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Fast and robust generation of singlet state via shortcuts to adiabatic passage

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Abstract

In this paper, we propose a protocol to fast and robustly generate two-atom singlet state by designing the evolution operator with the help of quantum Zeno dynamics. The population of the intermediate state can be controlled by system parameters. The pulses in the protocol can be fitted as Gaussian functions, which are beneficial to the experimental feasibility. Besides, the performance of various decoherence factors, such as spontaneous emission, cavity decay and fiber photon leakage, is discussed by numerical simulations. The results show that the protocol is fast and robust against decoherence and operational imperfection. Finally, the protocol is generalized to realize three-atom singlet state by the same principle.

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References

  1. Zheng, S.B., Guo, G.C.: Efficient scheme for two-atom entanglement and quantum information processing in cavity QED. Phys. Rev. Lett. 85, 2392 (2000)

    ADS  Google Scholar 

  2. Greenberger, D.M., Horne, M.A., Zeilinger, A.: Bell’s Theorem, Quantum Theory, and Conception of the Universe. Kluwer, Dordrecht (1989)

    Google Scholar 

  3. Dür, W., Vidal, G., Cirac, J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)

    MathSciNet  ADS  Google Scholar 

  4. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  5. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)

    MathSciNet  MATH  ADS  Google Scholar 

  6. Xia, Y., Song, J., Lu, P.M., Song, H.S.: Teleportation of an \(N\)-photon Greenberger–Horne–Zeilinger (GHZ) polarization entangled state using linear optical elements. J. Opt. Soc. Am. B 27, A1–A6 (2010)

    Google Scholar 

  7. Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., Wootters, W.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    MathSciNet  MATH  ADS  Google Scholar 

  8. Hillery, M., Buzek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)

    MathSciNet  MATH  ADS  Google Scholar 

  9. Cabello, A.: N-particle N-level singlet states: some properties and applications. Phys. Rev. Lett. 89, 100402 (2002)

    MathSciNet  MATH  ADS  Google Scholar 

  10. Mermin, N.D.: Quantum mechanics vs local realism near the classical limit: a Bell inequality for spins. Phys. Rev. D 22, 356 (1980)

    MathSciNet  ADS  Google Scholar 

  11. Cabello, A.: Supersinglets. J. Mod. Opt. 50, 1049 (2003)

    MathSciNet  MATH  ADS  Google Scholar 

  12. Chen, X., Lizuain, I., Ruschhaupt, A., Guéry-Odelin, D., Muga, J.G.: Shortcuts to adiabatic passage in two- and three-level atoms. Phys. Rev. Lett. 105, 123003 (2010)

    ADS  Google Scholar 

  13. Huang, B.H., Chen, Y.H., Wu, Q.C., Song, J., Xia, Y.: Fast generating Greenberger–Horne–Zeilinger state via iterative interaction pictures. Laser Phys. Lett. 13, 105202 (2016)

    ADS  Google Scholar 

  14. Kang, Y.H., Chen, Y.H., Huang, B.H., Song, J., Xia, Y.: Invariant-based pluse design for three-level systems without the rotating-wave approximation. Ann. der Phys. 529, 1700004 (2017)

    ADS  Google Scholar 

  15. Chen, Y.H., Shi, Z.C., Song, J., Xia, Y., Zheng, S.B.: Accelerating population transfer in a transmon qutrit via shortcuts to adiabaticity. Ann. der Phys. 530, 1700351 (2018)

    MathSciNet  ADS  Google Scholar 

  16. Wu, Q.C., Chen, Y.H., Huang, B.H., Shi, Z.C., Song, J., Xia, Y.: Protecting quantum state in time-dependent decoherence-free subspaces without the rotating-wave approximation. Ann. der Phys. 529, 1700186 (2017)

    MathSciNet  MATH  ADS  Google Scholar 

  17. Chen, Y.H., Shi, Z.C., Song, J., Xia, Y., Zheng, S.B.: Optimal shortcut approach based on an easily obtained intermediate Hamiltonian. Phys. Rev. A 95, 062319 (2017)

    ADS  Google Scholar 

  18. Huang, B.H., Kang, Y.H., Chen, Y.H., Wu, Q.C., Song, J., Xia, Y.: Fast quantum state engineering via universal SU(2) transformation. Phys. Rev. A 96, 022314 (2017)

