Dynamics of an exactly solvable model of cavity quantum electrodynamics
- Authors: Bashkirov E.K.1
-
Affiliations:
- Samara National Research University
- Issue: Vol 27, No 2 (2023)
- Pages: 250-269
- Section: Differential Equations and Mathematical Physics
- URL: https://journals.rcsi.science/1991-8615/article/view/145901
- DOI: https://doi.org/10.14498/vsgtu1992
- ID: 145901
Cite item
Full Text
Abstract
A system consisting of two identical qubits not-resonantly interacting with a thermal quantum field of a lossless resonator with a Kerr media via degenerate two-photon transition is considered. An exact solution of the quantum Liouville equation for the total density matrix of the considered system is obtained. To solve the quantum evolution equation we used the dressed states representation. The complete set of dressed states is found. The exact solution of the quantum Liouville equation is used to calculate the time dependencies of qubit-qubit entanglement parameter (negativity) for Bell type entangled qubits states. The results showed that Kerr nonlinearity can diminish the amplitudes of the Rabi oscillations of entanglement parameter and suppress the effect of sudden death of entanglement.
About the authors
Eugene K. Bashkirov
Samara National Research University
Author for correspondence.
Email: bashkirov.ek@ssau.ru
ORCID iD: 0000-0001-8682-4956
SPIN-code: 8870-9442
https://www.mathnet.ru/php/person.phtml?option_lang=rus&personid=23894
Dr. Phys. & Math. Sci., Professor, Professor, Dept. of General and Theoretical Physics
Russian Federation, 443086, Samara, Moskovskoye shosse, 34References
- Buluta I., Ashhab S., Nori F. Natural and artificial atoms for quantum computation, Rep. Prog. Phys., 2011, vol. 74, no. 10, 104401, pp. 1–34, arXiv: 1002.1871 [quant-ph]. EDN: PHMQQN. DOI: https://doi.org/10.1088/0034-4885/74/10/104401.
- Walther H., Varcoe B. T. H., Englert B.-G., Becker T. Cavity quantum electrodynamics, Rep. Prog. Phys, 2011, vol. 69, no. 5, pp. 1325–1382. EDN: WMZYEX. DOI: https://doi.org/10.1088/0034-4885/69/5/R02.
- Leibfried D., Blatt R., Monroe C., Wineland D. Quantum dynamics of single trapped ions, Rev. Mod. Phys., 2003, vol. 75, no. 1, pp. 281–324. EDN: YJDLXU. DOI: https://doi.org/10.1103/RevModPhys.75.281.
- Xiang Z.-L., Ashhab S., You J. Q., Nori F. Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems, Rev. Mod. Phys., 2013, vol. 85, no. 2, pp. 623–653. EDN: RJQAMF. DOI: https://doi.org/10.1103/RevModPhys.85.623.
- Georgescu I. M., Ashhab S., Nori F. Quantum simulation, Rev. Mod. Phys., 2014, vol. 88, no. 1, pp. 153–185. EDN: SQCURV. DOI: https://doi.org/10.1103/RevModPhys.86.153.
- Gu X., Kockum A.F., Miranowicz A., et al. Microwave photonics with superconducting quantum circuits, Phys. Repts., 2017, vol. 718–719, pp. 1–102. EDN: TECRZL. DOI: https://doi.org/10.1016/j.physrep.2017.10.002.
- Wendin G. Quantum information processing with super-conducting circuits: a review, Rep. Prog. Phys., 2017, vol. 80, no. 10, 106001. DOI: https://doi.org/10.1088/1361-6633/aa7e1a.
- Li G.-Q., Pan X.-Y. Quantum information processing with nitrogen–vacancy centers in diamond, Chinese Phys. B, 2018, vol. 27, no. 2, pp. 1–13, 020304. DOI: https://doi.org/10.1088/1674-1056/27/2/020304.
- Kim M. S., Lee J., Ahn D., Knight P. L. Entanglement induced by a single-mode heat environment, Phys. Rev. A, 2002, vol. 65, no. 4, 040101(R). EDN: YIXDNM. DOI: https://doi.org/10.1103/PhysRevA.65.040101.
