition guarantees that there are no diabatic transitions out of the dark state $\ket{D}$, and can be fulfilled by a sufficiently slow process (having a slow rate of change of $\theta$) or by a large enough gap (larger Rabi frequencies in $\Omega_0$).

In the next section we will see how the presence of detuning due to inhomogeneity affects this condition, as we are interested in engineering a protocol which attains adiabaticity for a tunable range of frequencies $\delta_\omega$ around $\omega_\mathrm{target}$ ($\Delta=0$).
We shall take the amplitude $\Omega_{\max}$ of the pulses as our main control parameter, and in the following determine an optimal value of the time delay $\tau$ between the pulses.

We simulate~\cite{JOHANSSON20131234} the STIRAP process by considering the ions to be initially in $\ket{1}$ and apply the pulses shown in Fig.~\ref{F2}(a).
The eigenvalues of the Hamiltonian in the presence of single photon detuning $\Delta$ are plotted in Fig.~\ref{F2}(b).
The final population $\mathcal{P}_3$ in $\ket{3}$ is shown in Fig.~\ref{F2}(c) as a function of the single-photon detuning $\Delta$ and pulse delay $\tau$.
For $\tau \ll \sigma$, both pulses are switched on almost simultaneously and both $\ket{1}$ and $\ket{3}$ are coupled to $\ket{2}$.
This leads to Rabi oscillations between the different states leaving population in the excited state at the final time.
However, for certain values of the detuning (around $|\Delta| \simeq 25 \sigma^{-1}$), perfect transfer into $\ket{3}$ is achieved.
These points represent two-photon resonant Raman processes and, unlike the STIRAP process, they are highly dependent on the Rabi frequencies and detuning.
For $\tau \gg \sigma$, the process breaks down due to the complete temporal separation of the two pulses.
The first pulse ($\Omega_{23}$) has no effect since all the population is in $\ket{1}$ while it is on, and the second pulse leads simply to Rabi oscillations between $\ket{1}$ and $\ket{2}$.
In-between these extreme limits, however, there is a regime where STIRAP works perfectly.
We fix $\tau=\sqrt{2}\sigma$, indicated by the green, dot-dashed line in panel Fig.~\ref{F2}(c), which has been found to be an optimal value for the delay in similar studies~\cite{RevModPhys.70.1003}.

\section{Hole burning \label{S3}}

We will now describe how STIRAP can be used for hole burning in an inhomogeneously broadened sample.
We initially neglect the effects of dephasing and decay ($\gamma_{21} = \gamma_{23} = \Gamma=0$ in the master equation~\eqref{E2}) but we shall discuss their implications for our results in Sec.~\ref{sec:decoherence}.

\subsection{Spectral hole profile}
Figure~\ref{F3}(a) shows $\mathcal{P}_3$ after the STIRAP pulses as a function of $\Delta$ and $\Omega_{\max}$.
We notice that for ions for which the pulses are very off-resonant, STIRAP fails and only ions with $\Delta\simeq 0$ are transferred to state $\ket{3}$.
However, as the strength of the pulses increases, the protocol becomes robust in a wider range of detunings,
and the width $\delta_\omega$ of the spectral hole increases.
This is due to a growing energy gap between the dark state and the relevant bright state (see Eqs.~\eqref{eq:bright_energies}, and our discussion below).

The spectral profile of the hole is shown in Fig.~\ref{F3}(b) for different values of $\Omega_{\max}$.
From these plots, it is evident that while small oscillations appear in the base of the spectral hole, with higher values of $\Omega_{\max}$ one can achieve a spectral hole with a fairly flat base and sharply defined edges beyond which the population in $\ket{3}$ decreases to zero.
It is noteworthy that the robustness of the STIRAP guarantees that the excited state $\ket{2}$ is never populated during this population transfer, which was also observed in our simulations.

We can address the width of the spectral hole by considering the effects of the single-photon detuning $\Delta$ on the adiabaticity condition.
In the presence of finite $\Delta$, one of the bright states ($\ket{+}$ for $\Delta>0$ and $\ket{-}$ for $\Delta<0$) decouples from the dark state $\ket{D}$ with an energy gap larger than $\Delta$.
Therefore, it is sufficient to consider only the adiabaticity condition involving the other eigenstate.
We focus our discussion on the case where $\Delta > 0$ and study the coupling with $\ket{-}$, and note that the reverse situation ($\Delta < 0$, coupling to $\ket{+}$) produces the expected symmetrical results.
The STIRAP adiabaticity condition~\eqref{E5} yields approximately $|\Delta| \ll \Omega_0^2 / 8\dot{\theta}$ which already gives the scaling of the width with the pulse parameters.
As seen from the green line in Fig.~\ref{F3}(a), defining the edge of the hole at $ \pm \Omega_0^2 / 16\dot{\theta}$ fits the numerical data with good agreement.

We may apply a simple model which captures the essential features of the STIRAP transition, and allows analytic insight regarding the width and detailed profile of the spectral hole and its dependence on the pulse parameters.
The model assumes that $\Omega_{0}(t)$ and $\phi(t)$ are constant while the mixing angle $\theta(t) = {\pi t}/{2 T}$ varies linearly between 0 and $\pi/2$ during a time $T$.
This approximates well the Gaussian pulses in Eqs.~(\ref{eq:Omega12}-\ref{eq:Omega23}) in the time interval between their maxima where the main part of the STIRAP process happens.

\begin{figure}
\centering
\includegraphics[width=0.38\textwidth]{F6v2.png}
\caption{Effects of decay and dephasing.
Spectral hole profile ($\mathcal{P}_3$) as a function of $\Delta$ for different values of (a) the excited state decay rates $\gamma_{21}=\gamma_{23}=\gamma$ and (b) the excited state dephasing rate $\Gamma$.
Results are shown for $\Omega_{\max} = 20\sigma^{-1}$.}
\label{fig:decoherence}
\end{figure}

In absence of dephasing and decay, a perturbative treatment yields the probability for a non-adiabatic transition out of the dark state~\cite{Messiah_1961},
\begin{align}
P_\mathrm{trans} &\simeq \frac{ \left| \int_{0}^{T} \braket{-}{\dot D} \exp\left[-{i \int_{0}^{t} \delta_\epsilon \, dt^\prime }\right] dt \right|^2}{ \left| \int_{0}^{T} \braket{-}{\dot D} dt \right|^2}.
\end{align}
Under the above conditions, both the energy gap $\delta_\epsilon \equiv (\varepsilon_{0} - \varepsilon_{-})$ and the non-adiabatic coupling $\braket{-}{\dot D}$ remain constant,
and we obtain an analytical estimate for the final population of state $\ket{3}$
\begin{align}
\label{eq:sinc}
\mathcal{P}_3 = 1-P_\mathrm{trans}
= 1-\sinc^2 \left(\frac{\pi \delta_\epsilon}{4 \dot\theta}\right) ,
\end{align}
where $\sinc(x) = \sin(x)/x$.
Note that
$\delta_\epsilon = ( \sqrt{\Delta^2 + \Omega^2_0} - \Delta ) / 2$
decreases monotonically as $\Delta$ increases.
The edge of the spectral hole is defined by the first zero of the $\sinc$ function, which occurs when
$\pi\delta_\epsilon/4\dot\theta = \pi$,
yielding
\begin{gather}
\Delta_\mathrm{edge} = \frac{\Omega_{0}^2}{16 \dot\theta} - 4 \dot\theta ,
\label{AE1}
\end{gather}
and a corresponding hole width of $\delta_\omega = 2\Delta_\mathrm{edge}$.
For $|\Delta| < \Delta_\mathrm{edge}$, $\mathcal{P}_3$ is close to 1, giving a flat plateau for the spectral hole ($\sinc^2(x) < 0.05$ for $x>\pi$).
For $|\Delta| > \Delta_\mathrm{edge}$, $\mathcal{P}_3$ rapidly decreases and for large $\Delta$, Eq.~\eqref{eq:sinc} can be approximated as $\mathcal{P}_3\simeq(\pi^2\Omega^4_0/768\dot{\theta}^2\Delta^2) + \mathcal{O}[1/\Delta^4]$.