    ADS  Google Scholar 

  19. Huang, B.H., Kang, Y.H., Chen, Y.H., Shi, Z.C., Song, J., Xia, Y.: Quantum state transfer in spin chains via shortcuts to adiabaticity. Phys. Rev. A 97, 012333 (2018)

    ADS  Google Scholar 

  20. Kang, Y.H., Wu, Q.C., Chen, Y.H., Shi, Z.C., Song, J., Xia, Y.: Accelerating adiabatic quantum transfer for three-level \(Lambda \)-type structure systems via picture transformation. Ann. Phys. 379, 102 (2017)

    MATH  ADS  Google Scholar 

  21. Kang, Y.H., Chen, Y.H., Shi, Z.C., Huang, B.H., Song, J., Xia, Y.: Nonadiabatic holonomic quantum computation using Rydberg blockade. Phys. Rev. A 97, 042336 (2018)

    ADS  Google Scholar 

  22. Kang, Y.H., Chen, Y.H., Shi, Z.C., Song, J., Xia, Y.: Fast preparation of \(W\) state with superconducting quantum interference devices by using dressed states. Phys. Rev. A 94, 052311 (2016)

    ADS  Google Scholar 

  23. Kang, Y.H., Chen, Y.H., Wu, Q.C., Huang, B.H., Song, J., Xia, Y.: Fast generation of \(W\) states of superconducting qubits with multiple qubits with multiple Schrödinger dynamics. Sci. Rep. 6, 36737 (2016)

    ADS  Google Scholar 

  24. Kang, Y.H., Chen, Y.H., Shi, Z.C., Huang, B.H., Song, J., Xia, Y.: Complete Bell-state analysis for superconducting-quantum-interference-device qubits with a transitionless tracking algorithm. Phys. Rev. 96, 022304 (2017)

    Google Scholar 

  25. Kang, Y.H., Chen, Y.H., Shi, Z.C., Huang, B.H., Song, J., Xia, Y.: Pulse design for multilevel systems by utilizing Lie transforms. Phys. Rev. A 97, 033407 (2018)

    ADS  Google Scholar 

  26. Kang, Y.H., Wu, Q.C., Huang, B.H., Song, J., Xia, Y.: Arbitrary quantum state engineering in three-state systems via counterdiabatic driving. Sci. Rep. 6, 38484 (2016)

    ADS  Google Scholar 

  27. Kang, Y.H., Huang, B.H., Lu, P.M., Xia, Y.: Reverse engineering of a Hamiltonian for a three-level system via the Rodrigues’ rotation formula. Laser Phys. Lett. 14, 025201 (2017)

    ADS  Google Scholar 

  28. Demirplak, M., Rice, S.A.: Adiabatic population transfer with control fields. J. Phys. Chem. A 107, 9937 (2003)

    Google Scholar 

  29. Demirplak, M., Rice, S.A.: On the consistency, extremal, and global properties of counterdiabatic fields. J. Chem. Phys. 129, 154111 (2008)

    ADS  Google Scholar 

  30. Torrontegui, E., Ibáildeñez, S., Martínez-Garaot, S., Modugno, M., del Campo, A., Gué-Odelin, D., Ruschhaupt, A., Chen, X., Muga, J.G.: Shortcuts to adiabaticity. Adv. At. Mol. Opt. Phys. 62, 117 (2013)

    ADS  Google Scholar 

  31. del Campo, A.: Shortcuts to adiabaticity by counterdiabatic driving. Phys. Rev. Lett. 111, 100502 (2013)

    Google Scholar 

  32. Chen, X., Torrontegui, E., Muga, J.G.: Lewis–Riesenfeld invariants and transitionless quantum driving. Phys. Rev. A 83, 062116 (2011)

    ADS  Google Scholar 

  33. del Campo, A., Rams, M.M., Zurek, W.H.: Assisted finite-rate adiabatic passage across a quantum critical point: exact solution for the quantum Ising model. Phys. Rev. Lett. 109, 115703 (2012)

