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Superadiabatic Shortcuts for Fast Generating Two-Atom Four-Dimensional Entanglement

  • Ju-Cheng Dong
  • Jin-Lei Wu
  • Xin Ji
Article

Abstract

We propose a scheme for rapidly generating two-atom four-dimensional entanglement based on superadiabatic shortcuts. In the scheme, the counterdiabatic Hamiltonian has the same form as that of the effective Hamiltonian, and the scheme avoids the disadvantage of the invariants-based scheme Dong et al. (Int. J. Theor. Phys. 57, 3149–3162, 2018), so the scheme is more feasible in experiment. In addition, numerical simulation results show that the scheme is robust against decoherence and variations in various parameters, and the two atoms four-dimensional entanglement can be generated with high fidelity.

Keywords

Four-dimensional entanglement Shortcuts to adiabaticity Superadiabatic iterations 

Notes

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No. 11464046.

References

  1. 1.
    Rauschenbeutel, A., Nogues, G., Osnaghi, S., Bertet, P., Brune, M., Raimond, J.M., Haroche, S.: Step-by-step engineered multiparticle entanglement. Science 288, 2024–2028 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    Pan, J.W., Daniell, M., Gasparoni, S., Weihs, G., Zeilinger, A.: Experimental demonstration of four-photon entanglement and high-fidelity teleportation. Phys. Rev. Lett. 86, 4435–4438 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    Song, J., Li, C., Zhang, Z.J., Jiang, Y.Y., Xia, Y.: Implementing stabilizer codes in noisy environments. Phys. Rev. A 96, 032336 (2017)ADSCrossRefGoogle Scholar
  4. 4.
    Lewis-Swan, R.J., Norcia, M.A., Cline, J.R.K., Thompson, J.K., Rey, A.M.: Robust spin squeezing via photon-mediated interactions on an optical clock transition. Phys. Rev. Lett. 121, 070403 (2018)ADSCrossRefGoogle Scholar
  5. 5.
    Li, C., Sampuli, E.M., Song, J., Xia, Y., Ding, W.: One-step engineering many-atom NOON state. New J. Phys. 20, 093019 (2018)ADSCrossRefGoogle Scholar
  6. 6.
    Cerf, N.J., Bourennane, M., Karlsson, A., Gisin, N.: Security of quantum key distribution using d-level systems. Phys. Rev. Lett. 88, 127902 (2002)ADSCrossRefGoogle Scholar
  7. 7.
    Kaszlikowski, D., Gnacinski, P., żukowski, M., Miklaszewski, W., Zeilinger, A.: Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits. Phys. Rev. Lett. 85, 4418–4421 (2000)ADSCrossRefGoogle Scholar
  8. 8.
    Zheng, S.B.: Production of three-dimensional entanglement for two atoms with a single resonant interaction. Phys. Lett. A 370, 110–112 (2007)ADSCrossRefGoogle Scholar
  9. 9.
    Song, J., Xia, Y., Song, H.S., Liu, B.: Four-dimensional entangled state generation in remote cavities. Eur. Phys. J. D 50, 91–96 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    Shao, X.Q., Wang, H.F., Chen, L., Zhang, S., Zhao, Y.F., Yeon, K.H.: Converting two-atom singlet state into three-atom singlet state via quantum Zeno dynamics. New J. Phys. 12, 023040 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    Li, W.A., Huang, G.Y.: Deterministic generation of a three-dimensional entangled state via quantum Zeno dynamics. Phys. Rev. A 83, 022322 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    Shen, L.T., Wu, H.Z., Chen, R.X.: Robust generation of a four-dimensional entangled state in separate cavities via quantum Zeno dynamics. J. Phys. B: At. Mol. Opt. Phys. 44, 205503 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    Liu, S., Li, J., Yu, R., Wu, Y.: Achieving three-dimensional entanglement between two spatially separated atoms by using the quantum Zeno effect. Phys. Rev. A 87, 062316 (2013)ADSCrossRefGoogle Scholar
