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Realization of superposition and entanglement of coherent and squeezed states in circuit quantum electrodynamics

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Abstract

We propose a new scheme for generating the superposition and entanglement of the coherent states and squeezed states by considering N superconducting charge qubits (or artificial two-level atoms) interacting with photons in a high finesse cavity on a chip, assisted by a strong driving field. By virtue of the parameters of this system, we can generate novel quantum states, for example, multiparty entangled states and Schrödinger cat states among the superconducting qubits, coherent states and squeezed states of the cavity. These states, whose amplitudes are about two orders greater than those from the atomic quantum electrodynamics in classical cavity, are important for understanding the boundary between quantum and classical behavior and can be utilized in experimental studies on decoherence. This device may be an architecture for future solid-state quantum computation and communication.

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References

  1. Bell J S. On the Einstein-Podolsy-Rosen paradox. Physics, 1964, 1: 195–200

    Google Scholar 

  2. Deutsch D. Quantum theory, the Church-Turing Principle and the universal quantum computer. Proc Roy Soc London A, 1985, 400: 97–109

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Ekert A K. Quantum cryptography based on Bell’s theorem. Phys Rev Lett, 1991, 67: 661–663

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Bennett C H, Brassard G, Mermin N D. Quantum cryptography without Bell’s theorem. Phys Rev Lett, 1992, 68: 557–559; Bennett C H. Quantum cryptography using any two nonorthogonal states. Phys Rev Lett, 1992. 68: 3121–3124

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Brune M, Hagley E, Dreyer J, et al. Observing the progressive decoherence of the “Meter” in a quantum measurement. Phys Rev Lett, 1996, 77: 4887–4890; Solano E, Agarwal G S, Walther H. Strong-drivingassisted multipartite entanglement in cavity QED. Phys Rev Lett, 2003, 90: 027903; Osnaghi1 S, Bertet1 P, Auffeves1 A, et al. Coherent control of an atomic collision in a cavity. Phys Rev Lett, 2001, 87: 037902; Zhang X H, Yang Z Y, Xu P P. Teleporting N-qubit unknown atomic state by utilizing the V-type three-level atom. Sci China Ser G-Phys Mech Astron, 2009, 52: 1034–1038

    Article  ADS  Google Scholar 

  6. Monroe C, Meekhof D M, King B E, et al. A “Schrödinger cat” superposition state of an atom. Science, 1996, 272: 1131–1136; Turchette Q A, Myatt C J, King B E, et al. Decoherence and decay of motional quantum states of a trapped atom coupled to engineered reservoirs. Phys Rev A, 2000, 62: 053807; Zhang Y J, Xia Y J, Man Z X. et al. Simulation of the Ising model, memory for Bell states and generation of four-atom entangled states in cavity QED. Sci China Ser G-Phys Mech Astron, 2009, 52: 700–707; Chai J H, Guo G C. Generation of sub-poisson light in a negative feedback and cascade 3-level system. Sci China Ser A-Math Phys Astron, 1993, 36: 209–216

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Chen C Y, Feng M, Gao K L. Superposition and entanglement of mesoscopic vacuum squeezed states in cavity QED. Phys Rev A, 2006, 73: 034305; Solano E, deMatosFilho R L, Zagury N. Mesoscopic superpositions of vibronic collective states of N trapped ions. Phys Rev Lett, 2001, 87: 060402; Zhang L, Wang C, Sun C P. Analysis of quasi-adiabatic dynamic process of a 3-level atom in a quantum cavity. Sci China Ser A-Math Phys Astron, 1996, 39: 758–765

    Article  ADS  Google Scholar 

  8. Hofheinz M, Weig E M, Ansmann M, et al. Nature, 2008, 454: 310–314; Fan H Y, Fan Y. Squeezing and displacing related two-mode squeezed coherent state. Chin Sci Bull, 1998, 43(11): 959–961

