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electrons are bound to the surface of superfluid helium by a weak image potential in addition to potentials from underlying electrostatic gates which control the position of these electrons on helium [ 1 - 4 ] .
electrons typically float in vacuum about 10 nm above the surface , forming a clean two dimensional electron system ( 2des ) .
it is a well studied system which has shown the highest mobility of any 2des [ 5 ] , and exhibited the first 2d wigner crystal [ 6 ] .
electron spins have been studied as possible quantum bits ( qubits ) , since they are natural two level quantum systems , but their coherence is rapidly degraded during transport in semiconductors . unlike other electron spins in heterostructure 2des systems , spins on the surface of helium reside in vacuum and are expected to suffer much less decoherence , especially from spin - orbit interactions [ 7 ] .
hence , the possibility of mobile qubits in a condensed matter system arises . using existing fabrication technology
we have shown that manipulating a large number of spins with a small number of gates is possible [ 8 ] .
devices with electrons confined in channels have been studied previously [ 9 - 13 ] .
similar to those , a standard complementary metal - oxide - silicon ( cmos ) process at sandia national laboratory was used to fabricate 2@xmath1 m deep , 3@xmath1 m wide channels [ 14 ] .
the upper metal interconnect layers are used to fabricate the channels and gates .
the topmost metal layer defines the channel width , and acts as a mask for etching the surrounding dielectric layers ( sio@xmath2 ) down to the underlying gate electrodes , running under 120 parallel channels ( see fig.1 ) .
electrons are photoemitted onto the sample from a zinc film placed a few millimeters above the device . by keeping the underlying gates positively biased with respect to the zinc film ,
electrons are attracted to the channels [ 15 ] .
the large gate labeled  right reservoir " is where the electrons are initially collected .
electrons collected over the reservoir are blocked from moving above the small gates by keeping the  door " gate dc - voltage negative ( repulsive ) with respect to the reservoir .
lowering the door gate potential allows a packet of electrons to moves from the reservoir to the electron detection gates ,  twiddle " and  sense " .
these electrons are detected through their capacitive coupling to the sense gate , which is connected to the gate of a nearby high electron mobility transistor ( hemt ) .
an ac - voltage is applied to the twiddle gate to push the electrons over the sense gate and pull them away .
the sense gate sees a periodic charge induced voltage , which is buffered by the hemt and detected using a lockin amplifier .
the small gates in the horizontal channels have a 3@xmath1 m period including a 0.5@xmath1 m gap .
these underlying gates to the left of detection gates are connected as a 3-phase ccd , with every third gate connected by on - chip vias to its clock rail in a lower metal layer .
each set of three gates ; @xmath3 , @xmath4 , and @xmath5 ; makes up one pixel for electron control .
a 2.5 @xmath1 m vertical channel connecting 120 horizontal channels has two extra gate electrodes , vccd@xmath2 and vccd@xmath6 .
these two gates and @xmath72 from the horizontal channel comprise a 3-phase ccd to bring electrons from one channel to the others . the device is wired and mounted in a cell that is cooled to 1.6k .
the cell is filled with superfluid helium up to about 1 cm below the device .
helium fills the channels by capillary action with the depth in the channel being determined by the device structure .
seven of the 120 parallel horizontal channels are seen , with a schematic cross - section to the right of the image .
the darker regions of the image are the channels with underlying gates , and the lighter areas are the metal layer between the channels .
electrons are confined above the helium in the channels by a positive dc bias ( 3v ) on the gates with respect to the top metal plane .
the 3-phase ccd connection is drawn schematically below the micrographs .
a cartoon above the channel image is a cut - away along the middle of a channel giving a scale view of the loading and detection gates .
the horizontal channels are interposed by two memory cells for electron storage and an interconnecting vertical ccd channel .
all gates used in these experiments run under and control electrons in all 120 channels in parallel . ]
unprecedented electron transfer efficiency has been demonstrated by clocking a packet of electrons back and forth along the horizontal channels for more than one billion pixels [ 8 ] .
when loading electrons from the reservoir onto the small gates , we initially clear out the ccd pixels and make sure that electrons in the right reservoir are blocked with the door gate closed ( negative ) .
electrons are loaded from the reservoir onto the twiddle and sense gates by opening and then closing the door . to achieve a desired pixel occupancy , the potential of the door gate
is lowered temporarily to bleed off excess electrons back to the reservoir .
after the initial charge measurement , a packet of electrons is moved into one pixel of the ccds and clocked along the channels using an appropriate voltage sequence , similar to the 3-phase ccd sequence first described by boyle and smith[16 ] .
the reliability of 2d transport in the channel array has also been tested using a vertical ccd channel .
a packet of electrons in lower half of the channels ( 60 channels ) are moved in a
 c " pattern : one pixel left , 60 pixels up , one pixel right , and then the sequence is reversed to return the electron packets to their starting point .
no measurable failure has been seen after a billion pixel cycles .
the sense gate runs under all 120 horizontal channels and thus measures the sum of the electrons in all of them .
the signal calibration in units of electrons per channel assumes perfect uniformity over 120 parallel channels .
when we see a signal corresponding to 120 electrons , we can not know whether there is one electron per channel or several electrons in some of the channels and none in the others .
the vertical channel can be utilized in a measurement of the distribution of electrons amongst the horizontal channels .
there are no reservoirs at the top or bottom of the array ( note that up and down are defined here by the orientation of fig .