  14. 14.
    Wu, Q.C., Ji, X.: Generation of steady three- and four-dimensional entangled states via quantum-jump-based feedback. Quantum Inf. Process. 12, 3167–3178 (2013)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Chen, F.C., Chen, M.F.: One-step generation of three-dimensional entanglement between a single atom and an atomic ensemble via quantum Zeno dynamics. Opt. Commun. 364, 29–36 (2016)ADSCrossRefGoogle Scholar
  16. 16.
    Chen, L.B., Shi, P., Zheng, C.H., Gu, Y.J.: Generation of three-dimensional entangled state between a single atom and a Bose-Einstein condensate via adiabatic passage. Opt. Express 20, 14547–14555 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    Chen, M.F., Wang, P., Ma, S.S.: One-step generation of four-dimensional entanglement via adiabatic passage in cavity quantum electrodynamics. Opt. Commun. 285, 4612–4615 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    Lu, M., Xia, Y., Song, J., Song, H.S.: Driving three atoms into a singlet state in an optical cavity via adiabatic passage of a dark state. J. Phys. B 46, 015502 (2013)ADSCrossRefGoogle Scholar
  19. 19.
    Liu, Q.G., Wu, Q.C., Leng, C.L., Liang, Y., Ji, X., Zhang, S.: Generation of atomic NOON states via adiabatic passage. Quantum Inf. Process. 13, 2801–2814 (2014)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Wei, X., Chen, M.F.: Preparation of multi-qubit W states in multiple resonators coupled by a superconducting qubit via adiabatic passage. Quantum Inf. Process. 14, 2419–2433 (2015)ADSCrossRefGoogle Scholar
  21. 21.
    Liang, Y., Su, S.L., Wu, Q.C., Ji, X., Zhang, S.: Adiabatic passage for three-dimensional entanglement generation through quantum Zeno dynamics. Opt. Express 23, 5064–5077 (2015)ADSCrossRefGoogle Scholar
  22. 22.
    Wu, J.L., Song, C., Xu, J., Yu, L., Ji, X., Zhang, S.: Adiabatic passage for one-step generation of n-qubit Greenberger–Horne–Zeilinger states of superconducting qubits via quantum Zeno dynamics. Quantum Inf. Process. 15, 3663–3675 (2016)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Song, C., Su, S.L., Wu, J.L., Wang, D.Y., Ji, X., Zhang, S.: Generation of tree-type three-dimensional entangled state via adiabatic passage. Phys. Rev. A 93, 062321 (2016)ADSCrossRefGoogle Scholar
  24. 24.
    Shao, X.Q., Zheng, T.Y., Oh, C.H., Zhang, S.: Dissipative creation of three-dimensional entangled state in optical cavity via spontaneous emission. Phys. Rev. A 89, 012319 (2014)ADSCrossRefGoogle Scholar
  25. 25.
    Shao, X.Q., You, J.B., Zheng, T.Y., Oh, C.H., Zhang, S.: Stationary three-dimensional entanglement via dissipative Rydberg pumping. Phys. Rev. A 89, 052313 (2014)ADSCrossRefGoogle Scholar
  26. 26.
    Su, S.L., Shao, X.Q., Wang, H.F., Zhang, S.: Preparation of three-dimensional entanglement for distant atoms in coupled cavities via atomic spontaneous emission and cavity decay. Sci. Rep. 4, 7566 (2014)CrossRefGoogle Scholar
  27. 27.
    Shao, X.Q., Wang, Z.H., Liu, H.D., Yi, X.X.: Dissipative preparation of a tripartite singlet state in coupled arrays of cavities via quantum feedback control. Phys. Rev. A 94, 032307 (2016)ADSCrossRefGoogle Scholar
  28. 28.
    Yang, Y.F., Chen, Y.H., Wu, Q.C., Kang, Y.H., Huang, B.H., Xia, Y.: Rapid generation of a three-dimensional entangled state for two atoms trapped in a cavity via shortcuts to adiabatic passage. Quantum Inf. Process. 16, 15 (2016)ADSCrossRefGoogle Scholar
  29. 29.
    Peng, R., Zheng, Y., Liu, S.W., Li, X.P., Wu, J.L., Ji, X.: Shortcuts to adiabaticity for rapidly generating two-atom qutrit entanglement. Quantum Inf. Process. 16, 172 (2017)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Yang, X.Q., Huang, D.Y., Xue, P., Gong, Y.Y., Wu, J.L., Ji, X.: Feasible superadiabatic-based shortcuts for the fast generation of 3D entanglement between two atoms. Laser Phys. Lett. 14, 055209 (2017)ADSCrossRefGoogle Scholar
