Abstract
In this work, we have investigated the adiabatic shortcut for nonlinear two-level system by adding a linear counter-adiabatic field in nonlinear LZ protocol. The results show that, unlike the linear two-level system, the fidelity between the target state and the final state is highly dependent on the type of nonlinear interaction and strength. The additional linear counter-adiabatic field can promote the adiabatic process on both repulsive and attractive interactions. For the repulsive interaction, the fidelity between the final state and the target state can always reach to 1 as the time duration increases. For the attractive interaction, the additional linear counter-adiabatic field can depress the critical effects which break the adiabaticity.
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References
Berry, M.V.: Transitionless quantum driving. J. Phys. A 42(36), 365303 (2009)
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)
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)
del Campo, A.: Shortcuts to adiabaticity by counterdiabatic driving. Phys. Rev. Lett. 111, 100502 (2013)
del Campo, A.: Frictionless quantum quenches in ultracold gases: A quantum-dynamical microscope. Phys. Rev. A 84, 031606 (2011)
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)
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)
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)
Chen, X., Torrontegui, E., Muga, J. G.: Lewis-riesenfeld invariants and transitionless quantum driving. Phys. Rev. A 83, 062116 (2011)
Milburn, G. J., Corney, J., Wright, E. M., Walls, D. F.: Quantum dynamics of an atomic bose-einstein condensate in a double-well potential. Phys. Rev. A 55, 4318 (1997)
Wu, B., Niu, Q.: Nonlinear landau-zener tunneling. Phys. Rev. A 61, 023402 (2000)
Micheli, A., Jaksch, D., Cirac, J. I., Zoller, P.: Many-particle entanglement in two-component bose-einstein condensates. Phys. Rev. A 67, 013607 (2003)
Tonel, A., Links, J., Foerster, A.: Quantum dynamics of a model for two josephson-coupled bose–einstein condensates. J. Phys. A 38(6), 1235 (2005)
Dou, F. Q., Fu, L. B., Liu, J.: High-fidelity fast quantum driving in nonlinear systems. Phys. Rev. A 89, 012123 (2014)
Dou, F. Q., Cao, H., Liu, J., Fu, L. B.: High-fidelity composite adiabatic passage in nonlinear two-level systems. Phys. Rev. A 93, 043419 (2016)
Chen, X., Ban, Y., Hegerfeldt, G. C.: Time-optimal quantum control of nonlinear two-level systems. Phys. Rev. A 94, 023624 (2016)
Dou, F. Q., Liu, J., Fu, L. B.: Fast quantum driving in two-level systems with interaction and nonlinear sweep. Phys. Rev. A 98, 022102 (2018)
Leggett, A. J.: Bose-einstein condensation in the alkali gases: Some fundamental concepts. Rev. Mod. Phys. 73, 307–356 (2001)
Cirac, J. I., Lewenstein, M., Mo, K., Zoller, P.: Quantum superposition states of Bose-Einstein condensates. Phys. Rev. A 57(2), 1208–1218 (1998)
Acknowledgements
This work is supported by National Natural Science Foundation of China (NSFC) (Grants No. 11875103), and the Scientific and Technological Program of Jilin Educational Committee during the Thirteenth Five-year Plan Period (Grant No. JJKH20180009KJ).
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Liu, J.H., Zhang, Y.N., Liu, Y. et al. Adiabatic Shortcut in Nonlinear Two-Level system. Int J Theor Phys 59, 507–513 (2020). https://doi.org/10.1007/s10773-019-04345-8
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DOI: https://doi.org/10.1007/s10773-019-04345-8