    ADS  Google Scholar 

  34. Muga, J.G., Chen, X., Ibáildeñez, S., Lizuain, I., Ruschhaupt, A.: Transitionless quantum drivings for the harmonic oscillator. J. Phys. B At. Mol. Opt. Phys. 43, 085509 (2010)

    ADS  Google Scholar 

  35. Muga, J.G., Chen, X., Ruschhaup, A., Guéry-Odelin, D.: FAST TRACK COMMUNICATION: frictionless dynamics of Bose–Einstein condensates under fast trap variations. J. Phys. B At. Mol. Opt. Phys. 42, 241001 (2009)

    ADS  Google Scholar 

  36. Chen, X., Ruschhaupt, A., Schmidt, S., del Campo, A., Guéry-Odelin, D., Muga, J.G.: Fast optimal frictionless atom cooling in harmonic traps: shortcut to adiabaticity. Phys. Rev. Lett. 104, 063002 (2010)

    ADS  Google Scholar 

  37. Berry, M.V.: Transitionless quantum driving. J. Phys. A 42, 365303 (2009)

    MathSciNet  MATH  Google Scholar 

  38. Lewis, H.R., Riesenfeld, W.B.: An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electomagnetic field. J. Math. Phys. 10, 1458 (1969)

    MATH  ADS  Google Scholar 

  39. Chen, Y.H., Xia, Y., Chen, Q.Q., Song, J.: Fast and noise-resistant implementation of quantum phase gates and creation of quantum entangled states. Phys. Rev. A 91, 012325 (2015)

    ADS  Google Scholar 

  40. Chen, Y.H., Xia, Y., Song, J., Chen, Q.Q.: Shortcuts to adiabatic passage for fast generation of Greenberger–Horne–Zeilinger states by transitionless quantum driving. Sci. Rep. 5, 15616 (2015)

    ADS  Google Scholar 

  41. Chen, Z., Chen, Y.H., Xia, Y., Song, J., Huang, B.H.: Fast generation of three-atom singlet state by transitionless quantum driving. Sci. Rep. 6, 22202 (2016)

    ADS  Google Scholar 

  42. Chen, Y.H., Xia, Y., Chen, Q.Q., Song, J.: Shortcuts to adiabatic passage for multiparticle in distant cavities: applications to fast and noise-resistant quantum population transfer, entangled states’ preparation and transition. Laser Phys. Lett. 11, 115201 (2014)

    ADS  Google Scholar 

  43. Chen, X., Muga, J.G.: Engineering of fast population transfer in three-level systems. Phys. Rev. A 86, 033405 (2012)

    ADS  Google Scholar 

  44. Torrontegui, E., Ibáildeñez, S., Chen, X., Ruschhaupt, A., Guéry-Odelin, D., Muga, J.G.: Fast atomic transport without vibrational heating. Phys. Rev. A 83, 013415 (2011)

    ADS  Google Scholar 

  45. Chen, X., Torrontegui, E., Stefanatos, D., Li, J.-S., Muga, J.G.: Optimal trajectories for efficient atomic transport without final excitation. Phys. Rev. A 84, 043415 (2011)

    ADS  Google Scholar 

  46. Damski, B.: Counterdiabatic driving of the quantum Ising model. J. Stat. Mech. 12, 2014 (2014)

    MathSciNet  Google Scholar 

  47. Song, X.K., Zhang, H., Ai, Q., Qiu, J., Deng, F.G.: Shortcut to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm. New J. Phys. 18, 023001 (2016)

    ADS  Google Scholar 

  48. Chen, Y.H., Huang, B.H., Song, J., Xia, Y.: Improving the stimulated Raman adiabatic passage via dissipative quantum dynamics. Opt. Commun. 380, 140 (2016)

    ADS  Google Scholar 

  49. del Campo, A.: Frictionless quantum quenches in ultracold gases: a quantum-dynamical microscope. Phys. Rev. A 84, 031606(R) (2011)

    ADS  Google Scholar 

  50. del Campo, A.: Fast frictionless dynamics as a toolbox for low-dimensional Bose–Einstein condensates. Eur. Phys. Lett. 96, 60005 (2011)

