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October 18, 2002, Workshop on Quantum Information Science. Status of Experiments on Charge- and Flux- Entanglements. 中央研究院 物理研究所 陳啟東. Objectives: Quantum computation and quantum communication. Quantum computer : formed by a system whose state is restricted to being

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slide2

Objectives: Quantum computation and quantum communication

Quantum computer: formed by a system whose state is restricted to being

an arbitrary superposition of two “basis” states.

Quantum-state engineering:

1. Atomic physics

2. Molecular physics

3. NMR

4. Solid-state devices

Advantages of Solid-state devices:

Easily embedded in electronic circuits

Scaled up to large registers

Solid-state devices:

1. Josephson junction systems

2. Quantum dots with discrete levels

3. Nanostructured materials with spin degrees of freedom

Two kinds of Josephson junction systems for quantum bits:

1. Charge qubit: controlled by gate voltages

2. Flux qubit: controlled by magnetic fields

slide3

Issues:

1. Limited phase coherence time Tj

and energy relaxation time Tl (usually Tl > Tj)

2. Read out of the final state of the system

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)

slide4

2e

2e

VC

source

drain

C1

C2

: the phase of superconducting order parameter of the island

Cg

gate

: gate charge = the control parameter

-Vb/2

+Vb/2

Vg

Charge Qubit in a Superconducting Single Electron Transistor

EC=charging energy; EJ=Josephson coupling energy

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

1

0

Oscillation betweenAandS

with angular frequency

Energy

A

EJ

S

0

1

Varying CgVg

1

0

slide5

E/EC

Qo/e

Superconducting single Cooper-pair box

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. Tsai

PRL, v. 79, p. 2328 (1997)

B-field on a SQUID

Current (pA)

SQUID

Qo/e

Frequency (GHz)

Qo/e

Qo/e

slide6

Pulse-induced current (pA)

Pulse width Dt (ps)

Superconducting single Cooper-pair box

Coherent control of macroscopic quantum states

in a single-Cooper-pair boxcoherent evolution

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

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

tcoherence=h/EJ

Non-adiabatic trigger

Dt

tcoherence=h/EJ

JQP current

With pulses

Without pulses

slide7

oscillation period = 15 ps

Charge Echo in a Cooper-Pair Box

Y. Nakamura,Yu. A. Pashkin, T. Yamamoto,and J. S. Tsai

z

0

PRL, 88, 047901 Jan, 2002

y

x

Hamiltonian in a spin-1/2 notation:

1

Dt=80ps

0.45e

Measuring time 20 ms  105 ensembles

slide8

Capacitor-shunted Superconducting Single Electron Transistor

Manipulating the Quantum State of an Electrical Circuit

D. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier, C. Urbina, D. Esteve, M. H. Devoret

Science 296, 886, May 2002

Ramsey fringe experiment

slide9

G=decay rate  5ms

at ib=0.993IC , w/2p=16.5GHz,

Dtmw=0.1ms, T=8mK

Single Josephson Junction:

Coherent Temporal Oscillations of Macroscopic Quantum States in a Josephson Junction

Yang Yu, Siyuan Han, Xi Chu, Shih-I Chu, Zhen Wang, Science, 296, 889 May (2002)

A 10mm×10mm NbN/AlN/NbN tunnel junction

Tunneling probability density P(t)  r11

Population of the upper level:

W0 ~ D < 5 Mrad/s

detuning

W0: on resonance Rabi oscillation frequency

slide10

Rabi Oscillations in a Large Josephson-Junction Qubit

John M. Martinis, S. Nam, and J. Aumentado, PRL, 89, 117901, Sep. 2002

slide11

Flux Qubit in a rf SQUID

In large self-inductance L limit:

For

, the first two terms forms a double well potential

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

Hamiltonian in a spin-1/2 notation:

slide12

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.

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