Top

Quantum Information Processing

Published in:

01-07-2021

Geometric discord in a dissipative double-cavity optomechanical system

Authors: Hamid Reza Baghshahi, Mohammad Haddad, Mohammad Javad Faghihi

Published in: Quantum Information Processing | Issue 7/2021

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this paper, we propose a theoretical scheme to study the dynamics of the geometric measure of quantum discord (GMQD) between two non-interacting qubits in a dissipative optomechanical system composed of two Fabry–Pérot cavities. In this system, each cavity contains a single-mode quantized radiation field which, in the rotating wave approximation, interacts with both mechanical resonator and two-level atom. In addition, the effects of dissipation are taken into account by considering cavity decay, losses of cavity mirror, and spontaneous emission from the atom. We start with the master equation approach and under some circumstances, we find a non-Hermitian Hamiltonian. Adopting this procedure yields the problem with an acceptable analytical solution. This means that all enough information in the study of the considered open quantum system is exactly obtained. Thereupon, we study the quantum correlations between the atoms with the help of the GMQD. It can be seen that the GMQD between two atoms can be controlled by the optomechanical coupling coefficient, the atom-field coupling strength and the dissipation parameters. Moreover, decreasing the coefficient of optomechanical coupling as well as reducing the strength of atom-field coupling improves the GMQD between two atoms. It is also mentioned that, taking the dissipation effects into account, we see that, as the time proceeds, the GMQD approaches to a stable value. In addition, eliminating the effect of spontaneous emission leads to a diminution in the amount of GMQD. Consequently, the quantum correlations between two atoms can be enhanced by considering the effect of spontaneous emission.

previous article Two-time correlation functions beyond quantum regression theorem: effect of external noise

next article Quantum walks on Sierpinski gasket and Sierpinski tetrahedron

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

Feng, Z.B., Wang, H.L., Yan, R.Y.: Quantum state transfer between an optomechanical cavity and a diamond nuclear spin ensemble. Quantum Inf. Process. 15(8), 3151–3167 (2016)ADSMathSciNetMATHCrossRef

Sete, E.A., Eleuch, H.: High-efficiency quantum state transfer and quantum memory using a mechanical oscillator. Phys. Rev. A 91, 032309 (2015)

Teh, R.Y., Kiesewetter, S., Reid, M.D., Drummond, P.D.: Simulation of an optomechanical quantum memory in the nonlinear regime. Phys. Rev. A 96, 013854 (2017)

Stannigel, K., Komar, P., Habraken, S.J.M., Bennett, S.D., Lukin, M.D., Zoller, P., Rabl, P.: Optomechanical quantum information processing with photons and phonons. Phys. Rev. Lett. 109, 013603 (2012)

Momenabadi, F.M., Baghshahi, H.R., Faghihi, M.J., Mirafzali, S.Y.: Stable entanglement in a quadripartite cavity optomechanics. Eur. Phys. J. Plus 136(1), 7 (2021)CrossRef

Taylor, M.A., Janousek, J., Daria, V., Knittel, J., Hage, B., Bachor, H.A., Bowen, W.P.: Biological measurement beyond the quantum limit. Nat. Photonics 7(3), 229 (2013)ADSCrossRef

Abadie, J., Abbott, B.P., Abbott, R., Abbott, T.D., Abernathy, M., Adams, C., Adhikari, R., Affeldt, C., Allen, B., Allen, G., et al.: A gravitational wave observatory operating beyond the quantum shot-noise limit. Nat. Phys. 7(12), 962 (2011)CrossRef

Salehi, M.J., Baghshahi, H.R., Mirafzali, S.Y.: Quantum correlation and squeezing dynamics of a dissipative nonlinear optomechanical oscillator: Heisenberg-Langevin approach. Eur. Phys. J. Plus 133(11), 471 (2018)CrossRef

Lee, J.H., Suh, J., Seok, H.: Dissipation-driven nonclassical-state generation in optomechanics with squeezed light. Phys. Rev. A 98, 043821 (2018)

10.

Nejad, A.A., Askari, H., Baghshahi, H.: Normal mode splitting in an optomechanical system: effects of coulomb and parametric interactions. J. Opt. Soc. Am. B 35(9), 2237–2243 (2018)ADSCrossRef

11.

Aspelmeyer, M., Kippenberg, T.J., Marquardt, F.: Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014)ADSCrossRef

12.

Brooks, D.W., Botter, T., Schreppler, S., Purdy, T.P., Brahms, N., Stamper-Kurn, D.M.: Non-classical light generated by quantum-noise-driven cavity optomechanics. Nature 488(7412), 476–480 (2012)ADSCrossRef

13.