    Google Scholar 

  51. Martínez-Garaot, S., Torrontegui, E., Chen, X., Modugno, M., Guéry-Odelin, D., Tseng, S.Y., Muga, J.G.: Vibrational mode multiplexing of ultracold atoms. Phys. Rev. Lett. 111, 213001 (2013)

    ADS  Google Scholar 

  52. Torrontegui, E., Martínez-Garaot, S., Ruschhaupt, A., Muga, J.G.: Shortcuts to adiabaticity: fast-forward approach. Phys. Rev. A 86, 013601 (2012)

    ADS  Google Scholar 

  53. Couvert, A., Kawalec, T., Reinaudi, G., Guéry-Odelin, D.: Optimal transport of ultracold atoms in the non-adiabatic regime. Europhys. Lett. 83, 13001 (2008)

    ADS  Google Scholar 

  54. Murphy, M., Jiang, L., Khaneja, N., Calarco, T.: High-fidelity fast quantum transport with imperfect controls. Phys. Rev. A 79, 020301(R) (2009)

    ADS  Google Scholar 

  55. Torrontegui, E., Chen, X., Modugno, M., Schmidt, S., Ruschhaupt, A., Muga, J.G.: Fast transport of Bose–Einstein condensates. New J. Phys. 14, 13031 (2012)

    Google Scholar 

  56. Palmero, M., Torrontegui, E., Guéry-Odelin, D., Muga, J.G.: Fast transport of two ions in an anharmonic trap. Phys. Rev. A 88, 053423 (2013)

    ADS  Google Scholar 

  57. Kang, Y.H., Chen, Y.H., Wu, Q.C., Huang, B.H., Xia, Y., Song, J.: Reverse engineering of a Hamiltonian by designing the evolution operators. Sci. Rep. 6, 30151 (2016)

    ADS  Google Scholar 

  58. Kang, Y.H., Shi, Z.C., Huang, B.H., Song, J., Xia, Y.: Fast and robust quantum information transfer in annular and radial superconducting networks. Ann. Der Phys. 529, 1700154 (2017)

    MathSciNet  ADS  Google Scholar 

  59. Misra, B., Sudarshan, E.C.G.: The Zeno’s paradox in quantum theory. J. Math. Phys. 18, 756 (1977)

    MathSciNet  ADS  Google Scholar 

  60. Itano, Wayne M., Heinzen, D.J., Bollinger, J.J., Wineland, D.J.: Quantum Zeno effect. Phys, Rev. A 41, 2295 (1990)

    ADS  Google Scholar 

  61. Facchi, P., Gorini, V., Marmo, G., Pascazio, S., Sudarshan, E.C.G.: Quantum Zeno dynamics. Phys. Lett. A 275, 12 (2000)

    MathSciNet  MATH  ADS  Google Scholar 

  62. Facchi, P., Pascazio, S., Scardicchio, A., Schulman, L.S.: Zeno dynamics yields ordinary constraints. Phys. Rev. A 65, 012108 (2002)

    ADS  Google Scholar 

  63. Facchi, P., Pascazio, S.: Quantum Zeno subspaces. Phys. Rev. Lett. 89, 080401 (2002)

    MathSciNet  MATH  ADS  Google Scholar 

  64. Facchi, P., Marmo, G., Pascazio, S.: Quantum Zeno dynamics and quantum Zeno subspaces. J. Phys. Conf. Ser. 196, 012017 (2009)

    Google Scholar 

  65. Yang, R.C., Li, G., Zhang, T.C.: Robust atomic entanglement in two coupled cavities via virtual excitations and quantum Zeno dynamics. Quantum Inf. Process. 12, 493 (2012)

    MathSciNet  MATH  ADS  Google Scholar 

  66. Serafini, A., Mancini, S., Bose, S.: Distributed quantum computation via optical fibers. Phys. Rev. Lett. 96, 101503 (2006)

    Google Scholar 

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Acknowledgements

This paper is supported by the science and technology research program of the education department of Jiangxi Province under Grants No. GJJ171286.

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Correspondence to Wu-Jiang Shan.

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Shan, WJ., Zhang, XP., Wang, WQ. et al. Fast and robust generation of singlet state via shortcuts to adiabatic passage. Quantum Inf Process 18, 22 (2019). https://doi.org/10.1007/s11128-018-2135-z

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