Volume 15, Issue 2 (Summer-Fall 2021)                   IJOP 2021, 15(2): 151-166 | Back to browse issues page


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Asili Firouzabadi N, Tavassoly M K. Interaction of a Three-Level Atom (Λ, V, Ξ) with a Two-Mode Field Beyond Rotating Wave Approximation: Intermixed Intensity-Dependent Coupling. IJOP. 2021; 15 (2) :151-166
URL: http://ijop.ir/article-1-464-en.html
1- Optics and Laser Group, Faculty of Physics, Yazd University, Yazd, Iran
Abstract:   (937 Views)
Recalling that the rotating wave approximation (RWA) is only valid in the weak coupling regimes, our purpose is to study the Hamiltonian dynamics of the interaction between various configurations of a three-level atom of Lambda, V, or Ladder-type distinctly with a two-mode radiation quantized field, while the RWA is not considered. Generally, this prevents one to achieve an analytical solution. Moreover, as we will show, using the perturbation theory analytical solution can be successfully obtained. According to our considerations, the contribution of counter rotating terms (CRTs) within the ordinary Hamiltonian is equivalent to arriving at some intermixed intensity-dependent atom-field coupling as functions of the two modes of the field, i.e., f(n_1, n_2). At last, via evaluating the time-dependent atom–field state vector, the effects of CRTs on a few nonclassical properties of the state of the system as atomic population inversion and photon statistics are numerically studied. It is observed that, the presence of CRTs in the Hamiltonian dynamics destroys the clear patterns of collapse-revival phenomena in the time behavior of the evaluated quantities.
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Type of Study: Research | Subject: Special
Received: 2021/08/13 | Revised: 2022/01/8 | Accepted: 2022/01/12 | Published: 2022/06/22

References
1. E.T. Jaynes and F.W. Cummings, "Comparison of quantum and semiclassical radiation theories with application to the beam maser," Proc. IEEE, Vol. 51, pp. 89-109, 1963. [DOI:10.1109/PROC.1963.1664]
2. X-S Li and N-Y Bei, "A generalized three-level Jaynes-Cummings model," Phys. Lett. A, Vol. 101, pp. 169-174, 1984. [DOI:10.1016/0375-9601(84)90517-6]
3. G. Benivegna and A. Messina, "New quantum effects in the dynamics of a two-mode field coupled to a two-level atom," J. Mod. Opt. Vol. 41, pp. 907-925, 1994. [DOI:10.1080/09500349414550871]
4. V. Buzek, "Jaynes-Cummings model with intensity-dependent coupling interacting with Holstein-Primakoff SU (1, 1) coherent state," Phys. Rev. A, Vol. 39, pp. 3196-3199, 1989. [DOI:10.1103/PhysRevA.39.3196] [PMID]
5. R.R. Puri, Mathematical Methods of Quantum Optics, Springer Series in Optical Sciences, 79, 2001. [DOI:10.1007/978-3-540-44953-9]
6. A.B. Klimov, I. Sainz, and S.M. Chumakov, "Resonance expansion versus the rotating-wave approximation," Phys. Rev. A, Vol. 68, pp. 063811 (1-8), 2003. [DOI:10.1103/PhysRevA.68.063811]
7. M. Abdel-Aty, "The Pancharatnam phase of a two-level atom in the presence of another two-level atom in a cavity," J. Opt. B, Vol. 5, pp. 349-354, 2003. [DOI:10.1088/1464-4266/5/4/304]
8. J.S. Pedernales, I. Lizuain, S. Felicetti, G. Romero, L. Lamata, and E. Solano, "Quantum Rabi model with trapped ions," Sci. Rep. Vol. 5, pp. 15472 (1-7), 2015. [DOI:10.1038/srep15472] [PMID] [PMCID]
9. D. Ballester, G. Romero, J.J. García-Ripoll, F. Deppe, and E. Solano, "Quantum simulation of the ultrastrong-coupling dynamics in circuit quantum electrodynamics," Phys. Rev. X, Vol. 2, pp. 021007 (1-6), 2012. [DOI:10.1103/PhysRevX.2.021007]