In order to apply this expression to the Gaussian pulses, we approximate the parameter values by those at the instant between the two pulses (i.e., Eqs.~(\ref{eq:Omega12}-\ref{eq:Omega23}) at $t=0$), giving
$\Omega_{0} \simeq \sqrt{2} e^{-\tau^2/8 \sigma^2} \Omega_{\max}$ and $\dot\theta \simeq \tau/2 \sigma^2$.
With these approximations, $\Delta_\mathrm{edge}$ is shown with a blue dot-dashed line in Fig.~\ref{F3}(a) which fits the numerical data with reasonable agreement.

We can also use Eq.~\eqref{eq:sinc} to understand the structure of the base of the hole as seen in Fig.~\ref{F3}(b).
The oscillatory structure is defined by the tail of the $\sinc$ function beyond its first zero.
The maximum value of the argument is $\pi\Omega_{0}/8\dot\theta$ (at $\Delta=0$) which dictates the number of oscillations and how flat the base appears (how far out the $\sinc$ tail it starts).
Figure~\ref{F3}(c) shows $\mathcal{P}_3$ as a function of $\Delta/\Delta_\mathrm{edge}$ and pulse intensity $\Omega_{\max}$.
This allows to see the generality of this simple model in predicting the cut off, and to visualize the structures of the spectral hole with its increasing flatness as $\Omega_{\max}$ increases.

\begin{figure}
\centerline{\includegraphics[width=0.36\textwidth]{F8.pdf}}
\caption{
Spectral hole profile ($\mathcal{P}_3$) for different values of the splitting $\omega_{13}$ between the stable state $\ket{1}$ and $\ket{3}$. The solid curve assumes that each laser couples only to the desired transition in the ions.
Results are shown for $\Omega_{\max} = 20\sigma^{-1}$ and $\Gamma= \gamma_{21}= \gamma_{23}= 0$.}
\label{fig:crossCoupling}
\end{figure}

\subsection{Effects of decay and dephasing}
\label{sec:decoherence}

While the results presented above signify that under ideal conditions STIRAP allows well defined and broad holes to be burned in an inhomogeneous profile, any realistic setup will experience experimental or fundamental limitations.
In the following, we study the effects of decay and dephasing on the hole burning process.

We show in Fig.~{\ref{fig:decoherence}}(a) the profile of the spectral hole for different decay rates of the excited state ($\gamma_{21}=\gamma_{23}\equiv \gamma\geq 0$).
We find that as the rate of decay increases, the flat profile of the spectral hole is lost.
Moreover, for very large values of $\gamma$ even the high fidelity at resonance is lost.

In Fig.~{\ref{fig:decoherence}}(b), it is seen that while our protocol is robust in the absence of non-radiative dephasing ($\Gamma\geq 0$) of the excited state, as the dephasing increases, the final population $\mathcal{P}_3$ in state $\ket{3}$ starts decreasing.
At variance with the effects of decay, however, the flatness of the hole is preserved as the fidelity decreases globally.

Our results shows thus, that for systems with large environmental couplings, the STIRAP hole burning protocol becomes inefficient.
However, realistic dephasing and decay rates are typically much smaller than the values considered in Fig.~{\ref{fig:decoherence}}~\cite{Casabone2018}, ensuring good performance for ions in quantum information processing tasks.

\subsection{Effects of off-resonant cross coupling}

\begin{figure*}
\centering
\includegraphics[width=\textwidth]{F4.png}
\caption{
Qubit isolation around a single target frequency $\omega_\mathrm{target}^{(n)}$ coinciding with the centre of the spectral hole.
(a) Pulse Rabi frequencies $\Omega_{12}(t)$ and $\Omega_{23}(t)$ and mixing angle $\theta(t)$ during the combined STIRAP and by rSTIRAP protocols.
(b) Final population $\mathcal{P}_1$ in state $\ket{1}$ as a function of the detuning and pulse amplitude of rSTIRAP.
(c) Final population $\mathcal{P}_1$ in state $\ket{1}$ in the presence and absence of dephasing for the pulses shown in (a). The inset shows a zoom-in on the central structure.
Results are shown for $\gamma_{21} = \gamma_{23} = 0$.
}
\label{fig:qubit}
\end{figure*}
This far we have assumed that each laser couples only to the desired transition in the ions.
For some ions, however, the detuning may be comparable to the splitting between the stable states ($|\Delta|\simeq \omega_{13}$), and one of the STIRAP laser pulses may unintentionally excite the wrong transitions, as described by the contributions to the Hamiltonian,
\begin{align}
\begin{split}
H_\mathrm{cc} =
\frac{\Omega_{23}(t)}{2}\Big(\ket{1}\bra{2}\e{-i\omega_{13} t} + \ket{2}\bra{1}\e{i\omega_{13} t} \Big)
\\
+ \frac{\Omega_{12}(t)}{2}\Big(\ket{3}\bra{2}\e{i\omega_{13} t} + \ket{2}\bra{3}\e{-i\omega_{13} t} \Big),
\end{split}
\end{align}
that were disregarded in Eq.~\eqref{E1}.

In Fig.~\ref{fig:crossCoupling} it is seen that as long as the level splitting is larger than the desired spectral hole (cf. the curve for $\omega_{13}=400\sigma^{-1}$), the effects of this cross-coupling are insignificant in the intended frequency range.
For smaller level splittings, however, the hole width is reduced, as STIRAP becomes completely ineffective and yields no final population in $\ket{3}$ for the resonances $\Delta = \pm \omega_{13}$ (cf. the dips for the $\omega_{13}=50\sigma^{-1}$ and $100\sigma^{-1}$ curves).
It is thus evident that the energy splitting imposes an upper bound $\delta_{\omega}\lesssim 2\omega_{13}$ to the width of the spectral hole.
Note that a similar restriction applies for conventional hole burning.

