technological issues of superconducting charge qubits oleg astafiev tsuyoshi yamamoto yasunobu...
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Technological issues ofsuperconducting charge qubits
Oleg Astafiev
Tsuyoshi YamamotoYasunobu Nakamura
Jaw-Shen Tsai
Dmitri Averin
NEC Tsukuba
- SUNY at Stony Brook
Yuri Pashkin
RIKEN
30 March 2004
Quantum Technologies 2004 Vancouver, Canada
- RIKEN
Outline
- introduction
- electrostatic coupling
- single-shot readout
- T1 and T2 measurement
- technological issues
gate
reservoir
box
++++
- - - -
• a single artificial two-level system
• ~108 conduction electrons in the box
n
kTEE
E
JC
C
4
n=0 1
Cooper-pair tunneling
E = (CgVg – 2ne)2/2C
Cooper-pair box
1
0
21
21
EE
EEH
J
J
0 1
0
1
21
20
2/1
2/0
eQEE
eQEE
gc
gc
M. Büttiker, 1987V. Bouchiat et al, 1995
Charge qubit based on Cooper-pair box
1
0
eigenstates:
charge states: 10 ,
EG ,
102
1
102
1
initializationcoherent superpositionread-out
2200 )()( JEQEQE
1/)( 00 eQEQE c
gate voltage
energy
tt
EJ
tE
p Jcos121
)1(
initial state0
coherent oscillations 1
2sin0
2cos
tEtE JJ
final state
Y. Nakamura et al, 1999
Josephson-quasiparticle cycle (Fulton et al., 1989)
2e
Cooper-pair box
JE
qp1 JE• detect the state • initialize the system to
1
0
CC EeVE 322
ee
qp1
qp2
+ probe
Final state read-out
Capacitively coupled charge qubits
pulse gate(common)
dc gate 2dc gate 1
probe 1probe 2
reservoir 2
qubit 2
reservoir 1
qubit 1
1 m
standarde-beam lithography+ angle evaporation
Cross SectionCross Section
capacitive couplingbox 2 box 1
I2 I1
Vb2 Vb1
Vp Vg1Vg2
I1 and I2 give infoon charge states
Hamiltoniancharge basis
En1n2 = Ec1(ng1–n1)² + Ec2(ng2–n2)² + Em(ng1–n1)(ng2–n2)
Ec1,2 = 4e²CΣ2,1/2(CΣ1,2CΣ2,1 – Cm²) 4e²CΣ2,1/2CΣ1,2CΣ2,1
ng1,2 = (Cg1,2Vg1,2 + CpVp)/2e
Em = 4e²Cm/(CΣ1CΣ2 – Cm2)
1112
1012
2101
2100
2
1
2
10
2
10
2
12
10
2
1
02
1
2
1
EEE
EEE
EEE
EEE
H
JJ
JJ
JJ
JJ
I00> I10> I01> I11>
I00>
I10>
I01>
I11>
Ec1, Ec2, Em
EJ1, EJ2
initial state
EJ1,2 ~ Em < Ec1,2
I00>
Oscillations at the double degeneracy
pulse gate
d c gate1d c gate2
10.50
10.
50
n g2
ng1
0,0
0,1
1,0
1,1
ng1 (= ng2)
time
superposition of four charge states!
I1I2
X
0,1
1,0
0,0
1,1
11011000)( 4321 cccct
E00 = E11
E10 = E01
Quantum beatings
))cos()1())cos()1(241
)1( 24
2322
tt
ccpI
operation point
ng1 (= ng2)0.50.45
p1
p2
time, ps0 1000
+
-
2f
+ 2
-
2
00exp)(
Hti
t
11011000)( 4321 cccct
Quantum beatings: experiment
theoretically expectedEJ1 = 13.4 GHzEJ2 = 9.1 GHzEm = 15.7 GHz
10.50
10.
50
n g2
ng1
0,0
0,1
1,0
1,1
L R
X
- +
0.6 ns
2.5 ns
EJ1
EJ2
0
1
2
3
4
01234
0
1
2
3
4
0.0 0.2 0.4 0.6 0.8 1.00
1
2
3
4
0 10 20 30
I 1 (
pA)
I 2 (
pA)
I 1 (
pA)
I 2 (
pA)
t (ns)
13.4 GHz
9.1 GHz
f (GHz)
Single-shot readout
2( + Ec)
EJconventionalreadout
reservoirprobepermanentlybiased !
qp ~ 1/10 ns
box
EJtrap+SETreadout
reservoirtrapkept unbiasedduring coherentevolution no qp relaxation!
qp = 0
box
Trap + SET readout
C
C
C
C C
s t
b t
s
b t
S E T
Tra p
R e s e rv o ir
R e a d o u t g a te
S E T g a te
C o n t ro l g a te
B o x
Tra
p g
ate
Bo
x ga
te
G b0
R e ad ou t
C o n tro lG b1
t0Gt1G
t
t
c
dt r
box + trap galvanically isolated from the leads !
no qp relaxation !no effect of the leads ! -20 -10 0 10 20
0
10
20
30
40
50
(2, 1)
(1, 1)
(2, 0)
(0, 1)
(1, 0)Vg
t (m
V)
Vgs
(mV)
(0, 0)
Nt2 = 2 N
t1 = 1
Nt0 = 0
Time trace
SET signal
control+readout
derivative of SET signal
Single-shot readout:coherent oscillations
200 400 600 800 10001.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
t (ps)
Vp1
(V
)
dead zones
degeneracy
no increase in T2
0 2000 4000 6000 80000.2
0.4
0.6
0.8P
tc (ps)
Relaxation ofcoherent oscillations
T1 measurement
• create 1 state by NA -pulse
• move slowly along the upper band
• stay for time • move slowly back
• repeat for different
0 1
-pulse
1 with probability exp(-/T1)
ng
E
time
0
1
T1 measurement: experiment
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.61E-4
1E-3
0.01
0.1
T2
T (
ns)
nG (e)
T1
NEC
Saclay
Chalmers
control substrate
pulse
-waves
pulse
SiNx
SiNx
SiO2
T1 T2
SiO2
group
5 ns 5 ns
5 ns 5 ns
1 s1.8 s
100 ns0.5 s
readout
RF-SET
dc probepulse probetrap+SETswitchingcurrent
Superconducting charge qubits
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)
Nb SET
AlOx Barrier
Nb islandNb lead