- Zhou L., Song H. S. Entanglement induced by a single-mode thermal field and criteria for entanglement, J. Opt. B: Quantum Semiclass. Opt., 2002, vol. 4, no. 6, pp. 425–429. EDN: BFJLSP. DOI: https://doi.org/10.1088/1464-4266/4/6/310.
- Bashkirov E. K. Entanglement induced by the two-mode thermal noise, Laser Phys. Lett., 2006, vol. 3, no. 3, pp. 145–150. EDN: LJNXSZ. DOI: https://doi.org/10.1002/lapl. 200510081.
- Bashkirov E. K., Stupatskaya M. P. The entanglement of two dipole-dipole coupled atoms induced by nondegenerate two-mode thermal noise, Laser Phys., 2009, vol. 19, no. 3, pp. 525–530. EDN: LLXFEF. DOI: https://doi.org/10.1134/S1054660X09030281.
- Bashkirov E. K., Mastyugin M. S. The influence of the dipole-dipole interaction and atomic coherence on the entanglement of two atoms with degenerate two-photon transitions, Opt. Spectrosc., 2014, vol. 116, no. 4, pp. 630–634. EDN: SKTKWP. DOI: https://doi.org/10.1134/S0030400X14040067.
- Bashkirov E. K., Mangulova E. G. Entanglement induced by two-mode thermal noise taking into account the dipole-dipole interaction and atomic coherence, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2013, no. 2(31), pp. 177–184 (In Russian). EDN: RAVQJB. DOI: https://doi.org/10.14498/vsgtu1160.
- Zhang B. Entanglement between two qubits interacting with a slightly detuned thermal field, Opt. Commun., 2010, vol. 283, no. 23, pp. 4676–4679. DOI: https://doi.org/10.1016/j.optcom.2010.06.094.
- Aguiar L. S., Munhoz P. P., Vidiella-Barranco A., Roversi J. The entanglement of two dipoledipole coupled in a cavity interacting with a thermal field, J. Opt. B: Quantum Semiclass. Opt., 2005, vol. 7, no. 12, pp. S769–S771. DOI: https://doi.org/0.1088/1464-4266/7/12/049.
- Bashkirov E. K., Mastyugin M. S. Entanglement of two qubits interacting with onemode quantum field, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2015, vol. 19, no. 2, pp. 205–220 (In Russian). EDN: UGXNVL. DOI: https://doi.org/10.14498/vsgtu1377.
- Yu T., Eberly J. H. Finite-time disentanglement via spontaneous emission, Phys. Rev. Lett., 2004, vol. 93, no. 14, 140404, arXiv: quant-ph/0404161. DOI: https://doi.org/10.1103/PhysRevLett.93.140404.
- Yu T., Eberly J. H. Sudden death of entanglement, Science, 2009, vol. 323, no. 5914, pp. 598–601, arXiv: 0910.1396 [quant-ph]. DOI: https://doi.org/10.1126/science.1167343.
- Wang F., Hou P.-Y., Huang Y. Y., et al. Observation of entanglement sudden death and rebirth by controlling a solid-state spin bath, Phys. Rev. B, 2018, vol. 98, no. 6, 064306, arXiv: 1801.02729 [quant-ph]. DOI: https://doi.org/10.1103/PhysRevB.98.064306.
- Sun G., Zhou Z., Mao B., et al. Entanglement dynamics of a superonducting phase qubit coupled to a two-level system, Phys. Rev. B, 2012, vol. 86, no. 6, 064502, arXiv: 1111.3016 [cond-mat.mes-hall]. DOI: https://doi.org/10.1103/PhysRevB.86.064502.
- Bashkirov E. K. Entanglement in Tavis-Cummings model with Kerr nonlinearity induced by a thermal noise, In: Saratov Fall Meeting 2020: Laser Physics, Photonic Technologies, and Molecular Modeling (Saratov, Russia), Proc. SPIE, 11846, 2021, 118460W. DOI: https://doi.org/10.1117/12.2588673.