\section{Qubit isolation \label{S4}}

We have shown how STIRAP can be utilized to create spectral holes with high fidelity.
In this section, we propose to follow that process with a set of \textit{reversed} STIRAP (rSTIRAP) pulses of lower intensity in order to bring some atoms back into state $\ket{1}$ and create narrow-band peaked structures at target frequencies $\omega_\mathrm{target}^{(n)}$ inside the burned hole.
This can be used, for instance, in quantum information processing to effectively create one or multiple isolated qubits in an inhomogeneous sample~\cite{PhysRevA.75.012304, OHLSSON200271}.

\subsection{Reversed STIRAP}
Assuming ideal conditions, after the initial STIRAP pulses, all ions inside the spectral hole are in state $\ket{3}$.
Therefore, a new set of reversed pulses
 ($\Omega_{12}$ acting before $\Omega_{23}$, i.e., $\tau < 0$ in Eqs.~(\ref{eq:Omega12}-\ref{eq:Omega23}))
will adiabatically bring back a selected band of them to the state $\ket{1}$.
As we discussed in the previous section, the width of the band is tunable through the pulse intensity, and less intense pulses thus allow us to bring back a much narrower band of the spectrum.
The set of STIRAP and rSTIRAP pulses in this process are depicted in Fig.~\ref{fig:qubit}(a), which also shows how the mixing angle $\theta(t)$ (blue, dotted line) varies from $0$ to $\pi/2$ for the STIRAP pulses, followed by its return to $0$ during the rSTIRAP pulses.

Figure~\ref{fig:qubit}(b) shows how the strength of the second set of pulses, $\Omega_{\max}^\mathrm{(r)}$, influences the final population in $\ket{1}$ for different values of $\Delta$ (after the hole has been created).
It is seen that, in a similar manner as for the original hole burning, the strength of the rSTIRAP pulses can indeed be used to control the width of the \textit{unburnt} frequency band.
The figure shows also the limit on how narrow these peaks can be created, as dictated by the adiabaticity condition: if $\Omega_{\max}^\mathrm{(r)}$ is too small, rSTIRAP fails for \textit{all} values of $\Delta$, resulting in a peak with less than unit population in $\ket{1}$.

\subsection{Isolation profiles}

We show in Fig~\ref{fig:qubit}(c) the profile of a narrow isolated peak inside a broad spectral hole, signifying that the combination of STIRAP and rSTIRAP processes can be successfully employed to create well-defined systems within a broad inhomogeneous ensemble.
The wiggles in the spectral hole, see Fig.~\ref{F3}, can cause a small loss of fidelity of the imprinted structures around the desired qubit.
However, for multi-qubit quantum computing protocols~\cite{OHLSSON200271}, the isolated emitters will dominate over the background.

It is possible to isolate multiple qubits inside the same broad spectral hole.
We illustrate this in Fig.~\ref{F6}, where the sequential application of five sets of rSTIRAP pulses with different target frequencies $\omega_\mathrm{target}^{(n)}$ yield five well-defined qubits inside the hole.
While here we have assumed the serial application of the different rSTIRAP pulses, it should also be possible to create an atomic frequency comb~\cite{PhysRevA.79.052329,PhysRevLett.104.040503}, i.e., a number of equidistant isolated qubits, by simultaneously applying the rSTIRAP pulses with an optical frequency comb, see also Ref~\cite{PhysRevA.98.043834} for a related proposal in a Doppler-broadened system.

\begin{figure}
\centering
\includegraphics[width=0.38\textwidth]{F7_crop.pdf}
\caption{
Multiple isolated qubits.
(a) Sketch of the STIRAP pulses and subsequent sets of rSTIRAP pulses with five different target frequencies $\omega_\mathrm{target}^{(n)}=\omega_\mathrm{target}+n\times500\sigma^{-1}$ with $n = -2,-1,0,1,2$.
(b) Final population $\mathcal{P}_1$ in state $\ket{1}$ after the train of pulses.
Results are shown for $\Omega_{\max} = 100 \sigma^{-1}$, $\Omega_{\max}^\mathrm{(r)} = 5 \sigma^{-1}$, $\gamma_{21}= \gamma_{23} = \Gamma = 0$.
}
\label{F6}
\end{figure}

\section{Outlook \label{S5}}

In this paper, we have shown how STIRAP can be used for coherent spectral hole burning with high fidelity and better control of the shape of the spectral hole.
We derived an analytical expression that estimates the width of the hole as a function of the pulse intensity and emphasize how a hole with well-defined edges may be obtained due the adiabaticity requirement in the STIRAP scheme.
Moreover, we proposed to apply additional sets of weaker STIRAP pulses to isolate qubits inside the spectral hole.
STIRAP is highly flexible in targeting any state and the entire process requires just two Gaussian pulses.

Our proposal is robust against variations in pulse parameters as long as the adiabaticity condition is fulfilled and against moderate decoherence in the excited state.
For clarity of presentation, we focused our attention on Gaussian pulses.
However, in a future study it would be interesting to consider the possibilities offered by more complex pulse shapes which may deliver spectral holes with sharper edges and other desirable features.

The parameters considered in this paper are compatible with the state-of-the-art developments in the experimental domain.
For instance, for Eu$^{3+}$ ions doped in an Y$_2$O$_3$ crystal~\cite{Casabone2018}, the two stable states in our model may be the hyperfine states $^7F_0$ and $^7F_2$ with transition frequencies $\omega_{12}= 5.167 \times 10^{14}$ Hz and $\omega_{23}= 4.903 \times 10^{14}$ Hz to the excited state $^5D_0$.
The excited state is known to have an inhomogeneous broadening of $22$ GHz ~\cite{Casabone2018}.
Assuming that one desires to create a spectral hole of width $\delta_\omega \sim 1$ MHz with isolated (qubit) structures of a few kHz wide inside, the dephasing and decay rates of $\Gamma = 0.785$ kHz and $\gamma = 45$ kHz are small and will not severely affect the efficiency of STIRAP.
In addition, the ground state separation is on the order of $\omega_{13} \simeq 0.3\times 10^{14}$ Hz $\gg \delta_\omega$, implying that off-resonant cross coupling is negligible for these systems.

\section{Acknowledgements}
We would like to thank Signe Seidelin and Bess Fang for discussions on possible candidate systems for our proposal.
K.~D. and K.~M. are supported by the European Union's Horizon 2020 research and innovation program (No. 712721, NanoQtech).
A.~H.~K. and K.~M. acknowledge support from the European Union FETFLAG program, Grant No. 820391 (SQUARE).
A.~B. and K.~M. are supported by the Villum Foundation.

