Abstract
Optomechanical cavities are one of the most important systems for observing quantum phenomena. In this paper, we investigated the quantum aspect of an optomechanical system made up of a two-level atom under two laser pump stimulation. One of the laser pumps drives the optical cavity, known as a longitudinal pump, while the second laser was used to excite the atom inside the cavity, directly and called as transverse pump. We observe the quasi-random walk of atom inside the cavity. Next, entanglement evolution among the atomic states and the other parts of the system with the von Neumann entropy measure was investigated. The study was done for distinctive atomic states in a strong coupling regime between the atom and field of cavity. Also, we investigated the evidence for non-Markovian behavior with trace distance measure. Our results demonstrate that the random walk of the atom can offer assistance to us to upgrade the entanglement between the inside atom mode and the other parts of the system for a long time. Furthermore, adding atomic motion provides evidence for the non-Markovian treatment of the system at the initial time.
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10 April 2024
A Correction to this paper has been published: https://doi.org/10.1007/s11082-024-06505-5
References
Abramovici, A., et al.: LIGO: The laser interferometer gravitational-wave observatory. Science 256, 325 (1992)
Aharonov, Y., Davidovich, L., Zagury, N.: Quantum random walks. Phys. Rev. A 48, 1687 (1993)
Aspelmeyer, M., Kippenberg, T.J., Marquardt, F.: Cavity optomechanics. Rev. Mod. Phys. 86, 1391 (2014)
Baghshahi, H.R., Tavassoly, M.K., Faghihi, M.J.: Entanglement criteria of two two-level atoms interacting with two coupled modes. Int. J. Theor. Phys. 54, 2839–2854 (2015)
Bai, C.H., Wang, D.Y., Zhang, S., Liu, S., Wang, H.F.: Atom-mirror entanglement: modulation-based atom-mirror entanglement and mechanical squeezing in an unresolved-sideband optomechanical system, Ann. Phys. 1800271 (2019).
Barzanjeh, Sh., Naderi, M.H., Soltanolkotabi, M.: Steady-state entanglement and normal-mode splitting in an atom-assisted optomechanical system with intensity-dependent coupling. Phys. Rev. A 84, 063850 (2011)
Bennett, C.H., Wiesner, S.J.: Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992)
Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)
Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824 (1996)
Bose, S., Jacobs, K., Knight, P.L.: Preparation of nonclassical states in cavities with a moving mirror. Phys. Rev. A 56, 4175 (1997)
Braginsky, V.B., Strigin, S.E., Vyatchanin, S.P.: Parametric oscillatory instability in Fabry-Perot interferometer. Phys. Lett. A 287, 331 (2001)
Brennete, F., Donner, T., Ritter, S., Bourdel, T., Köhl, M., Esslinger, T.: Cavity QED with a bose-einstein condensate. Nature 450, 268 (2007)
Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford. (2002)
Breuer, H.P., Laine, E.M., Piilo, J.: Measure for the degree of non-Markovian behavior of quantum processes in open systems. Phys. Rev. Lett. 103, 210401 (2009)
Breuer, H.P., Laine, E.M., Piilo, J., Vacchini, B.: Non-Markovian dynamics in open quantum systems. Rev. Mod. Phys. 88, 021002 (2016)
Brif, C., Mann, A.: Quantum statistical properties of the radiation field in a cavity with a movable mirror. J. Opt. B Quantum Semi Class. Opt. 2, 53 (2000)
Chen, X., Liu, Y.C., Peng, P., Zhi, Y., Xiao, Y.F.: Cooling of macroscopic mechanical resonators in hybrid atom-optomechanical systems. Phys. Rev. A 92, 033841 (2015)
Childs, A.M.: Universal computation by quantum walk. Phys. Rev. Lett. 102, 180501 (2009)
Childs, A.M., Goldstone, J.: Spatial search by quantum walk. Phys. Rev. A 70, 022314 (2004)
Cohen-Tannoudji, C.: Nobel lecture, nobel lecture: manipulating atoms with photons. Rev. Mod. Phys. 70, 707 (1998)
Deutsch, D., Ekert, A.: Quantum computation. Phys. World 11(3), 47 (1998)
Gardiner, C.W., Zoller, P.: Quantum Noise. Springer, New York. (2004)
Genes, C., Vitali, D., Tombesi, P.: Emergence of atom-light-mirror entanglement inside an optical cavity. Phys. Rev. A 77, 050307(R) (2008)
Gerry, C., Knight, P.: Introductory Quantum Optics. Cambridge University Press, Cambridge (2004)
Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)
Hammerer, K., Wallquist, M., Genes, C., Ludwig, M., Marquardt, F., Treutlein, P., Zoller, P., Ye, J., Kimble, H.J.: Strong coupling of a mechanical oscillator and a single atom. Phys. Rev. Lett. 103, 063005 (2009)
Hill, S.A., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022 (1997)
Hinkel, T., Ritsch, H., Genes, C.: A realization of a quasi-random walk for atoms in time-dependent optical potentials. Atoms 3(3), 433–449 (2015)
