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Quantum dynamics of a f-deformed opto-mechanical system. (English) Zbl 1517.81020

Summary: Based on the f-oscillator formalism, we introduce a nonlinear optomechanical framework which is constructed from the standard optomechanical system by deforming the single-mode photonic-field operators. Such a generalized optomechanical system describes an intensity-dependent interaction of a mechanical oscillator with a single-mode electromagnetic field. To gain insight into the effectiveness of the non-linearization processes, we investigate the role of the involving parameters especially the nonlinearity function that controls the entanglement and statistical properties of the photon-phonon state was considered. Thus, we apply the linear entropy measure and the Wigner function to quantify the entanglement and non-classical properties of this composite system and the condition in which quantum entanglement and negativity of the Wigner function can be enhanced and maximized has been identified. Thus, depending on an election of the nonlinearity function, one can observe different non-classical effects. These trends are compared with those obtained for the standard optomechanical system including photon-phonon interaction, too.

MSC:

81P40 Quantum coherence, entanglement, quantum correlations
94A17 Measures of information, entropy
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
81V80 Quantum optics
78A40 Waves and radiation in optics and electromagnetic theory
76Q05 Hydro- and aero-acoustics
Full Text: DOI

References:

[1] Jaynes, ET; Cummings, FW, Comparison of quantum and semiclassical radiation theories with application to the beam maser, Proc. IEEE., 51, 89 (1963) · doi:10.1109/PROC.1963.1664
[2] Gentile, TT; Hughey, BJ; Klepnner, D., Nonlinear Jaynes-Cummings model of atom-field interaction, Phys. Rev. A, 40, 5103 (1989) · doi:10.1103/PhysRevA.40.5103
[3] Moya-Cessa, H.; Buzek, V.; Kim, MS; Knight, PL, Intrinsic decoherence in the atom-field interaction, Phys. Rev. A, 48, 3900 (1993) · doi:10.1103/PhysRevA.48.3900
[4] Joshi, A.; Xiao, M., Atomic-coherence effect on the Jaynes-Cummings model with atomic motion, J. Opt. Soc. Am. B, 21, 1685 (2004) · doi:10.1364/JOSAB.21.001685
[5] Eberly, JH; Narozhny, NB; Sanchez-Mongragon, JJ, Periodic spontaneous collapse and revival in a simple quantum model, Phys. Rev. Lett., 44, 1323 (1980) · Zbl 1404.81338 · doi:10.1103/PhysRevLett.44.1323
[6] Rempe, G.; Walther, H., Observation of quantum collapse and revival in a one-atom maser, Phys. Rev. Lett., 58, 353 (1987) · doi:10.1103/PhysRevLett.58.353
[7] Mahdifar, A.; Jamshidi Farsani, M.; Bagheri Harouni, M., Curvature effects on the interaction of nonlinear sphere coherent states with a three-level atom, J. Opt. Soc. Am. B, 30, 2952 (2013) · doi:10.1364/JOSAB.30.002952
[8] Buck, B.; Sukumar, CV, Stark and Kerr effects on the dynamics of moving N-level atomic system, Phys. Lett. A, 81, 132 (1981) · doi:10.1016/0375-9601(81)90042-6
[9] Buzek, V., Jaynes-cummings model with intensity-dependent coupling interacting with Holstein-Primakoff SU(1,1) coherent state, Phys. Rev. A, 39, 3196 (1989) · doi:10.1103/PhysRevA.39.3196
[10] Crnugelj, J.; Martinis, M.; Mikuta-Martinis, V., Properties of a deformed Jaynes-Cummings model, Phys. Rev. A, 50, 1785 (1994) · Zbl 0941.81666 · doi:10.1103/PhysRevA.50.1785
[11] Cordero, S.; Recamier, J., The f-deformed Jaynes-Cummings model and its nonlinear coherent states, J. Phys. B: At. Mol. Opt. Phys., 44, 135502 (2011) · doi:10.1088/0953-4075/44/13/135502
[12] Tavis, M.; Cummings, FW, Exact solution for an N-molecule-radiatin-field-Hamiltonian, Phys. Rev., 170, 379 (1968) · doi:10.1103/PhysRev.170.379
