International Journal of Theoretical Physics

, Volume 58, Issue 3, pp 836–843 | Cite as

Quantum-Classical Correspondence for Adiabatic Shortcut in Two- and Three-Level Atoms

  • S. Y. Chen
  • Y. N. Zhang
  • J. Yang
  • H. D. LiuEmail author
  • H. Y. SunEmail author


The methods of quickly achieving the adiabatic effect through a non-adiabatic process has recently drawn widely attention both in quantum and classical regime. In this work ,we study the classical adiabatic shortcut for two- and three-Level atoms by transforming the quantum version into classical one via quantum-classical corresponding theory. The results shows that, the additional couplings between the oscillators can be used to speed up the adiabatic evolution of coupled oscillators. Furthermore, we find that the quantum-classical correspondence theory still holds for the couter-adiabatic driving Hamiltonian for the TQD. This means that, we can obtain the counter-adiabatic driving Hamiltonian for a classical system by averaging over its quantum correspondence in a quantum system. This provides a feasible way to study the classical adiabatic shortcut and the simulation for the quantum adiabatic shortcut in a classical system.


Adiabatic shortcut Quantum-classical correspondence Stimulated Raman adiabatic passage 



This work is supported by National Natural Science Foundation of China (NSFC) (Grants No. 11875103, 11775048, and No. 11747155), the Plan for Scientific and Technological Development of Jilin Province (Grant No. 20160520173JH), and the Scientific and Technological Program of Jilin Educational Committee during the Thirteenth Five-year Plan Period (Grant No. JJKH20180009KJ, and No. JJKH20181162KJ).


  1. 1.
    Rezek, Y., Kosloff, R.: Irreversible performance of a quantum harmonic heat engine. New J. Phys. 8(5), 83 (2006)ADSCrossRefGoogle Scholar
  2. 2.
    Berry, M.V.: Transitionless quantum driving. J. Phys. A 42(36), 365303 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Chen, X., Torrontegui, E., Muga, J.G.: Lewis-riesenfeld invariants and transitionless quantum driving. Phys. Rev. A 83, 062116 (2011)ADSCrossRefGoogle Scholar
  4. 4.
    Zhang, J., Shim, J.H., Niemeyer, I., Taniguchi, T., Teraji, T., Abe, H., Onoda, S., Yamamoto, T., Ohshima, T., Isoya, J., Suter, D.: Experimental implementation of assisted quantum adiabatic passage in a single spin. Phys. Rev. Lett. 110, 240501 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    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)ADSCrossRefGoogle Scholar
  6. 6.
    del Campo, A.: Shortcuts to adiabaticity by counterdiabatic driving. Phys. Rev. Lett. 111, 100502 (2013)ADSCrossRefGoogle Scholar
  7. 7.
    del Campo, A.: Frictionless quantum quenches in ultracold gases: a quantum-dynamical microscope. Phys. Rev. A 84, 031606 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    Chen, Y.H., Shi, Z.C., Song, J., Xia, Y.: Invariant-based inverse engineering for fluctuation transfer between membranes in an optomechanical cavity system. Phys. Rev. A 97(2), 023841 (2018)ADSCrossRefGoogle Scholar
  9. 9.
    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(1), 012326 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    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(5), 052109 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    Deffner, S., Jarzynski, C., del Campo, A.: Classical and quantum shortcuts to adiabaticity for scale-invariant driving. Phys. Rev. X 4, 021013 (2014)Google Scholar
  12. 12.
    Jarzynski, C., Deffner, S., Patra, A., Subaşı, Y.: Fast forward to the classical adiabatic invariant. Phys. Rev. E 95, 032122 (2017)ADSCrossRefGoogle Scholar
  13. 13.
    From classical nonlinear integrable systems to quantum shortcuts to adiabaticity. Phys. Rev. Lett. 117(7), 070401 (2016)Google Scholar
  14. 14.
    Jarzynski, C.: Generating shortcuts to adiabaticity in quantum and classical dynamics. Phys. Rev. A 88, 040101 (2013)ADSCrossRefGoogle Scholar
  15. 15.
    Deng, J., Wang, Q.H., Liu, Z., Hä, nggi, P., Gong, J.: Boosting work characteristics and overall heat-engine performance via shortcuts to adiabaticity: Quantum and classical systems. Phys. Rev. E 88, 062122 (2013)Google Scholar
  16. 16.
    Xiao, G., Gong, J.: Suppression of work fluctuations by optimal control: An approach based on Jarzynski’s equality. Phys. Rev. E 90(5), 052132 (2014)ADSCrossRefGoogle Scholar
  17. 17.
    Polchinski, J.: Weinberg’s nonlinear quantum mechanics and the einstein-podolsky-rosen paradox. Phys. Rev. Lett. 66, 397–400 (1991)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Heslot, A.: Quantum mechanics as a classical theory. Phys. Rev. D 31, 1341–1348 (1985)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Weinberg, S.: Testing quantum mechanics. Ann. Phys. 194(2), 336–386 (1989)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Wu, B., Liu, J., Niu, Q.: Geometric phase for adiabatic evolutions of general quantum states. Phys. Rev. Lett. 94, 140402 (2005)ADSCrossRefGoogle Scholar
  21. 21.
    Zhang, Q., Wu, B.: General approach to quantum-classical hybrid systems and geometric forces. Phys. Rev. Lett. 97, 190401 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    Stone, M.: Born-oppenheimer approximation and the origin of wess-zumino terms: Some quantum-mechanical examples. Phys. Rev. D 33, 1191–1194 (1986)ADSCrossRefGoogle Scholar
  23. 23.
    Gozzi, E., Thacker, W.D.: Classical adiabatic holonomy and its canonical structure. Phys. Rev. D 35, 2398–2406 (1987)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Liu, H.D., Wu, S.L., Yi, X.X.: Berry phase and hannay’s angle in a quantum-classical hybrid system. Phys. Rev. A 83, 062101 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    Chen, X., Lizuain, I., Ruschhaupt, A., Guéry-Odelin, D., Muga, J.G.:Google Scholar
  26. 26.
    Berry, M.V.: Classical adiabatic angles and quantal adiabatic phase. J. Phys. A 18(1), 15 (1985)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Torosov, B.T., Della Valle, G., Longhi, S.: Non-Hermitian shortcut to stimulated Raman adiabatic passage. Phys. Rev. A 89(6), 063412 (2014)ADSCrossRefGoogle Scholar
  28. 28.
    Wu, S., Huang, X., Li, H., Yi, X.: Adiabatic evolution of decoherence-free subspaces and its shortcuts. Phys. Rev. A 96(4), 042104 (2017)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Center for Quantum Sciences and School of PhysicsNortheast Normal UniversityChangchunChina
  2. 2.International Education Teachers SchoolChangchun Normal UniversityChangchunChina

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