    Article  ADS  Google Scholar 

  9. Hofheinz M, Wang H, Ansmannet M, et al. Synthesizing arbitrary quantum states in a superconducting resonator. Nature, 2009, 459: 546–549; Finkl J M, Bianchetti1 R, Baur M, et al. Dressed collective qubit states and the Tavis-Cummings model in circuit QED. Phys Rev Lett, 2009, 103: 083601; Romero G, Garcia-Ripoll J J, Solano E. Microwave photon detector in circuit QED. Phys Rev Lett, 2009, 102: 173602; Man Z X, Su F, Xia Y J. Efficient generation of Bell and W-type states in cavity QED. Chin Sci Bull, 2008, 53: 2410–2413

    Article  ADS  Google Scholar 

  10. DiCarlo L, Chow J M, Gambetta J M, et al. Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature, 2009, 460: 240–244; Kubanek A, Ourjoumtsev A, Schuster I, et al. Two-photon gateway in one-atom cavity quantum electrodynamics. Phys Rev Lett, 2008, 101: 203602; Huo W Y, Long G L. Entanglement and squeezing in solid state circuit. New J Phys, 2008, 10: 013026; Huo W Y, Long G L. Generation of squeezed states of nanomechanical resonator using three-wave mixing. Appl Phys Lett, 2008, 92: 133102; HuoWY, Long G L. Generating quantum entanglement in scalable superconducting charge qubits. Int J Quant Inform, 2007, 5(6): 829–836

    Article  ADS  Google Scholar 

  11. Wallraff A, Schuster D I, Blais A, et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature, 2004, 431: 162–167; Marthaler M, Schon G, Shnirman A. Photon-number squeezing in circuit quantum electrodynamics. Phys Rev Lett, 2008, 101: 147001

    Article  ADS  Google Scholar 

  12. Verdu J, Zoubi H, Koller Ch, et al. Strong magnetic coupling of an ultracold gas to a superconducting waveguide cavity. Phys Rev Lett, 2009, 103: 043603; Shen J T, Fan S H. Coherent single photon transport in one-dimensional waveguide coupled with superconducting quantum bits. Phys Rev Lett, 2005, 95: 213001

    Article  ADS  Google Scholar 

  13. Fay A, Hoskinson E, Lecocq F, et al. Strong tunable coupling between a superconducting charge and phase qubit. Phys Rev Lett, 2008, 100: 187003

    Article  ADS  Google Scholar 

  14. Lucero E, Hofheinz M, Ansmann M, et al. High-fidelity gates in a single Josephson qubit. Phys Rev Lett, 2008, 100: 247001; Yamamoto T, Pashkin Yu A, Astafiev O, et al. Demonstration of conditional gate operation using superconducting charge qubits. Nature, 2003, 425: 941–944

    Article  ADS  Google Scholar 

  15. Houck A A, Schreier J A, Johnson B R, et al. Controlling the spontaneous emission of a superconducting transmon qubit. Phys Rev Lett, 2008, 101: 080502; Wallraff A, Schuster D I, Blais A, et al. Sideband transition and two-tone spectroscopy of a superconducting qubit strongly coupled to on-chip cavity. Phys Rev Lett, 2007, 99: 050501

    Article  ADS  Google Scholar 

  16. Wang H, Hofheinz M, Ansmann M, et al. Measurement of the decay of Fock states in a superconducting quantum circuit. Phys Rev Lett, 2008, 101: 240401

    Article  ADS  Google Scholar 

  17. Blais A, Gambetta J, Wallraff A, et al. Quantum-information processing with circuit quantum electrodynamics. Phys Rev A, 2007, 75: 032329; Makhlin Y, Schön G, Shnirman A. Quantum-state engineering with Josephson junction devices. Rev Mod Phys, 2001, 73: 357–400

    Article  ADS  Google Scholar 

  18. Clarke J, Wilhelm Frank K. Superconducting quantum bits. Nature, 2008, 453: 1031–1042

    Article  ADS  Google Scholar 

  19. Davidovich L, Brune M, Raimond JM, et al. Mesoscopic quantum coherences in cavity QED: Preparation and decoherence monitoring schemes. Phys Rev A, 1996, 53: 1295–1309

