Thermal entanglement between two coupled two-level atoms in two-photon interacting with codirectional Kerr nonlinear coupler

Document Type : Full length research Paper

Authors

1 Department of Physics, Azarbaijan Shahid Madani University, Tabriz, Iran

2 Department of Physics, Faculty of Science, Payame Noor University,Tehran, Iran

3 Department of Physics, Faculty of Science, Azarbaijan Shahid Madani University, Tabriz, Iran

Abstract

In this paper, a Hamiltonian model that includes interaction of two two-level atoms with a codirectional Kerr nonlinear coupler via the Raman non-degenerate two-photon transition is introduced. The atomic interaction is assumed in the dipole-dipole form and the total system is also in thermal equilibrium with the environment. The total excitation number operator, as the constant of motion of system provides a decomposition of the Hilbert space of system into direct sums of invariant subspaces. As a result, the representation of the Hamiltonian becomes block-diagonal matrix. By diagonalizing each of blocks, we obtain eigenvalues and corresponding eigenstates of the Hamiltonian. Then we obtain thermal state of system in the whole Hilbert space and within its excitation subspaces. We quantify thermal entanglement between the atoms in the Hilbert space of system and within its excitation subspaces using the measure of concurrence. Finally, the effect of temperature and system parameters on the degree of thermal entanglement is investigated. The results show that in the subspaces with odd excitation number, the atomic thermal entanglement is thermally robust and remains constant.

Keywords

References

[1] A. Ekert and R. Jozsa, Quantum computation and Shor's factoring algorithm, Reviews of Modern Physics68 (1996) 733-753.       DOI:https://doi.org/10.1103/RevModPhys.68.733
[2] H.K. Lo, S. Popescu, T. Spiller, Introduction to Quantum Computation and Information, World Scientific, Singapore, (1998).
[3] S.M. Jensen, The nonlinear coherent coupler, IEE J. Quantum Electron 18 (1982) 1580-1583. DOI: 10.1109/JQE.1982.1071438
[4] A. Chefles, S.M. Barnett, Quantum theory of two-mode nonlinear directional couplers, Journal of Modern Optics 43 (1996) 709-727. DOI:10.1080/09500349608232778
[5] R. Horák, M. Bertolotti, C. Sibilia, J. Peřina, Quantum effects in a nonlinear coherent coupler, Journal of the Optical Society of America B 6 (1989) 199-204. DOI: https://doi.org/10.1364/JOSAB.6.000199
[6] M.J. Faghihi, M.K. Tavassoly, M. Hatami, Dynamics of entanglement of a three-level atom in motion interacting with two coupled modes including parametric down conversion, Physica A 407 (2014) 100-109.
DOI: https://doi.org/10.1016/j.physa.2014.03.092
 
[7] A.-S. F. Obada, A.A. Eied, Entanglement in a system of an Ξ -type three-level atom interacting with a non-correlated two-mode cavity field in the presence of nonlinearities, Optics Communications282 (2009) 2184-2191.
DOI:https://doi.org/10.1016/j.optcom.2009.02.038
 
[8] M.K. Tavassoly, F.Yadollahi, Dynamics of states in the nonlinear interaction regime between a three-level atom and generalized coherent states and their non-classical features, International Journal of Modern Physics B 26 (2012) 1250027.
DOI: https://doi.org/10.1142/S0217979212500270
 
[9] W.Z. Li, L.T. Shen, Sudden death and birth of two-atom entanglement with two thermal fields in coupled cavities, European Physical Journal D 67 (2013) 111.
DOI: https://doi.org/10.1140/epjd/e2013-30709-2
 
[10] M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge (2000).
 
[11] K. Zyczkowski, P. Horodecki, A. Sanpera, M. Lewenstein, Volume of the set of separable states, Physical Review A 58 (1998) 883-892. DOI: https://doi.org/10.1103/PhysRevA.58.883
 
[12] M.R. Abbasi, M.M. Golshan, Thermal entanglement of a two-level atom and bimodal photons in a Kerr nonlinear coupler, Physica A 392 (2013) 6161-6167.
DOI: 10.1016/j.physa.2013.07.068
[13] M.R. Abbasi, Thermal atom–atom entanglement in a nonlinear cavity, Physica A 426 (2015) 1-8.
DOI: https://doi.org/10.1016/j.physa.2015.01.048
 
[14] M.R. Abbasi, Thermal atom–atom entanglement in a bichromatic Kerr nonlinear coupler, Annals of Physics365 (2016)198-209.
DOI: https://doi.org/10.1016/j.aop.2015.10.024
 
[15] B. Mojaveri, A. Dehghani, M.A. Fasihi, T. Mohammadpour, Ground state and thermal entanglement between two two-level atoms interacting with a non-degenerate parametric amplifier: different sub-spaces, International Journal of Modern Physics. B 33 (2019) 1950035.
DOI: https://doi.org/10.1142/S0217979219500358
 
[16] Sh. Alizadeh, R. Safaiee, M.M. Golshan, Effect of temperature on photon–photon entanglement in a nonlinear nanocavity, Physica A 428 (2015) 133-139.
DOI: https://doi.org/10.1016/j.physa.2015.01.050
 
[17] B. Mojaveri, A. Dehghani, M.A. Fasihi, T. Mohammadpour, Thermal entanglement between two two-level atoms in a two-photon Jaynes-Cummings model with an added Kerr medium, International Journal of Theoretical Physics57 (2018) 3396-3409.
DOI: https://doi.org/10.1007/s10773-018-3853-9
Journal of Research on Many-body Systems
Volume 9, Issue 3 - Serial Number 22
December 2019
Pages 164-175

Files

History

  • Receive Date: 12 January 2019
  • Revise Date: 23 June 2019
  • Accept Date: 02 September 2019

Share

How to cite

Statistics