\bibstyle{apsrev4-1}

redpajama_set_name: RedPajamaArXiv


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The homeowner names were taken "as is" from the county auditor. We will attempt to update the directory periodically, but there are bound to be inaccuracies. Please contact the webmaster for corrections.
Information on this page was last updated on January 2, 2017.


text:
The law is a physique of rules that's designed to manage the blameworthy conduct of people. Law is a system of guidelines which might be created and enforced by means of social or governmental establishments to control habits 2 It has been defined both as "the Science of Justice" and "the Artwork of Justice". In the case of dominance, Federal law always prevails over state law as a result of the U.S. Structure gives the federal authorities superiority over the state authorities.
2. Law is generally divided into four principle classes, specifically; Pure law, the law of countries, public law, and personal or civil law. The controlling influence of such rules; the situation of society caused by their observance: maintaining law and order.
This data will not be provided as legal or prescriptive advice and you could check your local laws for specificity. A specialised dictionary protecting terms used in the numerous branches of the legal occupation, as civil law, criminal law, and company law.
The healthcare area is the topic of a bunch of federal statutes, rules, pointers, interpretive information, and mannequin guidance. three. take the law into one's own palms, to manage justice as one sees match without recourse to legal processes. Courts of law are a basic a part of the U.S. judicial system. To mete out justice as one sees match without due recourse to law enforcement companies or the courts.
The federal and state constitutions implicitly give the legislatures the ability to create administrative agencies. Studying case law helps the researcher perceive how the courts interpret statutes, and also how the courts analyze related points that are not lined within the statutes.
The lease laws in Malta dissect Maltese tenants into two categories: those that contracted their lease prior to 1995 and people who signed their lease contract after 1995. Laws have been made lest the stronger would possibly become all-powerful. State law refers back to the laws that each particular person state within the United States of America use to govern their residents. After the federal Structure, the very best laws are written laws, or statutes, handed by elected federal lawmakers.
The Clementine structure or decrees of Clement V., had been in like manner authenticated in 1317, by his successor, John XXII., who additionally revealed twenty constitutions of his own, referred to as the Extravagantes Joannis, all of which in some method reply to the novels of the civil law.
On the state stage, governors have comparable authority to make laws regarding state administrative businesses and state military personnel. Federal statutes are passed by Congress and signed into law by the president. E. Show your evidence to other folks; pals, household, non-public detectives, lawyers.
There are specific exceptions to trespassing laws together with law enforcement, meter readers and government surveyors. Roman law in the days of the Roman Republic and Empire was closely procedural, and lacked an expert authorized class. Mr. Chitty defines municipal law to be "a rule of civil conduct, prescribed by the supreme power in a state, commanding what shall be completed or what shall not be carried out." 1 Bl. Com.
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The hire laws in Malta dissect Maltese tenants into two categories: those that contracted their lease previous to 1995 and those who signed their lease contract after 1995. These type the physique of the Roman law, or corpus juris civilis, as printed about the time of Justinian. 7. Choose Swift, in his System of the Laws of Connecticut, prefers the term civil law, to that of municipal law. Historically, widespread-law courts administered the Common Law , that is, law based on prior decisions reasonably than statutes.
Providing a constitution for public worldwide law, the United Nations system was agreed throughout World Struggle II. The common law typically controls civil matters, comparable to contract disputes and private damage instances (torts). 3. The phrase "common law" occurs in the seventh article of the amendments of the structure of the United States.
Electrical Engineering And Pc Science
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The law is a physique of rules that's designed to control the blameworthy conduct of individuals. Along with handing staff a much decrease burden of proof than other forms of injunctive aid, the court docket should consider "the chilling impact on other staff asserting their rights underneath those laws in determining if non permanent injunctive reduction is simply and proper." Thus, the courtroom must contemplate an entirely new issue that only favors the employees.
three. Although profitable in the west, these laws weren't, even within the lifetime of the emperor universally obtained; and after the Lombard invasion they turned so totally uncared for, that both the Code and Pandects were lost until the twelfth century, A. D. 1130; when it is said the Pandects were by accident found at Amalphi, and the Code at Ravenna.
Examples embrace a Grasp of Laws , a Master of Legal Studies , a Bar Skilled Training Course or a Doctor of Laws), and are constituted in office by legal forms of appointment ( being admitted to the bar ). There are few titles of respect to signify famous lawyers, resembling Esquire , to point barristers of higher dignity, 127 128 and Physician of law , to point a person who obtained a PhD in Law.
All which lay in the identical confusion and disorder as the Roman civil law, until about the year 1151, when one Gratian, an Italian monk, animated by the invention of Justinian's Pandects, decreased the ecclesiastical constitutions also into some methodology, in three books, which he entitled Concordia discordantium canonum, however which are usually recognized by the name of Decretum Gratiani.
The healthcare field is the topic of a number of federal statutes, regulations, pointers, interpretive data, and model steering. I enjoyed learning about our laws and it is functions, as well as history. 3. A set of rules or rules dealing with a particular space of a authorized system: tax law; felony law. Trespassing is the act of someone unlawfully entering, walking on or residing on personal property.
U.S. law will be bewildering as a result of the laws of the assorted jurisdictions—federal, state, and native—are sometimes in conflict. King Hammurabi is revealed the code of laws by the Mesopotamian solar god Shamash , also revered as the god of justice.
Maltese Hire Laws
The law is a body of guidelines that's designed to regulate the blameworthy conduct of people. seventy eight Civil law codifications based mostly intently on Roman law, alongside some influences from religious laws similar to canon law , continued to unfold throughout Europe till the Enlightenment ; then, in the 19th century, each France, with the Code Civil , and Germany, with the Bürgerliches Gesetzbuch , modernised their authorized codes.
186 The law of the trendy firm started with the Joint Inventory Firms Act 1856 , passed within the United Kingdom, which provided buyers with a easy registration process to achieve limited liability underneath the separate legal character of the company.
lawan kata dari bersyukur terhadap nikmat allah adalah, lawang wangi dago bandung, lawan kata konflik
While you or somebody you like is facing felony fees, it is smart to start doing all of your analysis in order to better perceive the law and what you would possibly count on throughout the judicial course of. Nearly all legal laws are statutory, so common law rules are rarely utilized in felony circumstances. Case law analysis may also be performed utilizing the Internet For example, Cornell University's on-line Legal Information Institute ( ) offers recent and historic U.S. Supreme Court decisions, in addition to current New York appeals selections.
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Law Student Bids $8K For Lunch With Amal Clooney At Columbia Auction
The Law Of Corporate Finance And Monetary Markets

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Julia Cameron: "The creative process is a process of surrender, not control."
"The creative process is a process of surrender, not control... Mystery is at the heart of creativity. That, and surprise."
Julia Cameron (b. 1948) is an American artist and author famous for her 1992 self-help book The Artist's Way. Her artistic philosophy is founded on a belief that creativity is bred from self-confidence, personal development, and divine influence (rather than from the human ego). Cameron, who was once married to Martin Scorsese, is a prolific writer who has authored over three dozen books, plays, and film scripts.
You can follow Julia Cameron on Twitter. Her newest book is The Artist's Way for Parents: Raising Creative Children.