10. D. Lv, S. An, Z. Liu, J.N. Zhang, J.S. Pedernales, L. Lamata, E. Solano, and K. Kim, "Quantum simulation of the quantum Rabi model in a trapped ion," Phys. Rev. X, Vol. 8, pp. 021027 (1-11), 2018. [DOI:10.1103/PhysRevX.8.021027]
11. X. Li, M. Bamba, Q. Zhang, S. Fallahi, G.C. Gardner, W. Gao, M. Lou, K. Yoshioka, M.J. Manfra, and J. Kono, "Vacuum Bloch-Siegert shift in Landau polaritons with ultra-high cooperativity," Nature Photon. Vol. 12, pp. 324-329, 2018. [DOI:10.1038/s41566-018-0153-0]
12. D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, "Quantum dynamics of single trapped ions," Rev. Mod. Phys. Vol. 75, pp. 281-325, 2003. [DOI:10.1103/RevModPhys.75.281]
13. E.K. Irish and K. Schwab, "Quantum measurement of a coupled nanomechanical resonator-Cooper-pair box system," Phys. Rev. B, Vol. 68, pp. 155311-155318, 2003. [DOI:10.1103/PhysRevB.68.155311]
14. A. Wallraf, D.I. Schuster, A. Blais, L. Frunzio, R.S. Huang, J. Majer, S. Kumar, S.M. Girvin, and R.J. Schoelkopf, "Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics," Nature, Vol. 431, pp. 162-167, 2004. [DOI:10.1038/nature02851] [PMID]
15. I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C.J.P.M. Harmans, and J.E. Mooil, "Coherent dynamics of a flux qubit coupled to a harmonic oscillator," Nature, Vol. 431, pp. 159-162, 2004. [DOI:10.1038/nature02831] [PMID]
16. T. Liu, K.L. Wang, and M. Feng, "The generalized analytical approximation to the solution of the single-mode spin-boson model without rotating-wave approximation," Europhys. Lett. Vol. 86, pp. 54003 (1-6), 2009. [DOI:10.1209/0295-5075/86/54003]
17. S. Abdel-Khalek, Y.S. El-Saman, I. Mechai, and M. Abdel-Aty, "Geometric phase and entanglement of a three-level atom with and without rotating wave approximation," Brazilian J. Phys. Vol. 48, pp. 1-7, 2018. [DOI:10.1007/s13538-017-0537-5]
18. R.H. Xie, G.O. Xu, and D.H. Liu,, "Study of Nonclassical Features and Quantum Dynamics in the Jaynes-Cummings Model Without RWA" Commun. Theoret. Phys. Vol. 27, pp. 385-394, 1997. [DOI:10.1088/0253-6102/27/4/385]
19. J.S. Peng and G.X. Li, "Phase fluctuations in the Jaynes-Cummings model with and without the rotating-wave approximation," Phys. Rev. A, Vol. 45, pp. 3289 3294, 1992. [DOI:10.1103/PhysRevA.45.3289] [PMID]
20. J.S. Peng and G.X. Li, "Inhuence of the virtual-photon processes on the squeezing of light in the two-photon Jaynes-Cummings model," Phys. Rev. A, Vol. 47, pp. 3167-3172, 1993. [DOI:10.1103/PhysRevA.47.3167] [PMID]
21. K. Guo-Dong, F. Mao-Fa, O. Xi-Cheng, and D. Xiao-Juan, "Entanglement of two atoms interacting with a dissipative coherent cavity field without rotating wave approximation," Chin. Phys. B, Vol. 19, pp. 110303-110310, 2010. [DOI:10.1088/1674-1056/19/11/110303]
22. Q.H. Chen, Y. Yang, T. Liu, and K.L. Wang, "Entanglement dynamics of two independent Jaynes-Cummings atoms without the rotating-wave approximation," Phys. Rev. A, Vol. 82, pp. 052306 (1-7), 2010. [DOI:10.1103/PhysRevA.82.052306]
23. Z. Ling, S. He-shan, and Y. Li, "The two-photon degenerate Jaynes-Cummings model with and without rotating-wave approximation," Chin. Phys. Vol. 10, pp. 413-419, 2001. [DOI:10.1088/1009-1963/10/5/310]
24. Z. Ficek, J. Jing, and Z.G. Lü, "Role of the counter-rotating terms in the creation of entanglement between two atoms," Phys. Scripta, Vol. 140, pp. 014005 (1-6), 2010. [DOI:10.1088/0031-8949/2010/T140/014005]
