Technological issues of

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Quantum Technologies 2004 Vancouver, Canada
Technological issues of superconducting charge
qubits
Yuri Pashkin
RIKEN
Oleg Astafiev Tsuyoshi Yamamoto Yasunobu
Nakamura Jaw-Shen Tsai Dmitri Averin
- RIKEN
- SUNY at Stony Brook
30 March 2004
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Outline

• introduction
• electrostatic coupling
• single-shot readout
• T1 and T2 measurement
• technological issues

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Cooper-pair box
M. Büttiker, 1987 V. Bouchiat et al, 1995

• a single artificial two-level system
• 108 conduction electrons in the box

E (CgVg 2ne)2/2C
box
reservoir
Cooper-pair tunneling
- - - -
n0
1

gate
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Charge qubit based on Cooper-pair box
Y. Nakamura et al, 1999
eigenstates
energy
EJ
gate voltage
initialization coherent superposition read-out
final state
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Final state read-out
Josephson-quasiparticle cycle (Fulton et
al., 1989)
2e
Cooper-pair box

• detect the state
• initialize the system to

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Capacitively coupled charge qubits
standard e-beam lithography angle evaporation
I1 and I2 give info on charge states
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Hamiltonian
charge basis
EJ1,2 Em lt Ec1,2
initial state
I00gt
Ec1, Ec2, Em EJ1, EJ2
En1n2  Ec1(ng1n1)² Ec2(ng2n2)²
Em(ng1n1)(ng2n2) Ec1,2  4e²CS2,1/2(CS1,2CS2,1 
 Cm²) ? 4e²CS2,1/2CS1,2CS2,1 ng1,2  (Cg1,2Vg1,2
CpVp)/2e Em  4e²Cm/(CS1CS2  Cm2)
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Oscillations at the double degeneracy
E00 E11
E10 E01
0,0
I2
I1
1,0
dc gate1
0,1
dc gate2
1,1
pulse gate
ng1 ( ng2)
ng2
time
1,1
1
0,1
0.5
X
superposition of four charge states!
0
1,0
0,0
ng1
1
0.5
0
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Quantum beatings
? - ?
? - ?
? ?
? ?
2?
2?
operation point
ng1 ( ng2)
0.5
0.45
2?f
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Quantum beatings experiment
EJ1
ng2
1,1
1
0,1
X
EJ2
0.5
L
R
0
1,0
0,0
ng1
1
0.5
0
? - ?
? ?
theoretically expected EJ1 13.4 GHz EJ2 9.1
GHz Em 15.7 GHz
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Single-shot readout
EJ
EJ
trapSET readout
conventional readout
?qp 0
?qp 1/10 ns
?
?
?
?
trap kept unbiased during coherent evolution ? no
qp relaxation!
2(? Ec)
reservoir
reservoir
probe permanently biased !
box
box
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Trap SET readout
box trap galvanically isolated from the leads !
no qp relaxation ! no effect of the leads !
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Time trace
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Single-shot readout coherent oscillations
dead zones
degeneracy
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Relaxation of coherent oscillations
no increase in T2
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T1 measurement
E

• create 1 state by NA ?-pulse
• move slowly along the upper band
• stay for time ?
• move slowly back
• repeat for different ?

ng
?-pulse
?
with probability exp(-?/T1)
time
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T1 measurement experiment
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Superconducting charge qubits
control
substrate
T1
T2
group
readout
dc probe
NEC
pulse
SiNx
5 ns
5 ns
pulse probe
trapSET
switching current
1.8 ?s
0.5 ?s
SiO2
?-waves
Saclay
1 ?s
SiNx
100 ns
pulse
SiO2
Chalmers
5 ns
5 ns
RF-SET
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What next?
1. Qubit readout dc probe ? pulsed probe
trap SET 2. Qubit control NA pulses
? ?-waves 3. Materials qubit Al ?
Nb? substrate SiNx ? SiO2 4. Dependence of T1
and T2 on (1-3)
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Nb SET
Nb lead
Nb island
AlOx Barrier