[13] Agarwal, GS; Puri, RR, Collapse and revival phenomenon in the evolution of a resonant field in a Kerr-like medium, Phys. Rev. A, 39, 2969 (1989) · doi:10.1103/PhysRevA.39.2969
[14] Gora, P.; Jedrzejek, C., Nonlinear Jaynes-Cummings model, Phys. Rev. A, 45, 6816 (1992) · doi:10.1103/PhysRevA.45.6816
[15] Xie, R-H; Gong-ou, X.; Liu, D-H, Study of squeezing propertiesnin a two-level system, Aust. J. Phys., 48, 907 (1995) · doi:10.1071/PH950907
[16] Werner, MJ; Risken, H., Quantum optical electromagnetic field and Rabi oscillation in time-varying medium, Quantum Opt., 3, 185 (1991) · doi:10.1088/0954-8998/3/3/005
[17] Sivakumar, S., Nonlinear Jaynes-Cummings model of Atom-Field interaction, Int. J. Theo. Phys., 43, 2405 (2004) · Zbl 1059.81197 · doi:10.1007/s10773-004-7707-2
[18] Walentowitz, S.; Vogel, W., Quantum-mechanical counterpart of nonlinear optics, Phys. Rev. A, 55, 4438 (1997) · doi:10.1103/PhysRevA.55.4438
[19] de Matos, RL; Vogel, W., Engineering the Hamiltonian of a trapped atom, Phys. Rev. A, 58, R1661 (1998) · doi:10.1103/PhysRevA.58.R1661
[20] Bagheri Harouni, M.; Roknizadeh, R.; Naderi, MH, Q-deformed description of excitons and associated physical results, J. Phys. B: At. Mol. Opt. Phys., 42, 095501 (2009) · doi:10.1088/0953-4075/42/9/095501
[21] Aspelmeyer, M.; Kippenberg, TJ; Marquardt, F., Cavity optomechanics, Phys. Rev. Mod, 86, 1391 (2014) · doi:10.1103/RevModPhys.86.1391
[22] Weiss, T.; Nunnenkamp, A., Fast cooling in dispersively and dissipatively coupled optomechanics, Phys. Rev. A., 88, 023850 (2013) · doi:10.1103/PhysRevA.88.023850
[23] Barzanjeh, S.; Vitali, D.; Tombesi, P.; Milburn, G., Entangling optical and microwave cavity modes by means of a nanomechanical resonator, Phys. Rev. A., 84, 042342 (2011) · doi:10.1103/PhysRevA.84.042342
[24] Li, HK; Ren, XX; Liu, YC; Xiao, YF, Optomechanical electromagnetically induced transparency, Phys. Rev. A., 88, 053850 (2013) · doi:10.1103/PhysRevA.88.053850
[25] Liao, J.Q., Nori, F.: Photon blockade in quadratically coupled optomechanical systems, vol. 88, p 023853 (2013)
[26] Agarwal, GS; Tara, K., Nonclassical properties of states generated by the excitations on a coherent state, Phys, Rev. A, 43, 492 (1991) · doi:10.1103/PhysRevA.43.492
[27] Wang, XG, Two-mode nonlinear coherent states, Opt. Commun., 178, 365 (2000) · doi:10.1016/S0030-4018(00)00672-6
[28] Liang, X.; Guo, Q.; Yuan, W., Nonclassical Properties of an opto-mechanical system initially prepared in N-headed cat state and number state, Int. J. Theo. Phys., 58, 58 (2019) · Zbl 1412.81185 · doi:10.1007/s10773-018-3909-x
[29] Hassani Nadiki, M.; Tavassolya, MK; Yazdanpanah, N., A trapped ion in an optomechanical system: entanglement dynamics, Eur. Phys. J. D, 72, 110 (2018) · doi:10.1140/epjd/e2018-80778-6
[30] Buck, B.; Sukumar, CV, Exactly soluble model of atom-phonon coupling showing periodic decay and revival, Phys. Lett. A, 81, 132 (1981) · doi:10.1016/0375-9601(81)90042-6
[31] Khan, R, Massel, F., Heikkila, T.T.: Cross-Kerr nonlinearity in optomechanical systems, vol. 91 (2015)
[32] De los Santos-Sanchez, O.; Recamier, J., The f-deformed Jaynes-Cummings model and its nonlinear coherent states, J. Phys. B: At. Mol. Opt. Phys., 45, 015502 (2012) · doi:10.1088/0953-4075/45/1/015502
[33] de Matos Filho, RL; Vogel, W., Nonlinear coherent states, Phys. Rev. A, 54, 4560 (1996) · doi:10.1103/PhysRevA.54.4560
[34] Huerta Alderete, C.; Rodriguez-Lara, BM, Quantum simulation of driven para-Bose oscillators, Phys. Rev. A, 95, 013820 (2017) · doi:10.1103/PhysRevA.95.013820
[35] Huerta Alderete, C.; Villanueva Vergara, L.; Rodríguez-Lara, BM, Nonclassical and semiclassical para-Bose states, Phys. Rev. A, 95, 043835 (2017) · doi:10.1103/PhysRevA.95.043835
[36] Huerta Alderete, C.; Rodriguez-Lara, BM, Simulating para-Fermi oscillators, Sci. Rep., 8, 11572 (2018) · doi:10.1038/s41598-018-29771-2