Metcalfe, M.: Applications of cavity optomechanics. Appl. Phys. Rev. 1(3), 031105 (2014)

14.

Pirkkalainen, J.M., Cho, S., Massel, F., Tuorila, J., Heikkilä, T., Hakonen, P., Sillanpää, M.: Cavity optomechanics mediated by a quantum two-level system. Nat. Commun. 6(1), 1–6 (2015)CrossRef

15.

Liao, J.Q., Tian, L.: Macroscopic quantum superposition in cavity optomechanics. Phys. Rev. Lett. 116, 163602 (2016)

16.

Wang, D.Y., Bai, C.H., Wang, H.F., Zhu, A.D., Zhang, S.: Steady-state mechanical squeezing in a hybrid atom-optomechanical system with a highly dissipative cavity. Sci. Rep. 6(1), 1–8 (2016)

17.

Tan, H., Deng, W., Wu, Q., Li, G.: Steady-state light-mechanical quantum steerable correlations in cavity optomechanics. Phys. Rev. A 95, 053842 (2017)

18.

Cripe, J., Aggarwal, N., Singh, R., Lanza, R., Libson, A., Yap, M..J., Cole, G..D., McClelland, D..E., Mavalvala, N., Corbitt, T.: Radiation-pressure-mediated control of an optomechanical cavity. Phys. Rev. A 97, 013827 (2018)ADSCrossRef

19.

Liu, J.H., Zhang, Y.B., Yu, Y.F., Zhang, Z.M.: Photon-phonon squeezing and entanglement in a cavity optomechanical system with a flying atom. Front. Phys. 14(1), 12601 (2019)ADSCrossRef

20.

Liao, Q., Xiao, X., Nie, W., Zhou, N.: Transparency and tunable slow-fast light in a hybrid cavity optomechanical system. Opt. Express 28(4), 5288–5305 (2020)ADSCrossRef

21.

Yan, X.B., Cui, C.L., Gu, K.H., Tian, X.D., Fu, C.B., Wu, J.H.: Coherent perfect absorption, transmission, and synthesis in a double-cavity optomechanical system. Opt. Express 22(5), 4886–4895 (2014)ADSCrossRef

22.

Guo, Y., Li, K., Nie, W., Li, Y.: Electromagnetically-induced-transparency-like ground-state cooling in a double-cavity optomechanical system. Phys. Rev. A 90, 053841 (2014)

23.

El Qars, J., Daoud, M., Laamara, A.: Entanglement versus Gaussian quantum discord in a double-cavity opto-mechanical system. Int. J. Quantum Inf. 13(06), 1550041 (2015)MathSciNetMATHCrossRef

24.

Yan, X.B., Jia, W., Li, Y., Wu, J.H., Li, X.L., Mu, H.W.: Optomechanically induced amplification and perfect transparency in double-cavity optomechanics. Front. Phys. 10(3), 351–357 (2015)ADSCrossRef

25.

Huan, T., Zhou, R., Ian, H.: Dynamic entanglement transfer in a double-cavity optomechanical system. Phys. Rev. A 92, 022301 (2015)

26.

Wang, D.Y., Bai, C.H., Wang, H.F., Zhu, A.D., Zhang, S.: Steady-state mechanical squeezing in a double-cavity optomechanical system. Sci. Rep. 6, 38559 (2016)ADSCrossRef

27.

Chen, Z.X., Lin, Q., He, B., Lin, Z.Y.: Entanglement dynamics in double-cavity optomechanical systems. Opt. Express 25(15), 17237–17248 (2017)ADSCrossRef

28.

Chao, S.L., Xiong, B., Zhou, L.: Generating a squeezed-coherent-cat state in a double-cavity optomechanical system. Ann. Phys. (Berlin) 531(11), 1900196 (2019)ADSMathSciNetCrossRef

29.

Liao, Q.H., Dai, Y.Z., Nie, W.J., Liu, X., Liu, Y.C.: Cooling of mechanical resonator in a double-cavity system with two-level atomic ensemble. J. Phys. B: At., Mol. Opt. Phys. 53(8), 085402 (2020)

30.

Yan, X.B., Lu, H.L., Gao, F., Yang, L.: Perfect optical nonreciprocity in a double-cavity optomechanical system. Front. Phys. 14(5), 52601 (2019)ADSCrossRef

31.

Han, Y., Xue, L., Chen, B.: Generation of two-mode squeezing of mechanical oscillators in the multi-mode optomechanical systems. Quantum Inf. Process. 19(4), 1–12 (2020)MathSciNetCrossRef

32.