  31. 31.
    Wu, J.L., Su, S.L., Ji, X., Zhang, S.: Superadiabatic scheme for optimizing the fast generation of tree-type 3D entanglement. Ann. Phys. 386, 34–43 (2017)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    Dong, J.C., Wu, J.L., Ji, X.: Fast generation of four-dimensional entanglement between two spatially separated atoms via shortcuts to adiabatic passage. Int. J. Theor. Phys. 57, 3149–3162 (2018)CrossRefGoogle Scholar
  33. 33.
    Bergmann, K., Theuer, H., Shore, B.W.: Coherent population transfer among quantum states of atoms and molecules. Rev. Mod. Phys. 70, 1003–1025 (1998)ADSCrossRefGoogle Scholar
  34. 34.
    Král, P., Thanopulos, I., Shapiro, M.: Colloquium: coherently controlled adiabatic passage. Rev. Mod. Phys. 79, 53–77 (2007)ADSCrossRefGoogle Scholar
  35. 35.
    Chen, X., Lizuain, I., Ruschhaupt, A., Guéry-Odelin, D., Muga, J.G.: Shortcut to adiabatic passage in two- and three-level atoms. Phys. Rev. Lett. 105, 123003 (2010)ADSCrossRefGoogle Scholar
  36. 36.
    Chen, X., Torrontegui, E., Muga, J.G.: Lewis-riesenfeld invariants and transitionless quantum driving. Phys. Rev. A 83, 062116 (2011)ADSCrossRefGoogle Scholar
  37. 37.
    Chen, X., Muga, J.G.: Engineering of fast population transfer in three-level systems. Phys. Rev. A 86, 033405 (2012)ADSCrossRefGoogle Scholar
  38. 38.
    del Campo, A.: Shortcuts to adiabaticity by counter-adiabatic driving. Phys. Rev. Lett. 111, 100502 (2013)ADSCrossRefGoogle Scholar
  39. 39.
    Torrontegui, E., Ibáñez, S., Martínez-garaot, S., Modugno, M., del Campo, A., Gu-Odelin, D., Ruschhaupt, A., Chen, X., Muga, J.G.: Shortcuts to adiabaticity. Adv. At. Mol. Opt. Phys. 62, 117–169 (2013)ADSCrossRefGoogle Scholar
  40. 40.
    Martínez-Garaot, S., Torrontegui, E., Chen, X., Muga, J.G.: Shortcuts to adiabaticity in three-level systems using Lie transforms. Phys. Rev. A 89, 053408 (2014)ADSCrossRefGoogle Scholar
  41. 41.
    Ibáñez, S., Li, Y.C., Chen, X., Muga, J.G.: Pulse design without the rotating-wave approximation. Phys. Rev. A 92, 062136 (2015)ADSCrossRefGoogle Scholar
  42. 42.
    Song, X.K., Zhang, H., Ai, Q., Qiu, J., Deng, F.G.: Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm. New J. Phys. 18, 023001 (2016)ADSCrossRefGoogle Scholar
  43. 43.
    Chen, Y.H., Xia, Y., Wu, Q.C., Huang, B.H., Song, J.: Method for constructing shortcuts to adiabaticity by a substitute of counterdiabatic driving terms. Phys. Rev. A 93, 052109 (2016)ADSCrossRefGoogle Scholar
  44. 44.
    Baksic, A., Ribeiro, H., Clerk, A.A.: Speeding up adiabatic quantum state transfer by using dressed states. Phys. Rev. Lett. 116, 230503 (2016)ADSCrossRefGoogle Scholar
  45. 45.
    Chen, Y.H., Xia, Y., Chen, Q.Q., Song, J.: Efficient shortcuts to adiabatic passage for fast population transfer in multiparticle systems. Phys. Rev. A 89, 033856 (2014)ADSCrossRefGoogle Scholar
  46. 46.
    Chen, Y.H., Xia, Y., Chen, Q.Q., Song, J.: Shortcuts to adiabatic passage for multiparticles in distant cavities: applications to fast and noise-resistant quantum population transfer, entangled states’ preparation and transition. Laser Phys. Lett. 11, 115201 (2014)ADSCrossRefGoogle Scholar
  47. 47.
    Wu, J.L., Ji, X., Zhang, S.: Fast adiabatic quantum state transfer and entanglement generation between two atoms via dressed states. Sci. Rep. 7, 46255 (2017)ADSCrossRefGoogle Scholar
  48. 48.
