Status of Experiments on Charge- and Flux- Entanglements

1. 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

2. 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

3. 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)

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

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

11. 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:

12. 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.