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Quantum State Conversion in Two-Level System Without Rotating-Wave Approximation via Non-Hermitian Shortcuts to Adiabaticity

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Abstract

Adiabatic theorem has found many important applications in quantum physics. Shortcuts to adiabaticity can effectively accelerate adiabatic process. We consider a two-level system (TLS) without rotating-wave approximation (RWA). Here, we propose a scheme to implement quantum state completely transfer. In our scheme, by adding unbalanced imaginary terms, now the Hamiltonian of the system is non-Hermitian form, we can nullify the nonadiabatic coupling and achieve fast quantum state conversion with high fidelity. The perfect population transfer can be achieved within a short time.

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References

  1. Demirplak, M., Rice, S.A.: J. Phys. Chem. A 107, 9937 (2003)

    Article  Google Scholar 

  2. Huang, X.B., Chen, Y.H., Wang, Z.: Sci. Rep. 6, 25707 (2016)

    Article  ADS  Google Scholar 

  3. Sun, J., Lu, S.F., Liu, F.: Sci. China-Phys. Mech. Astron. 55, 1630 (2012)

    Article  ADS  Google Scholar 

  4. Chen, X., Lizuain, I., Ruschhaupt, A., Guéry-Odelin, D., Muga, J.G.: Phys. Rev. Lett. 105, 123003 (2010)

    Article  ADS  Google Scholar 

  5. Ibáñez, S., Chen, X., Muga, J.G.: Phys. Rev. A 87, 043402 (2013)

    Article  ADS  Google Scholar 

  6. Paul, K., Sarma, A.K.: Phys. Rev. A 94, 052303 (2016)

    Article  ADS  Google Scholar 

  7. Campbell, S., De Chiara, G., Paternostro, M., Palma, G.M., Fazio, R.: Phys. Rev. Lett. 114, 177206 (2015)

    Article  ADS  Google Scholar 

  8. Okuyama, M., Takahashi, K.: Phys. Rev. Lett. 117, 070401 (2016)

    Article  ADS  Google Scholar 

  9. Kang, Y.H., Chen, Y.H., Wu, Q.C., Huang, B.H., Xia, Y., Song, J.: Sci. Rep. 6, 30151 (2016)

    Article  ADS  Google Scholar 

  10. Martnez-Garaot, S., Torrontegui, E., Chen, X., Muga, J.G.: Phys. Rev. A 89, 053408 (2014)

    Article  ADS  Google Scholar 

  11. Opatrný, T., Mømer, K.: New J. Phys. 16, 015025 (2014)

    Article  ADS  Google Scholar 

  12. Ibáñez, S., Chen, X., Torrontegui, E., Muga, J.G., Ruschhaupt, A.: Phys. Rev. Lett. 109, 100403 (2012)

    Article  ADS  Google Scholar 

  13. Chen, Y.H., Wu, Q.C., Huang, B.H., Xia, Y., Song, J.: Phys. Rev. A 93, 052109 (2016)

    Article  ADS  Google Scholar 

  14. Song, X.K., Ai, Q., Qiu, J., Deng, F.G.: Phys. Rev. A 93, 052324 (2016)

    Article  ADS  Google Scholar 

  15. Takahashi, K.: Phys. Rev. E 87, 062117 (2013)

    Article  ADS  Google Scholar 

  16. Shi, X., Wei, L.F.: Laser. Phys. Lett. 12, 015204 (2015)

    Article  ADS  Google Scholar 

  17. Demirplak, M., Rice, S.A.: J. Phys. Chem. B 109, 6838 (2005)

    Article  Google Scholar 

  18. Demirplak, M., Rice, S.A.: J. Chem. Phys. 129, 154111 (2008)

    Article  ADS  Google Scholar 

  19. Del Campo, A.: Phys. Rev. Lett. 111, 100502 (2013)

    Article  ADS  Google Scholar 