[37] Mojaveri, B.; Dehghani, A.; Jafarzadeh, R., Nonlinear coherent states of the para-Bose oscillator and their non-classical features, Euro. Phys. J. Plus, 133, 346 (2018) · Zbl 1396.81115 · doi:10.1140/epjp/i2018-12163-2
[38] Dehghani, A.; Mojaveri, B., Generalized su(2) coherent states for the Landau levels and their nonclassical properties, Euro. Phys. J. D, 67, 179 (2013) · doi:10.1140/epjd/e2013-40550-2
[39] Mojaveri, B.; Dehghani, A., Even and odd Wigner negative binomial states: Nonclassical properties, Mod. Phys. Lett. A, 30, 1550198 (2015) · Zbl 1337.81046 · doi:10.1142/S0217732315501989
[40] Dehghani, A.; Mojaveri, B.; Shirin, S.; Faseghandis, SA, Parity deformed Jaynes-Cummings model: Robust maximally entangled states, Sci. Rep., 6, 38069 (2016) · doi:10.1038/srep38069
[41] Sargolzaeipor, S.; Hasanabadi, H.; Chung, WS, Superstatistics of two electrons quantum dot, Euro. Phys. J. Plus, 132, 128 (2017)
[42] Mojaveri, B.; Dehghani, A.; Ahmadi, Z.; Amiri, S., Interaction of a para-Bose state with two two-level atoms: control of dissipation by a local classical field, Euro. Phys. J. Plus, 135, 227 (2020) · doi:10.1140/epjp/s13360-020-00236-8
[43] Mojaveri, B.; Dehghani, A.; Ahmadi, Z., A quantum correlated heat engine based on the parity-deformed Jaynes-Cummings model: achieving the classical Carnot efficiency by a local classical field, Phys. Scr., 96, 115102 (2021) · doi:10.1088/1402-4896/ac1638
[44] Dehghani, A.; Mojaveri, B.; Jafarzadeh Bahrbeig, R., Entanglement transfer in a noisy cavity network with parity-deformed radiation fields, J. Opt. Soc. Am. B, 36, 1858 (2019) · Zbl 1433.81177 · doi:10.1364/JOSAB.36.001858
[45] Dehghani, A.; Mojaveri, B.; Jafarzadeh Bahrbeig, R., Two-qutrit entangled f-coherent states, Rep. Math. Phys., 87, 111 (2021) · Zbl 1527.81078 · doi:10.1016/S0034-4877(21)00015-X
[46] Lee, SY; Lee, CW; Nha, H.; kaszlikowski, D., Quantum phase estimation using a multi-headed cat state, J. Opt. Soc. Am. B, 32, 1186 (2015) · doi:10.1364/JOSAB.32.001186
[47] Suzuki, M., On the Convergence of Exponential Operators- the Zassenhaus Formula, BCH Formula and Systematic Approximants, Commun. Math. Phys., 57, 193 (1977) · Zbl 0366.47016 · doi:10.1007/BF01614161
[48] Scholz, D.; Weyrauch, M., A note on the Zassenhaus product formula, J. Math. Phys., 47, 033505 (2006) · Zbl 1111.17015 · doi:10.1063/1.2178586
[49] Cahill, KE; Glauber, RJ, Ordered Expansions in Boson Amplitude Operators, Phys Rev., 177, 5, 1857 (1969) · doi:10.1103/PhysRev.177.1857
[50] Wei, T-C; Nemoto, K.; Goldbart, PM; Kwiat, PG; Munro, WJ; Verstraete, F., Maximal entanglement versus entropy for mixed quantum states, Phys. Rev. A, 67, 022110 (2003) · doi:10.1103/PhysRevA.67.022110
[51] Buscemi, F.; Bordone, P.; Bertoni, A., Linear entropy as an entanglement measure in two-fermion systems, Phys. Rev. A, 75, 032301 (2007) · doi:10.1103/PhysRevA.75.032301
[52] Zurek, WH; Habib, S.; Paz, JP, Coherent states via decoherence, Phys. Rev. Lett., 70, 1187 (1993) · doi:10.1103/PhysRevLett.70.1187
[53] Vlastakis, B.; Kirchmair, G.; Leghtas, Z.; Nigg, SE; Frunzio, L.; Girvin, SM; Mirrahimi, M.; Devoret, MH; Schoelkopf, RJ, Deterministically encoding quantum information using 100-photon schrodinger cat states, Science., 342, 607 (2013) · Zbl 1355.81054 · doi:10.1126/science.1243289
[54] Scully, M.O., Zubairy, M.S.: Quantum optics. Cambridge University Press, Cambridge (1997)
[55] Bagheri Harouni, M.; Roknizadeh, R.; Naderi, MH, Spatial confinement effects on a quantum harmonic oscillator: nonlinear coherent state approach, J. Phys. A: Math. Theor., 42, 045403 (2009) · Zbl 1156.81406 · doi:10.1088/1751-8113/42/4/045403
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