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 physics 2. Molecular physics 3. NMR 4. Solid-state devices Objectives: Quantum computation and quantum communication Two kinds of Josephson junction systems for quantum bits: 1. Charge qubit: controlled by gate voltages 2. Flux qubit: controlled by magnetic fields 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 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 T l (usually T l > T  ) 2. Read out of the final state of the system

n: number operator of excess Cooper-pair charges on the island : the phase of superconducting order parameter of the island : gate charge = the control parameter E C =charging energy; E J =Josephson coupling energy Charge Qubit in a Superconducting Single Electron Transistor 2e -V b /2 VgVg sourcedrain gate 2e VCVC C1C1 C2C2 CgCg +V b /2 SS AA 00 00 11 11 EJEJ Energy Varying C g V g 00 11 Oscillation between  A  and  S  with angular frequency

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 (1997) SQUID E/ECE/EC Qo/eQo/e Qo/eQo/e Qo/eQo/e Frequency (GHz) Current (pA) Qo/eQo/e B-field on a SQUID Superconducting single Cooper-pair box

Y. Nakamura, Yu. A. Pashkin & J. S. Tsai Non-adiabatic trigger tt Without pulses With pulses t coherence = h / E J JQP current Nature, v. 398, p. 386, Apr, 1999 Pulse-induced current (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, Jan, 2002 Hamiltonian in a spin-1/2 notation: Charge Echo in a Cooper-Pair Box Y. Nakamura,Yu. A. Pashkin, T. Yamamoto, and J. S. Tsai oscillation period = 15 ps  t=80ps 0.45e Measuring time 20 ms  10 5 ensembles x y z  0 0  1 1

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 Capacitor-shunted Superconducting Single Electron Transistor Ramsey fringe experiment

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 10  m×10  m NbN/AlN/NbN tunnel junction Population of the upper level:   : on resonance Rabi oscillation frequency detuning  decay rate  5  s at i b =0.993I C,  /2  =16.5GHz,  t mw =0.1ms, T=8mK Tunneling probability density P(t)   11  0 ~  < 5 Mrad/s

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

Flux Qubit in a rf SQUID Hamiltonian in a spin-1/2 notation: 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

Charge: Theories: Shnirman, A., G. Schon, and Z. Hermon, 1997, ‘‘Quantum manipulations of small Josephson junctions,’’ Phys. Rev. Lett. 79, Shnirman, A., and G. Schon, 1998, ‘‘Quantum measurements performed with a single-electron transistor,’’ Phys. Rev. B 57, 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, 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, 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 Decoherenc e– ISQM ’98, edited by Y. A. Ono and K. Fujikawa (Elsevier, Amsterdam), p. 245.