    Article  ADS  Google Scholar 

  20. Raimond JM, Brune M, Haroche S. Manipulating quantum entanglement with atoms and photons in a cavity. Rev Mod Phys, 2001, 73: 565–582; Wang Y H, Song H S. Preparation of multi-atom specially entangled W-class state and splitting quantum information. Chin Sci Bull, 2009 54: 2599–2605

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Lutterbach L G, Davidovich L. Production and detection of highly squeezed states in a cavity QED. Phys Rev A, 2000, 61: 023813

    Article  ADS  Google Scholar 

  22. Myatt C J, King B E, Turchette Q A, et al. Decoherence of quantum superpositions through coupling to engineered reservoirs. Nature (London), 2000, 403: 269–273

    Article  ADS  Google Scholar 

  23. Gou S C, Steinbach J, Knight P L. Generation of mesoscopic superpositions of two squeezed states of motion for a trapped ion. Phys Rev A, 1997, 55: 3719–3723

    Article  ADS  Google Scholar 

  24. Sanders B C. Superposition of two squeezed vacuum states and interference effects. Phys Rev A, 1989, 39: 4284–4287; Yuen H P. Two photon coherent states of the radiation field. Phys Rev A, 1976, 13: 2226-2243; Walls D F. Squeezed states of light. Nature (London), 1983, 306: 141–146; Filip R, Mišta Jr L. Violation of Bell’s inequalities for a two-mode squeezed vacuum state in lossy transmission lines. Phys Rev A, 2002, 66: 044309

    Article  ADS  Google Scholar 

  25. Alexanian M, Bose S K. “Macroscopic” quantum superpositions: Atomfield entangled and steady states by two-photon processes. Phys Rev A, 2002, 65: 033819; Kitagawa A, Yamamoto K. Maximal entanglement of squeezed vacuum states via swapping with number-phase measurement. Phys Rev A, 2002, 66: 052312

    Article  ADS  Google Scholar 

  26. Wenger J, Fiurasek J, Tualle-Brouri R, et al. Pulsed squeezed vacuum measurements without homodyning. Phys Rev A, 2004, 70: 053812

    Article  ADS  Google Scholar 

  27. Fiurášek J, Cerf N J. How to measure squeezing and entanglement of Gaussian states without homodyning. Phys Rev Lett, 2004, 93: 063601; Zagoskin AM, Ilichev E, McCutcheon MW, et al. Controlled generation of squeezed states of microwave radiation in a superconducting resonant circuit. Phys Rev Lett, 2008, 101: 253602

    Article  ADS  Google Scholar 

  28. Mølmer K, Sørensen A. Multiparticle entanglement of hot trapped ions. Phys Rev Lett, 1999, 82: 1835–1838; Zhu S L, Wang Z D, Zanardi P. Unconventional geometric quantum computation. Phys Rev Lett, 2003, 91: 187902

    Article  ADS  Google Scholar 

  29. Schrödinger E. Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften, 1935, 23: 807–811

    Article  ADS  Google Scholar 

  30. Agarwal G S, Puri R R. Quantum theory of propagation of elliptically polarized light through a kerr medium. Phys Rev A, 1989, 40: 5179–5186

    Article  ADS  Google Scholar 

  31. Etaki S, Poot M, Mahboob I, et al. Motion detection of a micromechanical resonator embedded in a d.c. SQUID. Nat Phys, 2008, 4: 785–788

    Article  Google Scholar 

  32. Zhu S L, Wang Z D, Zanardi P. Geometric quantum computation and multiqubit entanglement with superconducting qubit inside a cavity. Phys Rev Lett, 2005, 94: 100502

