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