Abstract
A scheme is proposed to generate three-atom GHZ states by applying the inversely engineered control method on the basis of Lewis–Riesenfeld invariants. In the proposal, three atoms that have different configurations are trapped in a bimodal cavity. Numerical simulations indicate that our protocol has an obvious improvement of speed for the generation of GHZ states. Moreover, the present scheme is robust against both parameter fluctuations and dissipation.
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Greenberger, D.M., Horne, M.A., Zeilinger, A.: Going beyond Bell’s theorem. In: Kafatos, M. (ed.) Bell’s Theorem, Quantum Theory, and Conceptions of the Universe. Kluwer Academics, Dordrecht (1989)
Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)
Zhang, Z.J., Man, Z.X.: Multiparty quantum secret sharing of classical messages based on entanglement swapping. Phys. Rev. A 72, 022303 (2005)
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)
Gisin, N., Massar, S.: Optimal quantum cloning machines. Phys. Rev. Lett. 79, 2153 (1993)
Schupper, N., Friedmann, H., Matusovsky, M., Rosenbluh, M., Wilson-Gordon, A.D.: Propagation of high-intensity short resonant pulses in inhomogeneously broadened media. J. Opt. Soc. Am. B. 16, 001127 (1999)
Eilam, A., Wilson-Gordon, A.D., Friedmann, H.: Enhanced frequency conversion of nonadiabatic resonant pulses in coherently prepared \(\Lambda \) systems. Phys. Rev. A 73, 053805 (2006)
Ackerhal, J.R.: Resonant pulse excitation leading to ionization. Phys. Rev. A 17, 293 (1978)
Openov, L.A.: Resonant pulse operations on the buried donor charge qubits in semiconductors. Phys. Rev. B 70, 233313 (2004)
Panek, P., Becker, A.: Dark pulses for resonant two-photon transitions. Phys. Rev. A 74, 023408 (2006)
Vasilev, G.S., Kuhn, A., Vitanov, N.V.: Optimum pulse shapes for stimulated Raman adiabatic passage. Phys. Rev. A 80, 013417 (2009)
Bergmann, K., Theuer, H., Shore, B.W.: Coherent population transfer among quantum states of atoms and molecules. Rev. Mod. Phys. 70, 1003 (1998)
Yang, R.C., Lin, X., Ye, L.X., Chen, X., He, J., Liu, H.Y.: Generation of singlet states with Rydberg blockade mechanism and driven by adiabatic passage. Quantum Inf. Process. 15, 731 (2016)
Rangelov, A.A., Vitanov, N.V., Arimondo, E.: Stimulated Raman adiabatic passage into continuum. Phys. Rev. A 76, 043414 (2007)
Kral, P., Thanopulos, I., Shapiro, M.: Coherently controlled adiabatic passage. Rev. Mod. Phys. 79, 53 (2007)
Kuklinski, J.R., Gaubatz, U., Hioe, F.T., Bergmann, K.: Adiabatic population transfer in a three-level system driven by delayed laser pulses. Phys. Rev. A 40, 6741 (1989)
Lu, M., Xia, Y., Song, J., Song, H.Shan: Driving three atoms into a singlet state in an optical cavity via adiabatic passage of a dark state. J. Phys. B At. Mol. Opt. Phys. 46, 015502 (2013)
Vitanov, N.V., Suominen, K.A., Shore, B.W.: Creation of coherent atomic superpositions by fractional stimulated Raman adiabatic passage. J. Phys. B At. Mol. Opt. Phys. 32, 4535 (1999)
Dridi, G., Guérin, S., Hakobyan, V., Jauslin, H.R., Eleuch, H.: Ultrafast stimulated Raman parallel adiabatic passage by shaped pulses. Phys. Rev. A 80, 043408 (2009)
Eleuch, H., Guérin, S., Jauslin, H.R.: Effects of an environment on a cavity-quantum-electrodynamics system controlled by bichromatic adiabatic passage. Phys. Rev. A 85, 013830 (2012)
Amniat-Talab, M., Guérin, S., Jauslin, H.R.: Generation of entanglement via adiabatic passage. Phys. Rev. A 72, 012339 (2005)
Chen, X., Lizuain, I., Ruschhaupt, A., Guery-Odelin, D., Muga, J.G.: Shortcut to adiabatic passage in two- and three-Level atoms. Phys. Rev. Lett. 105, 123003 (2010)
Chen, X., Muga, J.G.: Engineering of fast population transfer in three-level systems. Phys. Rev. A 86, 033405 (2012)
Chen, X., Torrontegui, E., Muga, J.G.: Lewis–Riesenfeld invariants and transitionless quantum driving. Phys. Rev. A 83, 062116 (2011)
Lewis Jr., H.R., Riesenfeld, W.B.: An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent electromagnetic field. J. Math. Phys. 10, 1458 (1969)
Torrontegui, E., Martìnez-Garaot, S., Ruschhaupt, A., Muga, J.G.: Shortcuts to adiabaticity: fast-forward approach. Phys. Rev. A 86, 013601 (2012)
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 (2013)
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)
Lu, X.J., Chen, X., Ruschhaupt, A., Alonso, D., Guerin, S., Muga, J.G.: Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors. Phys. Rev. A 88, 033406 (2013)
Ruschhaupt, A., Chen, X., Alonso, D., Muga, J.G.: Optimally robust shortcuts to population inversion in two-level quantum systems. N. J. Phys. 14, 093040 (2012)
Xiao, Y.F., Zou, X.B., Guo, G.C.: Generation of atomic entangled states with selective resonant interaction in cavity quantum electrodynamics. Phys. Rev. A 75, 012310 (2007)
Zou, X.B., Xiao, Y.F., Guo, G.C.: Quantum phase gate through a dispersive atom–field interaction. Phys. Rev. A 75, 064301 (2007)
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)
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Grant Nos. 61308012 and 61275215), the Natural Science Foundation of Fujian Province of China (Grant Nos. 2013J01008 and 2012J01004) and the Foundation of Fujian Educational Department (Grant Nos. JA14075, JB13021 and JB12014).
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Ye, LX., Lin, X., Chen, X. et al. Generation of GHZ states with invariant-based shortcuts. Quantum Inf Process 15, 2785–2796 (2016). https://doi.org/10.1007/s11128-016-1303-2
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DOI: https://doi.org/10.1007/s11128-016-1303-2