25. Z. Chen, Y. Wang, T. Li, L. Tian, Y. Qiu, K. Inomata, F. Yoshihara, S. Han, F. Nori, J.S. Tsai, and J.Q. You, "Single-photon-driven high-order sideband transitions in an ultrastrongly coupled circuit-quantum-electrodynamics system," Phys. Rev. A, Vol. 96, pp. 012325 (1-12), 2017. [DOI:10.1103/PhysRevA.96.012325]
26. X. Zhang, N. Zhu, C.L. Zou, and H.X. Tang, "Optomagnonic whispering gallery microresonators," Phys. Rev. Lett. Vol. 117, pp. 123605-123610, 2016. [DOI:10.1103/PhysRevLett.117.123605] [PMID]
27. M.H. Naderi, "The Jaynes-Cummings model beyond the rotating-wave approximation as an intensity-dependent model: quantum statistical and phase properties," J. Phys. A: Math. Theor. Vol. 44, pp. 055304 (1-19), 2011. [DOI:10.1088/1751-8113/44/5/055304]
28. A.B. Klimov and S.M. Chumakov, A group-theoretical approach to quantum optics: models of atom-field interactions, John Wiley & Sons, 2009. [DOI:10.1002/9783527624003]
29. M.R. Nath, S. Sen, and G. Gangopadhyay, "Dynamics of cascade three-level system interacting with the classical and quantized field," Pramana - J. Phys. Vol. 61, pp. 1089-1100, 2003. [DOI:10.1007/BF02704404]
30. M. Rastegarzadeh and M.K. Tavassoly, "Interaction of a Λ-type three-level atom with a single-mode field without rotating wave approximation: perturbation theory approach," Phys. Scripta, Vol. 90, pp. 025103 (1-10), 2015. [DOI:10.1088/0031-8949/90/2/025103]
31. B. Buck and C.V. Sukumar, "Exactly soluble model of atom-phonon coupling showing periodic decay and revival," Phys. Lett. A, Vol. 81, pp. 132-135, 1981. [DOI:10.1016/0375-9601(81)90042-6]
32. C.V. Sukumar and B. Buck, "Multi-phonon generalisation of the Jaynes-Cummings model," Phys. Lett. A, Vol. 83, pp. 211-213, 1981. [DOI:10.1016/0375-9601(81)90825-2]
33. R. Pakniat, M.K. Tavassoly, and M.H. Zandi, "Entanglement swapping and teleportation based on cavity QED method using the nonlinear atom-field interaction: Cavities with a hybrid of coherent and number states," Opt. Commun. Vol. 382, pp. 381-385, 2017. [DOI:10.1016/j.optcom.2016.08.021]
34. M.K. Tavassoly and F. Yadollahi, "Dynamics of states in the nonlinear interaction regime between a three-level atom and generalized coherent states and their non-classical features," Int. J. Mod. Phys. B, Vol. 26, pp. 1250027-1250046, 2012. [DOI:10.1142/S0217979212500270]
35. H.R. Baghshahi and M.K. Tavassoly, "Dynamics of different entanglement measures of two three-level atoms interacting nonlinearly with a single-mode field," Eur. Phys. J. Plus, Vol. 130, pp. 1-13, 2015. [DOI:10.1140/epjp/i2015-15037-1]
36. A. Karimi and M.K. Tavassoly, "Quantum engineering and nonclassical properties of SU (1, 1) and SU (2) entangled nonlinear coherent states," J. Opt. Soc. Am. B, Vol. 31, pp. 2345-2353, 2014. [DOI:10.1364/JOSAB.31.002345]
37. L.N. Childs, A Concrete Introdution to Higher Algebra, Springer, 3rd Ed. 2008. [DOI:10.1007/978-0-387-74725-5]
38. S. Shahidani, M.H. Naderi, and M. Soltanolkotabi, "Dynamical evolution of nonclassical properties in cavity quantum electrodynamics with a single trapped ion," Int. J. Opt. Photon. Vol. 1, pp. 55-60, 2007.
39. M.H. Naderi, and S. Salimian Rizi, "Coherent transport of single photon in a quantum super-cavity with mirrors composed of λ-type three-level atomic ensembles," Int. J. Opt. Photon. Vol. 8, pp. 31-39, 2014.
40. M. Fani and M.H. Naderi, "Coherent transport of single photon in a quantum super-cavity with mirrors composed of λ-type three-level atomic ensembles," Int. J. Opt. Photon. Vol. 4, pp. 113-120, 2010.

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