    Article  MathSciNet  ADS  Google Scholar 

  33. Hayashi M, Matsumoto K. Quantum universal variable-length source coding. Phys Rev A, 2002, 62: 022311

    Article  MathSciNet  ADS  Google Scholar 

  34. Leibfried D, DeMarco B, Meyer V, et al. Experimental demonstration of a robust, high-fidelity geometric two-qubit phase. Nature, 2003, 422: 412–415; Chen C Y, Feng M, Zhang X L, et al. Strong-driving-assisted unconventional geometric logic gates in a cavity QED. Phys Rev A, 2006, 73: 032344; Zhu S L, Wang Z D, Yang K Y. Global-fidelity limits of state-dependent cloning of mixed states. Phys Rev A, 2003, 68: 034303

    Article  ADS  Google Scholar 

  35. Leibfried D, Barrett M D, Schaetz T, et al. Toward Heisenberg-limited spectorscopy with multiparticle entangled states. Science, 2004, 304: 1476–1478; Schmidt P O, Rosenband T, Langer C, et al. Spectroscopy using quantum logic. Science, 2005, 309: 749-752

    Article  ADS  Google Scholar 

  36. Blais A, Huang R S, Wallraff A, et al. Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation. Phys Rev A, 2004, 69: 062320

    Article  ADS  Google Scholar 

  37. Pashkin Yu A, Yamamoto T, Astafiev O, et al. Quantum oscillations in two coupled charge qubits. Nature (London), 2003, 421: 823–826

    Article  ADS  Google Scholar 

  38. Vion D, Aassime A, Cottet A, et al. Manipulating the quantum state of an electrical circuit. Science, 2002, 296: 886–889; Yu Y, Han S Y, Chu X, et al. Coherent temporal oscillations of macroscopic quantum states in a Josephson junction. Science, 2002, 296: 889–892

    Article  ADS  Google Scholar 

  39. Meunier T, Gleyzes S, Miaoli P, et al. Rabi oscillations revival induced by time reversal: A test of mesoscopic quantum coherence. Phys Rev Lett, 2005, 94: 010401; Auffeves A, Maioli P, Meunier T, et al. Entanglement of a mesoscopic field with an atom induced by photon graininess in a cavity. Phys Rev Lett, 2003, 91: 230405; Agarwal G S, Lange W, Walther H, et al. Intense-field renormalization of cavity-induced spontaneous emission. Phys Rev A, 1993, 48: 4555–4568

    Article  ADS  Google Scholar 

  40. Koch J, Yu T M, Gambetta J, et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys Rev A, 2007, 76: 042319; Ithier G, Collin E, Joyez P, et al. Decoherence in a superconducting quantum bit circuit. Phys Rev B, 2005, 72: 134519

    Article  ADS  Google Scholar 

  41. Simmonds R W, Lang K M, Hite D A, et al. Decoherence in Josephson phase qubits from junction resonators. Phys Rev Lett, 2004, 93: 077003; Martinis J M, Cooper K B, McDermott R, et al. Decoherence in Josephson qubits from dielectric loss. Phys Rev Lett, 2005, 95: 210503; Nakamura Y, Pashkin Yu A, Yamamoto T, et al. Charge echo in a Cooper-pair box. Phys Rev Lett, 2002, 88: 047901; Bertet P, Chiorescu I, Burkard G, et al. Dephasing of a superconducting qubit induced by photon noise. Phys Rev Lett, 2005, 95: 257002

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics and Information Engineering, Hunan Institute of Humanities, Science and Technology, Loudi, 417000, China

    ChangYong Chen

  2. Beijing National Laboratory for Condensated Matter Physics, Chinese Academy of Sciences, Beijing, 100190, China

    ChangYong Chen & Qing Sun

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  1. ChangYong Chen
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  2. Qing Sun
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Correspondence to ChangYong Chen.

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Chen, C., Sun, Q. Realization of superposition and entanglement of coherent and squeezed states in circuit quantum electrodynamics. Sci. China Phys. Mech. Astron. 54, 930–935 (2011). https://doi.org/10.1007/s11433-011-4280-6

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  • DOI: https://doi.org/10.1007/s11433-011-4280-6

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