We have investigated numerically the dynamics of quantum Fisher information (QFI) and quantum entanglement (QE) for N -level atomic system interacting with a coherent field in the presence of Kerr (linear and non-linear medium) and Stark effects. It is observed that the Stark and Kerr effects play a prominent role during the time evolution of the quantum system. The evolving quantum Fisher information (QFI) is noted as time grows under the non-linear Kerr medium contrary to the QE for higher dimensional systems. The effect of non-linear Kerr medium is greater on the QE as we increase the value of Kerr parameter. However, QFI and QE maintain their periodic nature under atomic motion. On the other hand, linear Kerr medium has no prominent effects on the dynamics of N -level atomic system. Furthermore, it has been observed that QFI and QE decay soon under the influence of Stark effect. In short, the N -level atomic system is found prone to the change of the Kerr medium and Stark effect for higher dimensional systems.
KeywordsQFIKerr EffectStark EffectN-Level Atomic System
Giovannetti, V., Lloyd, S. and Maccone, L. (2004) Quantum-Enhanced Measurements: Beating the Standard Quantum Limit. Science, 306, 1330-1336. https://doi.org/10.1126/science.1104149
Dowling, J. (2008) Quantum Optical Metrology—The Lowdown on High-N00N States. Contemporary Physics, 49, 125-143. https://doi.org/10.1080/00107510802091298
Helstrom, C.W. (1976) Quantum Detection and Estimation Theory. Academic Press, New York.
Holevo, A.S. (1982) Statistical Structure of Quantum Theory. North-Holland, Amsterdam.
Braunstein, S.L. and Caves, C.M. (1994) Statistical Distance and the Geometry of Quantum States. Physical Review Letters, 72, 3439. https://doi.org/10.1103/PhysRevLett.72.3439
Braunstein, S.L., Caves, C.M. and Milburn, G.J. (1996) Generalized Uncertainty Relations: Theory, Examples, and Lorentz Invariance. Annals of Physics, 247, 135-173. https://doi.org/10.1006/aphy.1996.0040
Hubner, M. (1992) Explicit Computation of the Bures Distance for Density Matrices. Physics Letters A, 163, 239-242. https://doi.org/10.1016/0375-9601(92)91004-B
Einstein, A., Podolsky, B. and Rosen, N. (1935) Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Physical Review, 47, 777. https://doi.org/10.1103/PhysRev.47.777
Schrdinger, E. (1935) Discussion of Probability Relations between Separated Systems. Mathematical Proceedings of the Cambridge Philosophical Society, 31, 555-563. https://doi.org/10.1017/S0305004100013554
Nielsen, M.A. and Chuang, I.L. (2000) Quantum Computation and Information. Cambridge University Press, Cambridge.
Bell, J. (1964) On the Einstein Podolsky Rosen paradox. Physics, 1, 195. https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195
Clauser, J., Horne, M., Shimony, A. and Holt, R. (1969) Proposed Experiment to Test Local Hidden-Variable Theories. Physical Review Letters, 23, 880. https://doi.org/10.1103/PhysRevLett.23.880
Huver, S.D., Wildfeuer, C.F. and Dowling, J.P. (2008) Entangled Fock States for Robust Quantum Optical Metrology, Imaging, and Sensing. Physical Review A, 78, Article ID: 063828. https://doi.org/10.1103/PhysRevA.78.063828
Berrada, K. (2013) Quantum Metrology with SU(1,1) Coherent States in the Presence of Nonlinear Phase Shifts. Physical Review A, 88, Article ID: 013817. https://doi.org/10.1103/PhysRevA.88.013817
Amico, L., Fazio, R., Osterloh, A. and Vedral, V. (2008) Entanglement in Many-Body Systems. Reviews of Modern Physics, 80, 517-576. https://doi.org/10.1103/RevModPhys.80.517
Nieuwenhuizen, T.M., Pomb, C., Furtado, C., et al. (2014) Quantum Foundations and Open Quantum Systems. World Scientific, Singapore. https://doi.org/10.1142/9238
Jaynes, E.T. and Cummings, F.W. (1963) Comparison of Quantum and Semiclassical Radiation Theories with Application to the Beam Maser. Proceedings of the IEEE, 51, 89-109. https://doi.org/10.1109/PROC.1963.1664