  20. Chen, Y.H., Xia, Y., Wu, Q.C., Huang, B.H., Song, J.: Phys. Rev. A 93, 052109 (2016)

    Article  ADS  Google Scholar 

  21. Kiely, A., Ruschhaupt, A.: J. Phys. B 47, 115501 (2014)

    Article  ADS  Google Scholar 

  22. Masuda, S., Rice, S.A.: Phys. Rev. A 89, 033621 (2014)

    Article  ADS  Google Scholar 

  23. Chen, X., Torrontegui, E., Muga, J.G.: Phys. Rev. A 83, 062116 (2011)

    Article  ADS  Google Scholar 

  24. Allen, L., Eberly, J.H.: Optical Resonance and Two-level Atoms. Dover, New York (1987)

    Google Scholar 

  25. Chan, S., Reid, M.D., Ficek, Z.: J. Phys. B 42, 065507 (2009)

    Article  ADS  Google Scholar 

  26. Irish, E.K.: Phys. Rev. Lett. 99, 259901 (2007)

    Article  ADS  Google Scholar 

  27. Klimov, A.B., Sainz, I., Chumakov, S.M.: Phys. Rev. A 68, 063811 (2003)

    Article  ADS  Google Scholar 

  28. Casanova, J., Romero, G., Lizuain, I., García-ripoll, J.J., Solano, E.: Phys. Rev. Lett. 105, 263603 (2010)

    Article  ADS  Google Scholar 

  29. Fedorov, A., Feofanov, A.K., Macha, P., Forn-díaz, P., Harmans, C.J.P.M., Mooij, J.E.: Phys. Rev. Lett. 105, 060503 (2010)

    Article  ADS  Google Scholar 

  30. Irish, E.K.: Phys. Rev. Lett. 99, 173601 (2007)

    Article  ADS  Google Scholar 

  31. Bourassa, J., Gambetta, J.M., Abdumalikov, A.A., Astafiev, O., Nakamura, Y., Blais, A.: Phys. Rev. A 80, 032109 (2009)

    Article  ADS  Google Scholar 

  32. Zhang, Y.Y., Chen, Q.H., Wang, K.L.: Phys. Rev. B 81, 121105 (2010)

    Article  ADS  Google Scholar 

  33. Lizuain, I., Muga, J.G., Eschner, J.: Phys. Rev. A 77, 053817 (2008)

    Article  ADS  Google Scholar 

  34. Liu, T., Wang, K.L., Feng, M.: Europhys. Lett. 86, 54003 (2009)

    Article  ADS  Google Scholar 

  35. Zheng, H., Zhu, S.Y., Zubairy, M.S.: Phys. Rev. Lett. 101, 200404 (2008)

    Article  ADS  Google Scholar 

  36. Ibáñez, S., Li, Y.C., Chen, X., Muga, J.G.: Phys. Rev. A 92, 062136 (2015)

    Article  ADS  Google Scholar 

  37. Niemczyk, T., Deppe, F., Huebl, H., Menzel, E.P., Hocke, F., Schwarz, M.J., Garcia-Ripoll, J.J., Zueco, D., Hümmer, T., Solano, E., Marx, A., Gross, R.: Nat. Phys. 6, 772 (2010)

    Article  Google Scholar 

  38. Ashhab, S., Nori, F.: Phys. Rev. A 81, 042311 (2010)

    Article  ADS  Google Scholar 

  39. Forn-Díaz, P., Lisenfeld, J., Marcos, D., García-Ripoll, J.J., Solano, E., Harmans, C.J.P.M., Mooij, J.E.: Phys. Rev. Lett. 105, 237001 (2010)

    Article  ADS  Google Scholar 

  40. Torosov, B.T., Valle, G.D., Longhi, S.: Phys. Rev. A 87, 052502 (2013)

    Article  ADS  Google Scholar 

  41. Torosov, B.T., Valle, G.D., Longhi, S.: Phys. Rev. A 89, 063412 (2014)

    Article  ADS  Google Scholar 

  42. Moiseyev, N.: Non-Hermitian Quantum Mechanics. Cambridge University Press, Cambridge (2011)

    Book  MATH  Google Scholar 

  43. Bender, C.M., Boettcher, S.: Phys. Rev. Lett. 80, 5243 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  44. Bender, C.M.: Rep. Prog. Phys. 70, 957 (2007)