    Liang, Y., Wu, Q.C., Su, S.L., Ji, X., Zhang, S.: Shortcuts to adiabatic passage for multiqubit controlled-phase gate. Phys. Rev. A 91, 032304 (2015)ADSCrossRefGoogle Scholar
  49. 49.
    Liang, Y., Song, C., Ji, X., Zhang, S.: Fast CNOT gate between two spatially separated atoms via shortcuts to adiabatic passage. Opt. Express 23, 23798–23810 (2015)ADSCrossRefGoogle Scholar
  50. 50.
    Zhang, J., Kyaw, T.H., Tong, D.M., Sjöqvist, E., Kwek, L.C.: Fast non-Abelian geometric gates via transitionless quantum driving. Sci. Rep. 5, 18414 (2015)ADSCrossRefGoogle Scholar
  51. 51.
    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)ADSCrossRefGoogle Scholar
  52. 52.
    Wu, J.L., Ji, X., Zhang, S.: Dressed-state scheme for a fast CNOT gate. Quantum Inf. Process. 16, 294 (2017)ADSMathSciNetCrossRefGoogle Scholar
  53. 53.
    Lu, M., Xia, Y., Shen, L.T., Song, J., An, N.B.: Shortcuts to adiabatic passage for population transfer and maximum entanglement creation between two atoms in a cavity. Phys. Rev. A 89, 012326 (2014)ADSCrossRefGoogle Scholar
  54. 54.
    Ye, L.X., Lin, X., Chen, X., He, J., Yang, R.C., Liu, H.Y.: Generation of GHZ states with invariant-based shortcuts. Quantum Inf. Process. 15, 2785–2796 (2016)ADSMathSciNetCrossRefGoogle Scholar
  55. 55.
    Shan, W.J., Xia, Y., Chen, Y.H., Song, J.: Fast generation of N-atom Greenberger–Horne–Zeilinger state in separate coupled cavities via transitionless quantum driving. Quantum Inf. Process. 15, 2359–2376 (2016)ADSMathSciNetCrossRefGoogle Scholar
  56. 56.
    Song, X.K., Ai, Q., Qiu, J., Deng, F.G.: Physically feasible three-level transitionless quantum driving with multiple schrödinger dynamics. Phys. Rev. A 93, 052324 (2016)ADSCrossRefGoogle Scholar
  57. 57.
    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)ADSCrossRefGoogle Scholar
  58. 58.
    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 schrödinger dynamics. Sci. Rep. 6, 36737 (2016)ADSCrossRefGoogle Scholar
  59. 59.
    Berry, M.V.: Quantum phase corrections from adiabatic iteration. Proc. R. Soc. Lond. A 414, 31 (1987)ADSMathSciNetCrossRefGoogle Scholar
  60. 60.
    Ibáñez, S., Chen, X., Torrontegui, E., Muga, J.G., Ruschhaupt, A.: Multiple schrödinger picture and dynamics in shortcuts to adiabaticity. Phys. Rev. Lett. 109, 100403 (2012)ADSCrossRefGoogle Scholar
  61. 61.
    Ibáñez, S., Chen, X., Muga, J.G.: Improving shortcuts to adiabaticity by iterative interaction pictures. Phys. Rev. A 87, 043402 (2013)ADSCrossRefGoogle Scholar
  62. 62.
    Serafini, A., Mancini, S., Bose, S.: Distributed quantum computation via optical fibers. Phys. Rev. Lett. 96, 010503 (2006)ADSCrossRefGoogle Scholar
  63. 63.
    Keller, M., Lange, B., Hayasaka, K., Lange, W., Walther, H.: A calcium ion in a cavity as a controlled single-photon source. New J. Phys. 6, 95 (2004)ADSCrossRefGoogle Scholar
  64. 64.
    Facchi, P., Pascazio, S.: Quantum zeno subspaces. Phys. Rev. lett. 89, 080401 (2002)ADSMathSciNetCrossRefGoogle Scholar
  65. 65.
    Sørensen, A.S., Mølmer, K.: Measurement induced entanglement and quantum computation with atoms. Phys. Rev. Lett. 91, 097905 (2003)ADSCrossRefGoogle Scholar
  66. 66.
    Kastoryano, M.J., Reiter, F., Sørensen, A.S.: Dissipative preparation of entanglement in optical cavities. Phys. Rev. Lett. 106, 090502 (2011)ADSCrossRefGoogle Scholar
  67. 67.
    Spillane, S.M., Kippenberg, T.J., Vahala, K.J., Goh, K. W., Wilcut, E., Kimble, H.J.: Ultrahigh-q toroidal microresonators for cavity quantum electrodynamics. Phys. Rev. A 71, 013817 (2005)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Physics, College of ScienceYanbian UniversityYanjiPeople’s Republic of China

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