Meschede, D. (1992) Cavity Quantum Electrodynamics. Reports on Progress in Physics, 211, 201-250. https://doi.org/10.1016/0370-1573(92)90110-L
Hansch, T.W. and Walther, H. (1999) Laser Spectroscopy and Quantum Optics. Reviews of Modern Physics, 71, S242-S252. https://doi.org/10.1103/RevModPhys.71.S242
Rempe, G., Walther, H. and Klein, N. (1987) Observation of Quantum Collapse and Revival in a One-Atom Maser. Physical Review Letters, 58, 353-356. https://doi.org/10.1103/PhysRevLett.58.353
Buck, B. and Sukumar, C.V. (1981) Exactly Soluble Model of Atom-Phonon Coupling Showing Periodic Decay and Revival. Physics Letters A, 81, 132-135. https://doi.org/10.1016/0375-9601(81)90042-6
Sukumar, C.V. and Buck, B. (1981) Multi-Phonon Generalisation of the Jaynes-Cummings Model. Physics Letters A, 83, 211-213. https://doi.org/10.1016/0375-9601(81)90825-2
Yurke, B. and Stoler, D. (1986) Generating Quantum Mechanical Superpositions of Macroscopically Distinguishable States via Amplitude Dispersion. Physical Review Letters, 57, 13-16. https://doi.org/10.1103/PhysRevLett.57.13
Gora, P. and Jedrzejek, C. (1992) Nonlinear Jaynes-Cummings Model. Physical Review A, 45, 6816. https://doi.org/10.1103/PhysRevA.45.6816
Buzek, V. and Jex, I. (1990) Dynamics of a Two-Level Atom in a Kerr-Like Medium. Optics Communications, 78, 425-435. https://doi.org/10.1016/0030-4018(90)90340-Y
Obada, A.-S.F., Eied, A.A. and Al-Kader Abd, G.M. (2008) Treatment of the Emission and Absorption Spectra for a Λ-Type Three-Level Atom Driven by a Single-Mode Field with Nonlinearities. Laser Physics Letters, 18, 1164-1175. https://doi.org/10.1088/0953-4075/39/7/001
Abdalla, M.S., Krepelka, J. and Perina, J.J. (2006) Effect of Kerr-Like Medium on a Two-Level Atom in Interaction with Bimodal Oscillators. Journal of Physics B: Atomic, Molecular and Optical Physics, 39, 1563-1577. https://doi.org/10.1088/0953-4075/39/7/001
Lai, Y.Z., Li, W.D. and Liang, J.Q. (1999) Adiabatic Transfer of Atomic Level-Occupation Probability Induced by Kerr-Like Medium. Optics Communications, 160, 240-244. https://doi.org/10.1080/09500340108240888
Berlin, G. and Aliaga, J.J. (2001) Quantum Dynamical Properties of a Two-Photon Non Linear Jaynes-Cummings Model. Journal of Modern Optics, 48, 1819-1829. https://doi.org/10.1080/09500340108240888
Schlicher, R.R. (1989) Jaynes-Cummings Model with Atomic Motion. Optics Communications, 70, 97-102. https://doi.org/10.1016/0030-4018(89)90276-9
Liu, J.-R. and Wang, Y.-Z. (1996) Motion-Quantized Jaynes-Cummings Models with an Arbitrary Intensity-Dependent Medium. Physical Review A, 54, 2326. https://doi.org/10.1103/PhysRevA.54.2326
Liu, J.-R. and Wang, Y.-Z. (1996) Velocity-Selective Population and Quantum Collapse-Revival Phenomena of the Atomic Motion for a Motion-Quantized Raman-Coupled Jaynes-Cummings Model. Physical Review A, 54, 2444-2450. https://doi.org/10.1103/PhysRevA.54.2444
Abdel-Wahab, N.H., Amin, M.E. and Mourad, M.F. (2002) Influence of the Stark Shift and the Detuning Parameters on the Entanglement Degree in a Two-Mode Coupling System. Journal of the Physical Society of Japan, 71, 2129-2132. https://doi.org/10.1143/JPSJ.71.2129
Zait, R.A. and Abdel-Wahab, N.H. (2002) Nonresonant Interaction between a Three-Level Atom with a Momentum Eigenstate and a One-Mode Cavity Field in a Kerr-Like Medium. Journal of Physics B, 35, 3701-3712. https://doi.org/10.1088/0953-4075/35/17/307
Zait, R.A. and Abdel-Wahab, N.H. (2002) Influence of Detuning and Kerr-Like Medium on the Interaction of a Three-Level Atom with Squeezed Two-Mode Cavity Field. Physica Scripta, 66, 452. https://doi.org/10.1238/Physica.Regular.066a00425
Abdel-Wahab, N.H. (2005) N-Level Atom in a Momentum Eigenstate Interacting with an (N-1) Mode Cavity Field. Physica Scripta, 71, 132-135. https://doi.org/10.1238/Physica.Regular.071a00132
Abdel-Wahab, N.H., Amin, M.E. and Taha, M. (2006) One-Mode Interaction with a Four-Level Atom in a Momentum Eigenstate. Fizika A, 2, 113-124.