- Salles A., de Melo F., Almeida M. P., et al. Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment, Phys. Rev. A, 2008, vol. 78, no. 2, 022322, arXiv: 0804.4556 [quant-ph]. DOI: https://doi.org/10.1103/PhysRevA.78.022322.
- Puri S, Boutin S., Blais A. Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving, Quantum Inf., 2017, vol. 3, no. 1, 18. DOI: https://doi.org/10.1038/s41534-017-0019-1.
- Manosh T. M., Ashefas M., Thayyullathil R. B. Effects of Kerr medium in coupled cavities on quantum state transfer, J. Nonlinear Opt. Phys. Mater., 2018, vol. 27, no. 3, 1850035. EDN: LFUINC. DOI: https://doi.org/10.1142/S0218863518500352.
- Al Naim A. F., Khan J. Y., Khalil E. M., Abdel-Khalek S. Effects of Kerr medium and Stark shift parameter on Wehrl entropy and the field puruty for two-photon Jaynes–Cummings model under dispersive approximation, J. Russ. Laser Res., 2019, vol. 40, no. 1, pp. 20–29. DOI: https://doi.org/10.1007/s10946-019-09764-w.
- Anwar S. J., Ramzan M., Khan M. K. Effect of Stark- and Kerr-like medium on the entanglement dynamics of two three-level atomic systems, Quant. Inform. Proc., 2019, vol. 18, no. 192, pp. 1–14. EDN: YXEFGH. DOI: https://doi.org/10.1007/s11128-019-2277-7.
- Adanmitonde A. J., Avossevou G. Y. H., Dossa F. A. Quantization of some generalized Jaynes–Cummings models in a Kerr-like medium, Theoret. and Math. Phys., 2020, vol. 203, no. 3, pp. 824–836. EDN: VQTJGW. DOI: https://doi.org/10.1134/S0040577920060082.
- Aldaghfag S. A., Berrada K., Abdel-Khalek S. Entanglement and photon statistics of two dipole-dipole coupled superconducting qubits with Kerr-like nonlinearities, Results in Phys., 2020, vol. 16, 102978. EDN: DSKEYY. DOI: https://doi.org/10.1016/j.rinp.2020.102978.
- Kirchmair G., Vlastakis B., Leghtas Z., et al. Observation of quantum state collapse and revival due to the single-photon Kerr effect, Nature, 2013, vol. 495, no. 7440, pp. 205–209. DOI: https://doi.org/10.1038/nature11902.
- Evseev M. M., Bashkirov E. K. Thermal entanglement in Tavis–Cummings model with Kerr nonlinearity, In: 2020 International Conference on Information Technology and Nanotechnology (ITNT) (26–29 May 2020, Samara, Russia), 2020, 9253347. EDN: YCMKXI. DOI: https://doi.org/10.1109/ITNT49337.2020.9253347.
- Bashkirov E. K. Dynamics of two-photon Tavis–Cummings model with Kerr media, In: 2022 VIII International Conference on Information Technology and Nanotechnology (ITNT) (23–27 May 2022, Samara, Russia), 2022, 9848606. EDN: ZAMPVK. DOI: https://doi.org/10.1109/ITNT55410.2022.9848606.
- Mlynek J. A., Abdumalikov A. A., Fink J. M., et al. Demonstrating W-type entanglement of Dicke states in resonant cavity quantum electrodynamics, Phys. Rev. A, 2012, vol. 86, no. 5, 053838. DOI: https://doi.org/10.1103/PhysRevA.86.053838.
- Peres A. Separability criterion for density matrices, Phys. Rev. Lett., 1996, vol. 77, no. 8, pp. 1413–1415. DOI: https://doi.org/10.1103/PhysRevLett.77.1413.
- Horodecki M., Horodecki P., Horodecki R. Separability of mixed states: necessary and sufficient conditions, Phys. Lett. A, 1996, vol. 223, no. 1–2, pp. 1–8. EDN: ANQBTF. DOI: https://doi.org/10.1016/S0375-9601(96)00706-2.
Supplementary files