text:
Home Board of Trustees Minutes Board of Trustees minutes, 1969 Mar. 19
Board of Trustees minutes, 1969 Mar. 19
SPECIAL MEETING OF THE BOARD OF TRUSTEES OF THE TRUSTEES OF
Trustees' Room.   Executive Building I,    NOTICE OF MEETING.
March 19,   1969
The Board of Trustees of The Trustees of Purdue University convened in special meeting in the Trustees' Roorh of the Executive Building of the Uni¬ versity at 10:00 am on Wednesday.   March 19,   1969,   pursuant to action by the Board on March 4,   I969,  XVII,  and further pursuant to the following-notice mailed to each member of the Board by the Secretary on March 10,   1969:
Pursuant to action by the Board of Trustees on March 4-5,   I969,  there will be a special meeting of the Board of Trustees of The Trustees of Purdue University on Wednesday,   March 19,   1969,   convening in Executive Session at 10:00 am CDT and in General Session at approximately 2:30 pm CDT, in the Trustees' Room of the Executive Building of the University,   in order to:
1, Consider and act upon the following -
a. Proposed increases in student tuition and fees
b. Student Bill of Rights
c    Recognition of Student Organizations
d.    Proposals concerning The Purdue Exponent;
2. Consider and act upon any other matter or business which may come
before said meeting.
II. ROLL CALL,   EXECUTIVE SESSION,  MARCH 19,   1969.
President Knoy called the meeting to order in Executive Session at 10:00 am.    All members of the Board except one were present as follows; Mrs.  White,   Messrs.   Brumfield,  Graham,  Heine,  Knoy,   Rumely,  Walb and Wilson.    The absence of Mr.   Hillenbrand was excused by consent of the Board.    Also present were President Hovde,   Hawkins and Lawshe,   Counsel Schilling.  Attorney Bodle,   Executive Assistant to the President Hicks, Business Manager and Assistant Treasurer Finn,   Mr.   Hentschel.   Treasurer of Purdue Research Foundation.   Mr.   Smalley,   Director of University Residences and Purdue Memorial Union,  Mr.  Wade,   Director of Physical Plant,   Miss Stone,   Dean of Women,   Mr.   Roberts,   Dean of Men,   Messrs. Schaller and Topping of University News Service,  Assistant Morris and Secretary Skinner.    Mr.   Tombaugh,   Director of Division of Financial Aids, was present for part of the meeting.
III. DISCUSSION OF PROPOSED INCREASES IN SIU DENT TUITION AND FEES,
President Hovde recalled discussions at the Trustees meeting on March 4-5,   1969,  which had led to authorization of University officers to proceed with preparation of a final recommendation for increases in student
Title Board of Trustees minutes, 1969 Mar. 19
Title on Piece Special meeting of the Board of Trustees of the trustees of Purdue University
URI ark:/34231/c6wm1c7t
Color Management Bookeye 3 internal
Transcript 114 SPECIAL MEETING OF THE BOARD OF TRUSTEES OF THE TRUSTEES OF PURDUE UNIVERSITY Trustees' Room. Executive Building I, NOTICE OF MEETING. March 19, 1969 The Board of Trustees of The Trustees of Purdue University convened in special meeting in the Trustees' Roorh of the Executive Building of the Uni¬ versity at 10:00 am on Wednesday. March 19, 1969, pursuant to action by the Board on March 4, I969, XVII, and further pursuant to the following-notice mailed to each member of the Board by the Secretary on March 10, 1969: Pursuant to action by the Board of Trustees on March 4-5, I969, there will be a special meeting of the Board of Trustees of The Trustees of Purdue University on Wednesday, March 19, 1969, convening in Executive Session at 10:00 am CDT and in General Session at approximately 2:30 pm CDT, in the Trustees' Room of the Executive Building of the University, in order to: 1, Consider and act upon the following - a. Proposed increases in student tuition and fees b. Student Bill of Rights c Recognition of Student Organizations d. Proposals concerning The Purdue Exponent; 2. Consider and act upon any other matter or business which may come before said meeting. II. ROLL CALL, EXECUTIVE SESSION, MARCH 19, 1969. President Knoy called the meeting to order in Executive Session at 10:00 am. All members of the Board except one were present as follows; Mrs. White, Messrs. Brumfield, Graham, Heine, Knoy, Rumely, Walb and Wilson. The absence of Mr. Hillenbrand was excused by consent of the Board. Also present were President Hovde, Hawkins and Lawshe, Counsel Schilling. Attorney Bodle, Executive Assistant to the President Hicks, Business Manager and Assistant Treasurer Finn, Mr. Hentschel. Treasurer of Purdue Research Foundation. Mr. Smalley, Director of University Residences and Purdue Memorial Union, Mr. Wade, Director of Physical Plant, Miss Stone, Dean of Women, Mr. Roberts, Dean of Men, Messrs. Schaller and Topping of University News Service, Assistant Morris and Secretary Skinner. Mr. Tombaugh, Director of Division of Financial Aids, was present for part of the meeting. III. DISCUSSION OF PROPOSED INCREASES IN SIU DENT TUITION AND FEES, President Hovde recalled discussions at the Trustees meeting on March 4-5, 1969, which had led to authorization of University officers to proceed with preparation of a final recommendation for increases in student
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Home Lifestyle Health
NMA Tasks Ayade On CONMESS For Doctors
The Tide - November 28, 2018
HIV/AIDS: FG To Increase Access To Test, Treatment
Immunisation: Health Ministry Targets Rural Communities
Health The Tide - November 21, 2018
Towards ensuring that the on-going Maternal, Newborn and Child Health Week (MNCHW)/ Maternal Neo-natal Tetanus Elimination campaign achieves its target of over 80 percent,...
NMA Seeks Improved Doctors, Nurses' Relationship
The Nigeria Medical Association (NMA) has called for the reintroduction of the old good working relationship that existed between medical practitioners and nurses to...
Natural Methods To Manage Breast Cancer
A study has revealed that one major cause of breast cancer is wearing tight bras for more than 12hours. According to the study, a woman...
Family Planning: Board Assures On TCI Sustenance
The Head of Research at the Rivers State Primary Healthcare Management Board, Dr Mina Whyte, says the on-going The Change Initiative (TCI) project on...
UHC: 'Nigeria Needs 155,000 Additional Doctors'
Nigeria needs additional 155,000 doctors at the ratio of one doctor to 1,000 people to achieve the Universal Health Coverage (UHC), Prof. Usman Ahmed,...
RSG To Adopt New Method For Contraceptives Usage
Health The Tide - November 7, 2018
Towards ensuring effective family planning uptake in Rivers State, the Rivers State Government will soon commence a new method of administering contraceptives. Making this known...
How To Improve Memory Power And Focus
Health TheTideAdmin - January 7, 2018
Memory loss can strike anybody anytime of time. It is generally found in matured individuals. The regular reasons for memory loss can be considered...
Best Medical Student Gets N250,000 Cheque
Health The Tide - December 6, 2017
The College of Health Sciences (CHS) of University of Abuja (UNIAbuja) on Sunday presented a N250,000 cheque to Dr Adamu Bara, the Best Medical...
NPHCDA Renovates 95 PHC Facilities
The National Primary Health Care Development Agency (NPHCDA) says it revitalised and renovated 95 of the 110 earmarked Primary Health Care (PHC) facilities under...
Maintain Integrity In Patients' Management, Registrar Tells Doctors
The Registrar, Medical and Dental Council of Nigeria (MDCN), Dr Tajudeen Sanusi has urged the 18 pioneer medical doctors of University of Abuja (UNIAbuja)...


text:
Q: How do you calculate the volume of a $3D$ parallelepiped? Find the volume of the parallelepiped with vertices $(0,0,0)$, $(3,0,0)$, $(0,5,1)$, $(3,5,1)$, $(2,0,5)$, $(5,0,5)$, $(2,5,6)$, and $(5,5,6)$.
When in $2D$, I usually rely on the Shoelace Formula to solve these types of questions. How do you do this when it's in $3D$?