Holstein, T., Primakoff, H.: Field dependence of the intrinsic domain magnetization of a ferromagnet. Phys. Rev. 58, 1098 (1940)
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)
Ian, H., Gong, Z.R., Liu, Y.-X., Sun, C.P., Nori, F.: Cavity optomechanical coupling assisted by an atomic gas. Phys. Rev. A 78, 013824 (2008)
Imamog, A., Awschalom, D.D., Burkard, G., Di Vincenzo, D.P., Loss, D.: Quantum information processing using quantum dot spins and cavity QED. Phys. Rev. Lett. 83(20), 4204 (1999)
Imran, M., Abbas, T., Islam, R., Ikram, M.: Cavity QED based tuneable, delayed-choice quantum eraser. Annals of Phys. 364, 160 (2016)
Imran, M., Islam, R., Saeed, M.H., Ikram, M.: Quantum three-box paradox: a proposal for atom optics implementation. Quantum Inf. Process. 20, 1–18 (2021)
Islam, R., Haider, S.A., Abbas, T., Ikram, M.: Matter-wave teleportation via cavity-field trans-pads. Laser Phys. Lett. 13, 105204 (2016)
Islam, R., Ikram, M., Mujtaba, A.H., Abbas, T.: Double slit experiment with quantum detectors: mysteries, meanings, misinterpretations, and measurement. Laser Phys. Lett. 15, 015208 (2018)
Johansson, J.R., Nation, P.D., Nori, F.: QuTiP: An open-source Python framework for the dynamics of open quantum systems. Comp. Phys. Commun. 183, 1760–1772 (2012)
Johansson, J.R., Nation, P.D., Nori, F.: QuTiP: an open-source Python framework for the dynamics of open quantum systems. Comp. Phys. Commun. 184, 1234 (2013)
Kumar, A.: Multiparty quantum mutual information: an alternative definition. Phys. Rev. A 96, 012332 (2017)
Laine, E.M., Piilo, J., Breuer, H.-P.: Measure for the non-Markovianity of quantum processes. Phys. Rev. A 81, 062115 (2010)
Leibrandt, D.R., Labaziewicz, J., Vuletic, V., Chuang, I.L.: Cavity sideband cooling of a single trapped ion. Phys. Rev. Lett. 103, 103001 (2009)
Man’ko, V.I., Marmo, G., Zaccaria, F., Sudarshan, E.C.G.: f-Oscillators and nonlinear coherent states. Phys. Scr. 55, 528 (1997)
Marshall, W., Simon, C., Penrose, R., Bouwmeester, D.: Towards quantum superpositions of a mirror. Phys. Rev. Lett. 91, 159903 (2003)
Mc, J.D., Cullen, P.M., Wright, E.M.: Mirror confinement and control through radiation pressure. Opt. Lett. 9, 193 (1984)
Meystre, P., Wright, E.M., Cullen, J.D.M., Vignes, E.: Theory of radiation-pressure-driven interferometers. J. Opt. Soc. Am. 2, 1830 (1985)
Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655 (2012)
Mohammadi, M., Jami, S.: Time evolution of entanglement and trace distance in an atom-cavity system described with a random walk and non-random walk states.". Optik 181, 582–587 (2019)
Mohammadi, M., Jami, S., KhazaeiNezhad, M.: Entanglement dynamics in the atom-cavity system with atom quasi-random walk behavior. Opt. Quantum Electron. 54, 12 (2022)
Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press, Cambridge, England. (2000)
Phillips, W.D.: Nobel lecture, nobel lecture: laser cooling and trapping of neutral atoms. Rev. Mod. Phys. 70, 721 (1998)
Pirandola, S., Mancini, S., Vitali, D.: Erratum: Conditioning two-party quantum teleportation within a three-party quantum channel. Phys. Rev. A 71, 042326 (2005)
Poldy, R., Buchler, B.C., Close, J.D.: Single-atom detection with optical cavities. Phys. Rev. A 78, 013640 (2008)
Rivas, A., Huelga, S.F., Plenio, M.B.: Quantum non-Markovianity: characterization, quantification and detection. Rep. Prog. Phys. 77, 094001 (2014)
Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge. (1997)
Shenvi, N., Kempe, J., Birgitta Whaley, K.: Quantum random-walk search algorithm. Phys. Rev. A 67, 052307 (2003)
Uhlmann, A.: Fidelity, and concurrence of conjugated states. Phys. Rev. A 62, 032307 (2000)
Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)
Wallquist, M., Hammerer, K., Zoller, P., Genes, C., Ludwig, M., Marquardt, F., Treutlein, P., Ye, J., Kimble, H.J.: Single-atom cavity QED and optomicromechanics. Phys. Rev. A 81, 023816 (2010)
Wang, J., Manouchehri, K.: Physical Implementation of Quantum Walks. Springer, Berlin (2014)
Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)
Zhang, W.Z., Cheng, J., Li, W.D., Zhou, L.: Optomechanical cooling in the non-Markovian regime. Phys. Rev. A 93, 063853 (2016)
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Mohammadi, M., Jami, S. & Khazaei Nezhad, M. Enhancing entanglement and non-Markovianity in an optomechanical system via atom quasi-random walk motion. Opt Quant Electron 56, 258 (2024). https://doi.org/10.1007/s11082-023-05707-7
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DOI: https://doi.org/10.1007/s11082-023-05707-7