1 ) . by progressively shifting the electrons up or down ,
electrons are ejected . when the remaining electrons are moved across to the sense gate , the signal is reduced .
as long as the devices are not overcharged during the initial photoemission , bringing the underlying gates to the potential of the metal top plane serves to kick electrons out of the channels , probably out onto the thin van der waals helium film covering the top metal plane .
it is likely that these ejected electrons are immobilized by the roughness of the metal in this area , though for the analysis of these data it is sufficient to know , experimentally , that the ejected electrons do not return to the channels .
figure 2(a ) plots the results of two vertical clocking experiments where electrons are clocked up or down 120 pixels .
one pixel cycle using @xmath72 , vccd@xmath2 , and vccd@xmath6 brings a packet of electrons up or down one channel . in the experiment , an electron packet in each channel
is loaded from the reservoir , measured over the detection gates , and then clocked in the horizontal channels to the vertical ccd , over @xmath72 .
this packet of electrons is clocked 12 pixels up or down and then brought back horizontally to the detection gates for a new measurement .
this cycle continues until electrons from all 120 horizontal channels have been ejected at the top or bottom of the device .
the data shows that all the groups of 12 channels , except the topmost 12 , have approximately equal populations .
the experiments were done after a specific loading ( by photoemission ) of the right reservoir . by repeating such an experiment for many reservoir loading levels , we find that the population of all 120 channels are equalized when the right reservoir has been well - filled by photoemission .
( a ) measurement of the electron population of the horizontal channels for a typical initial loading of electrons . the circle ( blue ) and triangle ( red ) data points represent electron signals as the vertical channel is clocked upwards and downwards , respectively .
the electron signal is normalized to the initial loading ; about 1600 electrons , or approximately 13.5 electrons per channel .
the dashed black lines show a linear depopulation which would correspond to perfctly uniform channel occupation .
( b ) total number of electrons in all the channels after the c - pattern experiment .
the electron signal is measured after each time the electrons were clocked up 10 pixels . a constant signal through the first 60 pixel cycles and
then a linear decay confirm a uniform occupancy of the lower 60 channels . ]    after the c - pattern transport efficiency experiment described above , electrons occupying the lower 60 channels were brought to the vertical channel to measure the charge uniformity .
electrons are clocked 10 pixels up and then brought across to the detection gates .
the electron signal does not decrease for the first 60 pixel cycle which says that the top 60 channels are unoccupied , as expected ( these channels were emptied by the c - pattern ) .
the electron signal decreases linearly after 60 pixel cycles , which confirms the uniformity of bottom 60 channels ( see fig .
manipulating a large number of qubits is necessary for applications in quantum computing .
the charge - coupled device with electrons on the surface of helium has shown undetectably rare electron transfer failure , allowing electrons to be positioned at any of more than four thousand distinct sites by controlling only five electrostatic gates .
this interpretation rests on the assumption that all the channels are approximately equally populated .
non uniformity could affect the interpretation of the clocking result , and it raises the question as to whether we can expect uniform occupancy for qc applications .
we have shown that channel uniformity is achievable with the electron loading methods we have established , and have verified it using the vertical channel .
we would like to thank s. shankar and g. sabouret for helpful discussions and j. donnal for the electronics to apply clock voltages to the ccd .
work at princeton was supported by the nsf under grant nos .
ccf-0726490 and dmr-1005476 .
additionally , this work was performed , in part , at the center for integrated nanotechnologies , a u.s .
department of energy , office of basic energy sciences user facility .
sandia is a multiprogram laboratory operated by sandia corporation , a lockheed martin co. , for the united states department of energy under contract no .
de - ac04 - 94al85000 .
conference travel was supported by the nsf under grant no .
dmr-0844115 and icam - i2cam , 1 shields avenue , davis , ca 95616 .
electrons floating on the surface of superfluid helium have been suggested as promising mobile spin qubits . 
 three micron wide channels fabricated with standard silicon processing are filled with superfluid helium by capillary action . 
 photoemitted electrons are held by voltages applied to underlying gates . 
 the gates are connected as a 3-phase charge - coupled device ( ccd ) . starting with approximately one electron per channel , 
 no detectable transfer errors occur while clocking @xmath0 pixels . 
 one channel with its associated gates is perpendicular to the other 120 , providing a ccd which can transfer electrons between the others . 
 this perpendicular channel has not only shown efficient electron transport but also serves as a way to measure the uniformity of the electron occupancy in the 120 parallel channels .