Status of Experiments on

Charge- and Flux- Entanglements

October 18, 2002, Workshop on Quantum Information Science

中央研究院 物理研究所陳啟東

Quantum-state engineering:1. Atomic physics2. Molecular physics3. NMR4. Solid-state devices

Objectives: Quantum computation and quantum communication

Two kinds of Josephson junction systems for quantum bits:1. Charge qubit: controlled by gate voltages2. Flux qubit: controlled by magnetic fields

Advantages of Solid-state devices:Easily embedded in electronic circuitsScaled up to large registers

Solid-state devices:1. Josephson junction systems2. Quantum dots with discrete levels3. Nanostructured materials with spin degrees of freedom

Quantum computer : formed by a system whose state is restricted to being an arbitrary superposition of two “basis” states.

Sources of dephasing:1. External leads (for qubit manipulations)2. Noise (e.g. 1/f) from the control signal (e.g. gate voltages)

Directions to minimize dephasing:1. Low temperatures.2. Choosing suitable coupling parameters.3. Switch on measurements only needed

(to minimize dissipative processes)

Issues: 1. Limited phase coherence time T

and energy relaxation time Tl (usually Tl > T) 2. Read out of the final state of the system

cos4 2JgC EnnEΗ

n: number operator of excess Cooper-pair charges on the island

: the phase of superconducting order parameter of the island

in

eVCn ggg 2 : gate charge = the control parameter

nJgCJC nnnnEnnnnEHnEE 11

2

14 basis, in , For 2

EC=charging energy; EJ=Josephson coupling energy

Charge Qubit in a Superconducting Single Electron Transistor2e

-Vb/2Vg

source drain

gate

2eVC

C1 C2

Cg

+Vb/2

S

A

0

0

1

1

EJEne

rgy

Varying CgVg

0 1

Oscillation between A and S

with angular frequency

JSA EEE

102

1S 10

2

1A

Spectroscopy of Energy-Level Splitting between Two Macroscopic Quantum States of Charge Coherently Superposed by Josephson Coupling

Y. Nakamura, C. D. Chen, and J. S. TsaiPRL, v. 79, p. 2328 (1997)

SQUID E/E

C

Qo/e

1qp

Qo/eQo/e

Fre

quen

c y

(GH

z)

Cur

rent

(pA

)

Qo/e

B-f

ield

on

a SQ

UID

Superconducting single Cooper-pair box

Y. Nakamura, Yu. A. Pashkin & J. S. Tsai

20

Non-adiabatic trigger

t

Without pulses

With pulses

tcoherence=

h/E

J

JQP current

Nature, v. 398, p. 386, Apr, 1999

Pul

se-i

nduc

ed c

urre

nt (

pA

)

Pulse width t (ps)

t coherence=h/E J

Coherent control of macroscopic quantum states in a single-Cooper-pair box coherent evolution

Superconducting single Cooper-pair box

PRL, 88, 047901 Jan, 2002

xxzzctrl BBH ˆ2

1ˆ

2

1

Hamiltonian in a spin-1/2 notation:

gCchz nEEB 214 Jx EB

Charge Echo in a Cooper-Pair BoxY. Nakamura,Yu. A. Pashkin, T. Yamamoto, and J. S. Tsai

22000 ; JEQEQEQEhf

oscillation period = 15 ps

t=80ps

0.45e

23 ps150 exp envelope Gaussian t

Measuring time 20 ms 105 ensembles

xy

z 0

1

Manipulating the Quantum State of an Electrical CircuitD. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier, C. Urbina, D. Esteve, M. H. DevoretScience 296, 886, May 2002

Capacitor-shunted Superconducting Single Electron Transistor

Ramsey fringe experiment

Single Josephson Junction:Coherent Temporal Oscillations of Macroscopic Quantum States in a Josephson JunctionYang Yu, Siyuan Han, Xi Chu, Shih-I Chu, Zhen Wang, Science, 296, 889 May (2002)

A 10m×10m NbN/AlN/NbN tunnel junction

tet

2

2

20

11 2sin

Population of the upper level:

: on resonance Rabi oscillation frequency

220 i

01 EEdetuning

decay rate 5s

at ib =0.993IC , /2=16.5GHz, tmw=0.1ms, T=8mK

Tunneling probability density P(t) 11

0 ~ < 5 Mrad/s

Rabi Oscillations in a Large Josephson-Junction QubitJohn M. Martinis, S. Nam, and J. Aumentado, PRL, 89, 117901, Sep. 2002

23

000 1 322height barrier potential IIIIU

41

02

1

004

1

p 1 22 :freq osc.plasma IICII

J

XXJ C

Q

LE

222cos

22

0

Η

Flux Qubit in a rf SQUID

xxzzctrl BBH ˆ2

1ˆ

2

1Hamiltonian in a spin-1/2 notation:

gCchz nEEB 214 Jx EB

iQ

In large self-inductance L limit: 142

0

L

EJL

20 XFor , the first two terms forms a double well potential

Effective two-state system formed by the lowest states in the two wells

Charge:Theories:Shnirman, A., G. Schon, and Z. Hermon, 1997, ‘‘Quantum manipulations of small Josephson junctions,’’ Phys. Rev. Lett. 79, 2371.Shnirman, A., and G. Schon, 1998, ‘‘Quantum measurements performed with a single-electron transistor,’’ Phys. Rev. B 57, 15 400.Makhlin, Y., G. Schon, and A. Shnirman, 1999, ‘‘Josephson-junction qubits with controlled couplings,’’ Nature (London) 386, 305.Averin, D. V., 1998, ‘‘Adiabatic quantum computation with Cooper pairs,’’ Solid State Commun. 105, 659.

Experiments:Bouchiat, V., 1997, Ph.D. thesis (Universite´ Paris VI).Nakamura, Y., C. D. Chen, and J. S. Tsai, 1997, ‘‘Spectroscopy of energy-level splitting between two macroscopic quantum

states of charge coherently superposed by Josephson coupling,’’ Phys. Rev. Lett. 79, 2328.Nakamura, Y., Y. A. Pashkin, and J. S. Tsai, 1999, ‘‘Coherent control of macroscopic quantum states in a single-Cooper-pair

box,’’ Nature (London) 398, 786.

Flux:Theories:Ioffe, L. B., V. B. Geshkenbein, M. V. Feigelman, A. L. Fauche´ re, and G. Blatter, 1999, ‘‘Quiet sds Josephson junctions for

quantum computing,’’ Nature (London) 398, 679.Mooij, J. E., T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, 1999, ‘‘Josephson persistent current qu-bit,’’

Science 285, 1036.

Experiments:Friedman, J. R., V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, 2000, ‘‘Detection of a Schroedinger’s cat state in an

rf-SQUID,’’ Nature (London) 406, 43.van der Wal, C. H., A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, S. Lloyd, and J. E. Mooij,

2000, ‘‘Quantum superposition of macroscopic persistent-current states,’’ Science 290, 773.Cosmelli, C., P. Carelli, M. G. Castellano, F. Chiarello, R. Leoni, and G. Torrioli, 1998, in Quantum Coherence and

Decoherence–ISQM ’98, edited by Y. A. Ono and K. Fujikawa (Elsevier, Amsterdam), p. 245.