    Article  ADS  Google Scholar 

  45. Mostafazadeh, A.: J Math. Phys. 43, 205 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  46. Mostafazadeh, A.: J. Phys. A 36, 7081 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  47. Uzdin, R., Günther, U., Rahav, S., Moiseyev, N.: J. Phys. A: Math. Theor. 45, 415304 (2012)

    Article  Google Scholar 

  48. Reyes, S.A., Olivares, F.A., Morales-Molina, L.: J. Phys. A: Math. Theor. 45, 444027 (2012)

    Article  ADS  Google Scholar 

  49. Hang, C., Huang, G., Konotop, V.V.: Phys. Rev. Lett. 110, 083604 (2013)

    Article  ADS  Google Scholar 

  50. Ibánez, S., Muga, J.G.: Phys. Rev. A 89, 033403 (2014)

    Article  ADS  Google Scholar 

  51. Ibánez, S., Martinez-Garaot, S., Chen, X., Torrontegui, E., Muga, J.G.: Phys. Rev. A 84, 023415 (2011)

    Article  ADS  Google Scholar 

  52. Paul, K., Sarma, A.K.: Phys. Rev. A 91, 053406 (2015)

    Article  ADS  Google Scholar 

  53. Kenmoe, M.B., Tchouobiap, S.E.M., Sadem, C.K., Tchapda, A.B., Fai, L.C.: J. Phys. A 48, 095303 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  54. Schilling, R., Vogelsberger, M., Garanin, D.A.: J. Phys. A: Math. Gen. 39, 13727 (2006)

    Article  ADS  Google Scholar 

  55. Rüter, C. E., Makris, K.G., El-Ganainy, R., Christodoulides, D.N., Segev, M., Kip, D.: Nat. Phys. 6, 192 (2010)

    Article  Google Scholar 

  56. El-Ganainy, R., Makris, K.G., Christodoulides, D.N.: Phys. Rev. A 86, 033813 (2012)

    Article  ADS  Google Scholar 

  57. Hristova, H.S., Rangelov, A.A., Montemezzani, G., Vitanov, N.V.: Phys. Rev. A 93, 033802 (2016)

    Article  ADS  Google Scholar 

  58. Chen, X., Torrontegui, E., Muga, J.G.: Phys. Rev. A 83, 062116 (2011)

    Article  ADS  Google Scholar 

  59. Chen, X., Lizuain, I., Ruschhaupt, A., Gu éry-Odelin, D., Muga, J.G.: Phys. Rev. Lett. 105, 123003 (2010)

    Article  ADS  Google Scholar 

  60. Zhang, J., Shim, J.H., Niemeyer, I., Taniguchi, T., Teraji, T., Abe, H., Onoda, S., Yamamoto, T., Ohshima, T., Isoya, J., Suter, D.: Phys. Rev. Lett. 110, 240501 (2013)

    Article  ADS  Google Scholar 

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Acknowledgments

This work is supported by National Natural Science Foundation of China (NSFC) under Grants No.11347013, Scientific Research Fundation of the Education Department of Jilin Province under Grants No. JJKH20190764KJ, and Specialized Fund for the Doctoral Research of Jilin Engineering Normal University under Grants No. BSKJ201825, XYB201820.

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Authors and Affiliations

  1. Institute for Interdisciplinary Quantum Information Technology, Jilin Engineering Normal University, Changchun, 130052, China

    Hong Li, Si-Qi Zhang, Mei-Xuan Li, Ming Guo & Li-Jun Song

  2. Jilin Engineering Laboratory for Quantum Information Technology, Changchun, 130052, China

    Hong Li, Si-Qi Zhang, Mei-Xuan Li, Ming Guo & Li-Jun Song

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  1. Hong Li
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  2. Si-Qi Zhang
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  3. Mei-Xuan Li
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Correspondence to Li-Jun Song.

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Li, H., Zhang, SQ., Li, MX. et al. Quantum State Conversion in Two-Level System Without Rotating-Wave Approximation via Non-Hermitian Shortcuts to Adiabaticity. Int J Theor Phys 58, 2692–2702 (2019). https://doi.org/10.1007/s10773-019-04159-8

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