A: You can use something called the "three dimensional scalar product". A parallelepiped is uniquely determined by three vectors $u, v, w$, and the volume is given by $|u\cdot(v\times w)|$. In this case, your three vectors are $u = (3, 0, 0), v = (0, 5, 1), w = (2, 0, 5)$.
You'll see this is similar to what you're used to, because for a 2D parallelogram determined by vectors $u, v$, the area is $u\times v$
Edit Just to be sure - are you familiar with the dot product and cross product? Suppose $u = (u_1, u_2, u_3), v = (v_1, v_2, v_3)$. Then $u\cdot v = u_1v_1+u_2v_2+u_3v_3$, and $u\times v = (u_2v_3-u_3v_2, u_3v_1-u_1v_3, u_1v_2-u_2v_1)$

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Searching for the next digital marketing strategy with most searchable content is the most challenging task at present. The scenario becomes more complicated for the ever-changing global market when you are creating the most searchable content. Changing trend and evolution of digital marketing requires your expertise to predict for the next big thing to come and sky-rocket your business.
All the game is about spinning the information and communication. What does that mean? You must create a strategic content planning what people love to search.
Work on the presentation of the content and supporting information.
I was quite inquisitive to research about the next focus to work. Here I share you what I find and how it can impact your business.
Content marketing does not depend on the type of the industry you belong to or super skill of your English writing. Rather effective content marketing relies on the ideation of your analysis, your fluid style of writing, attractive title, information-rich framing and smooth search engine crawling. Google or Bing algorithm determines the relevancy of the query and your content information accordingly, and the success of the most searchable content depends on that content marketing strategy.
Rather than investing lot of money in the marketing, you must plan content strategy according to the pain point of the search query and provide solution accordingly. Automatically the engagement factor will follow.
I am concerned about the digital marketing industry, but you may not be the same. Still, the research strategy can give you a brief overview on the next big thing. Creating most searchable content depends on the analysis of the industry trend and that can open the key to your content marketing strategy. For the time being, you can put on my shoes and share the same interest with me.
The graph above is pretty promising to search for what I should focus next. So the same you must follow in your industry as per the trend.
Once you find the topic, it is the easiest way to point out the most used queries in Google. Here, in this case, you can find that content marketing for e-commerce is getting popular.
You can use this free tool also to get the auto search feature. And the result, you can find out the possible searching terms.
How to satisfy the customers with your most searchable content?
Effective content is the best advice for the customers who are searching for the suggestions from online. Before major decision making, the customers are searching for the credibility of the brand. Research finds that 80% of customers with more than billing of $500, search for the online consultation.
There your content should rank in front of them when they are gathering information. You have the high chance to impress at the time of decision making.
Here you can have the choice of topic that you are comfortable. But before proceeding, don't forget to check the keyword in Google keyword tool. There are few more alternatives to Google keyword tool. They are – Ubersuggest.io, Bing keyword research tool, keyword tool.io, SERPS keyword research tool and much more.
The good news is that if you are not planning on paying any extra bucks, Google keyword research tool and SERPS will show the search volume data.
Question and answer sites like Quora or Yahoo Answers are excellent to know the queries of the people, and that will help you to find out the topic.
It will show you an excellent visual representation of the search query on a particular keyword. You can experiment to select the title.
Apart from the online research, offline data gathering is equally important to collect queries. On the manual level, you must search for the face to face interaction with the individual for the detailed content.
Asking the employees about the common queries they face every day on the brand. Include them in your content.
Your market research analysts are the mine of real information. Interview them and fetch the market data about the brand and represent the data with proper analysis.
Look at the comments and questions on your content on the blog and the social media pages. That will develop your introspection on the content strategy.
Engagement on the content comes from the presentation in a most attractive way. So after gathering information, never forget to add visual with the content which explains the information.
Try to add a descriptive bracket in the title of your website to clarify the type of content. If a visitor is searching for images or the infographic, he will have the maximum possibility to click.
After completing your content, the next challenge is to share your content and gain organic visitors. You must log on to social bookmarking sites to share your content and share them on social media.
In a time of social sharing sites like Facebook, Twitter or Linkedin, you can also share in the same interest groups. It impacts on the virality of your content.
Use # hashtag carefully. You search # in http://hashtagify.me and use the tag intelligently on social media to spread your content more effectively.
Create content for the users and optimize it for the search engine. Content marketing is evergreen digital marketing for your website. So start reading and increase your knowledge on preferred industry. Success is not so far.


text:
Historical Clinical and Risk (HCR): version 3 (CPD event)
Our two-day workshop examines the latest version of Historical Clinical and Risk (HCR), a comprehensive set of professional guidelines for violence risk assessment, formulation and management.
All CPD courses
Forensic Academy
Historical Clinical and Risk (HCR): version 3
About our trainers
Date and time: Date for 2019 to be confirmed.
Location: Forensic Academy, The University of Manchester
Fee: £599 (Manual, if required, is £75)
Book online: To be confirmed.
Contact us: Email forensic.academy@manchester.ac.uk or phone +44 (0)161 306 7802
Violence risk assessment is a critical part of service delivery in health care, social service, criminal justice, and occupational settings.
Version 3 of the Historical Clinical and Risk (HCR-20) is the latest version of a comprehensive set of professional guidelines for violence risk assessment, formulation and management based on the Structured Professional Judgement (SPJ) model.
Our workshop will enable attendees to understand the differences between the current and previous version of the tool and learn how to use it to assess, formulate and manage violence risk.
This workshop will be of interest to professional staff working in mental health and social services, the criminal justice system, prisons and forensic mental health services who have experience with risk assessment, in particular the HCR-20 version 2 and other SPJ measures.
It will be of particular interest to professionals who currently use the HCR-20 regularly and are hoping to make the transition to version 3.
Following the training, participants will be able to:
highlight the main changes from Version 2;
understand the items and administration of the HCR-20 V3;
provide a rationale for using the HCR-20 V3 in clinical practice;
discuss recent UK research on V3;
use the HCR-20 V3 manual to assess, formulate and manage violence risk.
Cheryl Knowles
Cheryl Knowles is a Forensic Psychologist within an NHS forensic mental health care hospital in Lancashire. She is also an Honorary Lecturer at The University of Manchester.
She has wide-ranging experience in the use of risk assessment within prison settings, probation and forensic psychiatric care.
Her research interests lie in the areas of multi-disciplinary approaches to risk assessment and intervention planning, positive behaviour support, staff resilience and service user lived experiences in forensic settings.
How to book your place
Details of how to book will be made available here when a date has been confirmed.
Email: forensic.academy@manchester.ac.uk


