Qubits Using Single Electrons Over a Dielectric. John Goodkind Physics Department University of California, San Diego Collaborators: Manyam Pilla, Xinchang Zhang, Alex Syshchenko, Brian Naberhuis Mrk Dykman, MSU, Arnold Dahm CWRU Work supported by ARO and NSF.
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John Goodkind
Physics Department
University of California, San Diego
Collaborators:
Manyam Pilla, Xinchang Zhang, Alex Syshchenko, Brian Naberhuis
Mrk Dykman, MSU, Arnold Dahm CWRU
Work supported by ARO and NSF
d
Some properties of the system must be confined laterally over a microelectrode.
Thus the Schrodinger equation for the system of interest is that of a 1D hydrogen atom with a modified charge.
For liquid helium =1.05723, =6.955103
For solid Neon = 1.24, = 0.0268
 that of a 1D hydrogen atom with a modified charge.
L
2
2
e
2
h
=
=

y
=

U
zExp
[
z
/
l
]
0
0
2
3
/
2
2
l
2
ml
l
æ
ö
1
1
1
z
y
=


2
ç
÷
z
z
Exp
[
]
1
3
/
2
2
l
2
l
è
ø
l
2
We will use the first two of these eigenstates as qubits.
,
U
U
,
=
/4
1
0
For liquid helium
l = 7.64 nm, U1 – U0 ~ 118 GHz
Confirmed by experimental measurements.
For solid Neon l =1.98 nm, U2 – U1 = 2.1 THz. At this frequency optical techniques can be used
In order to change the state of the qubit we will apply a microwave pulse at frequency, W. This adds a time dependent potential to the Hamiltonian.
If U1  U0, this will cause transitions between states at the “Rabi” frequency.
R 1 GHz per V/cm
The time dependent problem can be solved by expanding the time dependent wave function in terms of the eigenstates of the time independent Hamiltonian and then using the interaction representation.
We write the expansion as microwave pulse at frequency,
The the coupled differential equations for the cn(t) are:
The confining force in the plane can be designed so that in plane resonance frequency is comparable to E2 – E1.
The fields shown are for 1 Volt applied to the electrodes. In practice we can achieve > 20 GHz in plane resonance frequency so that transitions will be induced only between the same in plane states.
Ez must be reduced to 400 V/cm over the electrodes. Can be done by superimposing a uniform field.
On resonance
C2(0)=0
C1(0)=1
Red = real, green= imaginary
Off resonance (10 plane resonance frequency is comparable to E3)
Potentials applied to the electrodes shift the energy level spacing as described above (about 1.4 GHz for 100 Volt/cm). Thus, if we use fixed microwave frequency individual electrons will be tuned into resonance by adjusting the DC potentials. This provides the ability to address individual qubits.
Logic operations require interactions between qubits and for this case it is due to the Coulomb field of the electrons.
d = 500 nm and <(z1 – z2)> between the first excited state and the ground state for helium is 34.4 nm. Expand and keep only first order terms.
The last term leads to a SWAP operation when two qubits are in resonance.
This interaction also leads to an electric field from one electron on the other when the two are in different states (different elevations above the surface). This shifts the resonance frequencies so that if for qubit #1 when qubit #2 is in the ground state then #1 will not respond to the microwave radiation when #2 is in the excited state. This provides the CNOT operation.
In state fields on both qubits the same, the states 10> and 01> are degenerate.
The qubits will oscillate between these two states at frequency
If the fields are held in this condition for a time, T, then the system will end up in state
cos[WRT]10>+isin[WRT]01>
For WRT = p/2 this becomes the swap gate.
Numerical solution for the time dependence of the real and imaginary parts of the two wavefunctions yields:
Resonance oscillations
SWAP operation by detuning after ½ cycle. (Wiggles after
field shift occur because the basis functions are not Eignefunctions of the Hamiltonian.)
P.M.Platzman, M.I. Dykman, Science 284, 1967 (1999)
M.I. Dykman, P.M.Platzman, P. Seddighrad Submitted for publication August, 02 (calculations including horizontal confinement)
The ripplons are overdamped in imaginary parts of the two wavefunctions yields:3He and do not exist in solid Neon. No ripplon induced sidebands. No superfluid film covering everything.
Decay due to coupling to phonons varies as vs3 so that it will become negligible in solid Neon.
15 mm square chip. Ground plane will cover only the lead wires of the left and right triangles.
Thickness gauge capacitors
Location of microelectrodes and leads to be written by ebeam lithography
0.80 imaginary parts of the two wavefunctions yields:
0.75
Porous Si
n+Si
4
0.70
x10
Au
Au
PS
0 V
/I
0.65
E
I
Vbias

e
VPS

e
0.60
collector
HP33120A Signal
Generator
2
3
4
5
6
7
8
9
10
1/f (msec)
Electrometer
IPS
~
VPS
VE
Schematic of experimental setup to measure properties of the PS diode. Individual pulses from the HP33120A of the form shown are applied. The frequency setting of the generator determines the slope of the sawtooth.
The frequency dependence of the efficiency of production of emission current, IE .
IPS (mA)
VPS (V)
Superconducting microbolometers imaginary parts of the two wavefunctions yields:
Tests with short wire, 1 m by 40 by150 nm thick Aluminum (shown without ground plane)
· Three TC’s corresponding to transitions of the three different lead widths
· Operated only close to TC = 1.2K
· Resistance pulse height is fixed, width (duration) depends on energy
· Total number of electrons in area of detector less than one per pulse so that only a fraction of pulses cause change in resistance
· Field configuration was incorrect for 100% efficiency (alignment too critical). New meander pattern described below.
DetectorsThe meander pattern is calculated to give 100% detection
efficiency with a misalignment as large as 1 mm. R=5 k.
Holes through the chip between meander patterns to allow electrons to pass from the source to the microelectrodes.
Edges of the meander pattern and the ground plane.
1.5 cm square chip with 1 mm square opening in the ground plane at the center.
Raw and filtered data from a resistance change caused by electron impact. The decay is the electronic time constant of the AC coupled signal.
Resistance transitions due to electron impacts from pulses of ~55 electrons/ mm2 at 1 second intervals.
Lower TC by ion implantation in Ti or W.
tunnel diode electron source imaginary parts of the two wavefunctions yields:
transition edge detectors
lower plate
Schematic of the systemmicrostructure
liquid He film