Abdel-Wahab, N.H. (2008) A Moving Four-Level N-Type Atom Interacting with Cavity Fields. Journal of Physics B: Atomic Molecular and Optical Physics, 41, Article ID: 105502. https://doi.org/10.1088/0953-4075/41/10/105502
Fan, A. and Wang, Z.-W. (1994) Phase, Coherence Properties and the Numerical Analysis of the Field in the Nonresonant Jaynes: Cummings Model. Physical Review A, 49, 1509. https://doi.org/10.1103/PhysRevA.49.1509
Haken, H. and Wolf, H.C. (2004) Atomund Quantenphysik, Einfuhrung in Die Experimentellen und Theoretischen Grundlagen. 8th Edition, Springer, Berlin.
Alsing, P., Guo, D.-S. and Carmichael, H.J. (1992) Dynamic Stark Effect for the Jaynes-Cummings System. Physical Review A, 45, 5135-5143. https://doi.org/10.1103/PhysRevA.45.5135
Wallraff, A., Schuster, D.I., Blais, A., Frunzio, L., Huang, R.-S., Majer, J., Kumar, S., Girvin, S.M. and Schoelkopf, R.J. (2004) Strong Coupling of a Single Photon to a Superconducting Qubit Using Circuit Quantum Electrodynamics. Nature, 431, 162-167. https://doi.org/10.1038/nature02851
Alsing, P. and Zubairy, M.S. (1987) Collapse and Revivals in a Two-Photon Absorption Process. Journal of the Optical Society of America B, 4, 177-184. https://doi.org/10.1364/JOSAB.4.000177
Swain, S. (1994) Systematic Method for Deriving Effective Hamiltonians. Physical Review A, 49, 2816. https://doi.org/10.1103/PhysRevA.49.2816
Brune, M., Raimond, J.M. and Haroche, S. (1987) Theory of the Rydberg-Atom Two-Photon Micromaser. Physical Review A, 35, 154-163. https://doi.org/10.1103/PhysRevA.35.154
Agarwal, G.S. and Puri, R.R. (1986) Exact Quantum-Electrodynamics Results for Scattering, Emission, and Absorption from a Rydberg Atom in a Cavity with Arbitrary Q. Physical Review A, 33, 1757-1764. https://doi.org/10.1103/PhysRevA.33.1757
Obada, A.S.F., Ahmed, M.M.A., Khalil, E.M. and Ali, S.I. (2013) Entangled Two Two-Level Atoms Interacting with a Cavity Field in the Presence of the Stark Shift Terms. Optics Communications, 287, 215-223. https://doi.org/10.1016/j.optcom.2012.08.091
Jamal Anwar, S., Ramzan, M. and Khan, K. (2017) Dynamics of Entanglement and Quantum Fisher Information for N-Level Atomic System under Intrinsic Decoherence. Quantum Information Processing, 16, 142. https://doi.org/10.1007/s11128-017-1589-8
Berrada, K., Abdel-Khalek, S. and Obada, A.S.F. (2012) Quantum Fisher Information for a Qubit System Placed Inside a Dissipative Cavity. Physics Letters A, 376, 1412-1416. https://doi.org/10.1016/j.physleta.2012.03.023
Berrada, K., Abdel-Khalek, S. and Raymond Ooi, C.H. (2012) Quantum Metrology with Entangled Spin-Coherent States of Two Modes. Physical Review A, 86, Article ID: 033823. https://doi.org/10.1103/PhysRevA.86.033823
Wootters,W.K. (2001) Entanglement of Formation and Concurrence. Quantum Information and Computation, 1, 27-44.
Lu, X., Wang, X. and Sun, C.P. (2010) Quantum Fisher Information Flow and Non-Markovian Processes of Open Systems. Physical Review A, 82, Article ID: 042103. https://doi.org/10.1103/PhysRevA.82.042103
Barndorff-Nielsen, O.E., Gill, R.D. and Jupp, P.E. (2003) On Quantum Statistical Inference. Journal of the Royal Statistical Society Series B, 65, 775-816. https://doi.org/10.1111/1467-9868.00415
Abdel-Khalek, S. (2011) Dynamics of a Moving Five-Level Atom Interacting with Cavity Fields. Journal of Russian Laser Research, 32, 86-93. https://doi.org/10.1007/s10946-011-9192-4
Abdel-Khalek, S. (2013) Quantum Fisher Information for Moving Three-Level Atom. Quantum Information Processing, 12, 3761-3769. https://doi.org/10.1007/s11128-013-0622-9
Enaki, N.A. and Ciobanu, N. (2008) Quantum Trapping Conditions for Three-Level Atom Flying through Bimodal Cavity Field. Journal of Modern Optics, 55, 589-598. https://doi.org/10.1080/09500340701721868