text:
Casper Promo Codes
pillowtalk@casper.com
The Early Bird Gets … Stupid?
By Alyse Borkan | Sep 25, 2014
Generally speaking, one in ten people is a morning lark. Early to bed, early to rise, these people are way too happy in the morning. Two in ten are night owls: those who enjoy staying up late and then have to rush to work in the morning because they overslept. The rest of us fall somewhere on the spectrum between them.
The early bird may get the worm, but the early bird is sort of dumb, according to some recent research. IQ and sleep patterns are linked. Intelligent people are much more likely to stay up later than their more dense counterparts. Morning larks are dumb, night owls are smart.
A survey of young Americans shows that those with IQs less than 75, on average, went to sleep at 11:41 p.m. Normal IQs, ranging from 90 to 110, went to sleep 30 minutes later, and the super intelligent (IQ over 125) waited another 20 minutes still.
IQ < 75 90 < IQ < 110 IQ > 125
Weekday 11:41 p.m. – 7:20 a.m. 12:10 a.m. – 7:32 a.m. 12:29 a.m. – 7:52 a.m.
Weekend 12:35 a.m. – 10:09 a.m. 1:13 a.m. – 10:14 a.m. 1:44 a.m. – 11:07 a.m.
Being a night owl isn't a normal thing for humans, regardless of how smart we are. Our circadian rhythms point us toward a more morning-lark-type state. Study author Satoshi Kanazawa says that humans have the "unique ability, consciously and cognitively, to override their internal biological clock and its rhythmic outputs."
So in other words, night owls are sooo smart that they're even outsmarting their own bodies. Stay up late tonight, you might learn something.
— Josh Segal
Entertainment | Nov 21
How To Go To Sleep Early When You're Used To Staying Up Late
Sleep | Aug 5
Is Your Pet Ruining Your Sleep?
News | Nov 21
Week In Sleep: It's All Happening
Sleep | Jan 22
Week in Sleep: 3, 2, 1, HIBERNATE
Sleep | Jun 21
9 Excuses To Go To Bed Early On The Longest Day Of The Year
News | Sep 18
Is There Really A Gene That Lets You Function With Less Sleep?
Casper Mattress Reviews
Casper Pillow Reviews
Casper Sheets Reviews


Initially, the play was set to be "Rashomon," a Japanese drama about the mysterious murder of a samurai. However, it seemed that students at AISB didn't have interest in such heavy themes; and consequently, the play was switched to something more comedic.
The title, "The Complete Works of Shakespeare in 90 Minutes," is practically self-explanatory; it's a fast-paced collection of highlights from all 37 of Shakespeare's plays. It will be performed by eight actors, which makes it particularly special. Because there are so few people, each will play multiple characters throughout the performance.
Have you had little experience with Shakespeare? Caster says there is absolutely no need to worry. The complex ideas have been simplified, and all necessary context in understanding the humor will be provided to us. If the unique language is a barrier, that's not a problem either; the play is written in modernized English. "Even the younger audience that don't understand all the words can come and enjoy the physical comedy of it," Caster explains.
11), Gal (Grade 10), and Ian (Grade 9).
Although not so many people showed up for the auditions, Caster gave them some improvisation ideas to test if they were qualified to perform for the play.
"They just literally ran with them. You can ask them… I was scream-laughing," says Caster, recalling their performance.
Thanks to Gal's little humorous story, we expect a lively performance by the cast members.
Rehearsals have been taking place twice a week. Currently, they are still working through the script, sorting out the props, actions, and exits. Although there won't be any open-rehearsals available for students to come and watch, a short trailer will be performed in an assembly prior to the performance dates.
Hope to see you there (in the theater). And in the meantime, if you want to get a head start on Shakespeare, here's a wondrous website f'r thee: Shakespearean to Modern English Translator.


text:
RETURN OF THE MAC
Newcastle legend Malcolm Macdonald in talks over ambassadorial role after being banned by Mike Ashley and Steve Bruce
Graham Nickless
Supermac IS BACK at his beloved Newcastle thanks to the new Saudi owners.
Malcolm Macdonald has been welcomed with open arms by Amanda Staveley and the United board.
Newcastle legend Malcolm Macdonald is set for a return to the club in an ambassadorial roleCredit: Hulton Archive - Getty
The St James' Park icon was banned four times by Mike Ashley and Steve BruceCredit: Getty
An excited Macdonald is revelling in the new positive atmosphere surrounding St James' Park after years of negativity.
And the former England and Arsenal star believes the arrival of new head coach Eddie Howe has lifted the club, anticipating an 'amazing journey' for the Geordies over the next decade.
Toon goalscoring legend Macdonald scored 95 goals in 187 appearances for the Magpies.
But he was barred FOUR times from the club by previous owner Mike Ashley and former manager Steve Bruce.
Now he's back in favour with the new regime and is negotiating an ambassadorial role on match days.
Local newspaper columnist Macdonald, 71, said: "Bruce fell out with all the United supporters early on and he certainly fell out with me, that's for sure.
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"Me and a few experienced journalists often got barred from the press box.
"But within 24 hours of the new people taking over and announcing the deal, they were in touch with all newspapers saying everybody's welcome back.
"Amanda has been absolutely spot-on since she arrived and I've met all the board and all the people who have been involved in the take-over.
"I have every confidence that they will do exceptionally well for the club but they are not going to rush it.
"They will take their time and make sure they get it all absolutely right.
"I've actually been in the chairman's suite and met everybody in the take-over just weeks after being barred.
"They just absolutely fill me with the utmost confidence that they are going to do a cracking job at Newcastle."
It's going to be an amazing journey
Malcolm Macdonald
Macdonald has also been lifted by the arrival of the new head coach.
He added: "I am hugely excited by Howe's appointment who will, of course, be very well supported by the board.
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"There is only one Premier League club in the North East and all eyes will be on Newcastle.
"But for once here is a manager who is very serious about what he does, knows what to do and how to do it.
"He gets the very best out of people and works hard at it but at the same time he is going to be hugely supported in each and any way that it is possible.
"And the journey of the next decade is going to be quite incredible for all those who support and are employed by Newcastle United.
"It's going to be an amazing journey."
Newcastle boss Eddie Howe shows Magpies fans a sign of things to come as he arrives for first training session at 6:55AM
Amanda Staveley
Mike Ashley
Steve Bruce


EH became known to us when he attended a Workshop 5 project at Feltham back in 2013. He worked well during the project and showed strong leadership skills, although he was struggling elsewhere in the prison due to peer pressure; he had recently had bleach thrown in his eyes by another prisoner, who had been from his area outside, because EH had not participated in a fight between boys from his area and some other group. So from the day we met him we noticed that he was somebody who was really trying to change his life around.
His work on the project was good and we continued to support him with mentoring sessions where possible until his release. He was still enrolled in college whilst in prison and was having work sent in; his focus on achieving his qualifications to go to University and study music was impressive, especially given the circumstances he endured. When he came out of prison he called us and asked for mentoring support; we had one meeting with him, in which he talked about going on to University the following year and in the meantime getting a job and keeping his head down, but then he went off the radar.
Some months later he contacted us again and explained that he had been arrested and spent some time in prison on remand (because of his previous record) but that the incident had involved people he used to know and he was dragged in by way of association.
Now out again, he made more serious attempts at getting on the OS program and showed greater commitment to the programme and working with OS mentor Todd Speakman.
Over the last 8 months EH has attended Todd's studio in North West London regularly, learning about the studio business from the ground up and getting a chance to work on his composition and mixing. Recently, with Todd's help, he has pulled together an impressive array of musicians and singers to help him record his debut EP, which features all his own material. During this time Todd has supported EH through his work life and search for jobs and has been instrumental in getting applications off to Universities and securing two offers. Eventually EH decided to go to Southampton to study, partly because the course seemed like the right one, but also because it was far from home where he still feared people from his past.
EH has shown intelligence, commitment, patience and resolve over the last 2 years to arrive at this place. His criminal activities would earn him over £1000 per week prior to his jail sentence, and he readily admits he found it hard to learn to live on less money. But he managed it. He constantly said he was still too close to certain influences around his area that threatened to pull him back into criminality, but he worked hard at avoiding them. With the help of OS he has not only been able to envisage what a more positive future might look, but he has experienced it in the work he has done in Todd's studio, where he has interacted with professional musicians, music business people and young people who he has guided and mentored musically in the process of putting together his EP. He even ate humble pie and happily took a lesson from a 17 year old singer/guitar player on how to effectively set up instagram/twitter/FB so it would work as the perfect online tool for promoting his musical activity.


The General Data Protection Regulation (GDPR), which will be enforceable on May 25th, 2018, is a regulation from the European Parliament, the Council of the European Union and the European Commission that attempts to strengthen and unify data protection for all individuals within the European Union (EU). It also addresses the export of personal data outside the EU. When the GDPR takes effect, it will replace the data protection directive of 1995.
This post will address how ReSci is compliant with the GDPR. Please note that this post is for informational purposes only, and should not be used for legal advice. We at ReSci encourage you to work with legal counsel to determine precisely how the GDPR might impact your business. The GDPR website also has good FAQs, which covers who it affects, changes, penalties, and more.
Expansion of definitions of personal and sensitive data: any information relating to an identified or identifiable individual; meaning, information that could be used, on its own or in conjunction with other data, to identify an individual.
Silence, pre-ticked boxes or inactivity does not constitute consent; data subjects must explicitly opt-in to the storage, use and management of their personal data.
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The below will cover both explicit ways that ReSci complies, as well as best practices for how you pass over data and use our platform.
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subscribers and contacts to re-request consent in accordance with the GDPR requirements, or rely on a different lawful basis for your processing under the GDPR.
You should review any ReSci integrations or add-ons that you are using (or plan to use), and any terms associated with those, to ensure that you have adequately disclosed potential data processing activities associated with your use of those services to your subscribers and contacts.
You may want to consider updating your privacy statement to include language that specifically identifies ReSci as one of your processors and delineates the applicable processing activities performed by ReSci, such as the collection (e.g., via sign-up forms) and storage and processing of personal data, and the transfer of personal data for your own purposes (e.g., reporting).
Derek Kwan is COO and VP of Product for Retention Science. With 15+ years experience in marketing and ad tech, Derek previously led product innovation at Yahoo!. He also trains his game theory skills in his spare time as a poker player. Follow Derek on Linkedin!


Rotate at high speed or low speed with multi-speed setting for testing.
Test rotation speed, temperature, rotation period time, and present on man-machine interface touch screen. Test finished stop automatically.
Equip with pressurizing system to test pressure durable life of oil seals.


From the Find and List Roles screen, chose Add New.
Assign the permissions and save the role.
Create any other roles that will be added to the group. Remember you can assign roles from multiple applications to a group, so you may create roles in several applications for a user group. When you have all the roles defined, create the user group.
Create a name for the group, and click Save.
In the Find and List Users screen, select the users you want to add to the group, and click Add Selected when you are done.
On the Find and List Roles page, Select the roles you want to add, then click Add Selected when you are done.
A user can also be assigned to groups within the End User Configuration Page.
In conclusion, like many other parts of CUCM administration, Cisco uses a multi-layer configuration to assign permissions to users. While there may seem to be more configuration up front, it offers a great deal of scalability, and once configured correctly simplifies administration by allowing for very specific groups of user rights to be assigned.
The one area that I think could be improved would be some ability to assign right restricted to a subset of devices/users/etc. like you can assign OU permissions in Active Directory.


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Posted on September 27, 2016 by Portsmouth Daily Times
Bentley signs Legislative Transparency pledge
Calls on Nicholls to follow suit
By Portia Williams - portiawilliams@civitasmedia.com
GREENUP COUNTY, Ky. — Danny Bentley-R, candidate Representative of the 98th District, recently signed a Legislative Pension Transparency Pledge, and is calling on his opponent, Lewis Nicholls to do the same.
Danny Bentley announced Monday he has signed the Bluegrass Institute for Public Policy Solution's 'Legislative Pension Transparency' pledge and has called on Lew Nicholls to follow suit, as stated in a press release.
"The state employee and teacher pension systems are underfunded and lost money in the market last year. Many beneficiaries are worried there may be nothing left for them when they retire," said Bentley "Meanwhile, the legislative pension system is fully funded and doing well in the market."
The state's liability for our educators' retirements are as follows: Greenup County Schools at $74,703,628, Raceland School District at $28,904,004, & Russell Ind. Schools at $60,898,003. (47 percent shortfall ), according to reports.
"Despite fully funding their retirement and ignoring their obligations to public employees, House Democrats have refused attempts to let Kentuckians know what they stand to collect when they retire," said Bentley "The Democratic Chairman of the committee that handles the pension systems even told a reporter in reference to legislative pension transparency 'frankly, I don't think that's the public's business.'
"We have short changed the hardworking Kentuckians who serve the Commonwealth. The least we can do is be open and honest about the benefits elected officials have voted for themselves. I'm proud to sign this pledge and hope my opponent will as well so the voters have some confidence that their whoever wins will go to Frankfort to represent the people, not enrich themselves."
Nicholls told The Daily Times that he is not cognizant of the Legislative Pension Transparency pledge that Bentley is calling upon him to sign.
"This is the first that I have heard of it. I would have to see what it is that he (Bentley) is calling upon me to do," Nicholls said. "I can tell you this, I do support trying to fix our pensions for teachers, and also for retired teachers. If he wants me to sign something before even looking at it, I can't do that I'm going to have to see what it is he is talking about."
Nicholls also said that he would willing to submit a comment in regard to the pledge after reviewing the information.
By Portia Williams
portiawilliams@civitasmedia.com
Reach Portia Williams at 740-464-3862, or on Twitter @PortiaWillPDT.
Hi! A visitor to our site felt the following article might be of interest to you: Bentley signs Legislative Transparency pledge. Here is a link to that story: https://www.portsmouth-dailytimes.com/news/10933/bentley-signs-legislative-transparency-pledge