Huang, S., Agarwal, G.S.: Robust force sensing for a free particle in a dissipative optomechanical system with a parametric amplifier. Phys. Rev. A 95, 023844 (2017)

33.

Liao, C.G., Xie, H., Shang, X., Chen, Z.H., Lin, X.M.: Enhancement of steady-state bosonic squeezing and entanglement in a dissipative optomechanical system. Opt. Express 26(11), 13783–13799 (2018)ADSCrossRef

34.

Mehmood, A., Qamar, S., Qamar, S.: Effects of laser phase fluctuation on force sensing for a free particle in a dissipative optomechanical system. Phys. Rev. A 98, 053841 (2018)

35.

Huang, S., Chen, A.: Improving the cooling of a mechanical oscillator in a dissipative optomechanical system with an optical parametric amplifier. Phys. Rev. A 98, 063818 (2018)

36.

Liao, C.G., Chen, R.X., Xie, H., He, M.Y., Lin, X.M.: Quantum synchronization and correlations of two mechanical resonators in a dissipative optomechanical system. Phys. Rev. A 99, 033818 (2019)

37.

de Moraes Neto, G.D., Montenegro, V., Teizen, V.F., Vernek, E.: Dissipative phonon-Fock-state production in strong nonlinear optomechanics. Phys. Rev. A 99, 043836 (2019)

38.

Nadiki, M.H., Tavassoly, M.: The amplitude of the cavity pump field and dissipation effects on the entanglement dynamics and statistical properties of an optomechanical system. Opt. Commun. 452, 31–39 (2019)ADSCrossRef

39.

Xiong, B., Li, X., Chao, S.L., Yang, Z., Peng, R., Zhou, L.: Strong squeezing of duffing oscillator in a highly dissipative optomechanical cavity system. Ann. Phys. 532(4), 1900596 (2020)CrossRef

40.

Vitali, D., Gigan, S., Ferreira, A., Böhm, H., Tombesi, P., Guerreiro, A., Vedral, V., Zeilinger, A., Aspelmeyer, M.: Optomechanical entanglement between a movable mirror and a cavity field. Phys. Rev. Lett. 98(3), 030405 (2007)

41.

Wang, Y.D., Clerk, A.A.: Reservoir-engineered entanglement in optomechanical systems. Physical review letters 110(25), 253601 (2013)

42.

Wang, G., Huang, L., Lai, Y.C., Grebogi, C.: Nonlinear dynamics and quantum entanglement in optomechanical systems. Physical review letters 112(11), 110406 (2014)

43.

Cheng, J., Zhang, W.Z., Zhou, L., Zhang, W.: Preservation macroscopic entanglement of optomechanical systems in non-markovian environment. Sci. Rep. 6(1), 1–8 (2016)

44.

Bai, C.H., Wang, D.Y., Zhang, S., Liu, S., Wang, H.F.: Modulation-based atom-mirror entanglement and mechanical squeezing in an unresolved-sideband optomechanical system. Ann. Phys. (Berlin) 531(7), 1800271 (2019)ADSMathSciNetCrossRef

45.

Hu, C.S., Liu, Z.Q., Liu, Y., Shen, L.T., Wu, H., Zheng, S.B.: Entanglement beating in a cavity optomechanical system under two-field driving. Phys. Rev. A 101(3), 033810 (2020)

46.

Jennewein, T., Simon, C., Weihs, G., Weinfurter, H., Zeilinger, A.: Quantum cryptography with entangled photons. Phys. Rev. Lett. 84, 4729–4732 (2000)ADSCrossRef

47.

Yang, X., Bai, M.q., Mo, Z.w., Xiang, Y.: Bidirectional and cyclic quantum dense coding in a high-dimension system. Quantum Inf. Process. 19(2), 43 (2020)

48.

Anagha, M., Mohan, A., Muruganandan, T., Behera, B..K., Panigrahi, P..K.: A new scheme of quantum teleportation using highly entangled brown et al. state: an IBM quantum experience. Quantum Inf. Process 19(5), 1–12 (2020)MathSciNetCrossRef

49.

D’ambrosio, V., Spagnolo, N., Del Re, L., Slussarenko, S., Li, Y., Kwek, L.C., Marrucci, L., Walborn, S.P., Aolita, L., Sciarrino, F.: Photonic polarization gears for ultra-sensitive angular measurements. Nat. Commun. 4(1), 1–8 (2013)

50.

Koike, S., Takahashi, H., Yonezawa, H., Takei, N., Braunstein, S.L., Aoki, T., Furusawa, A.: Demonstration of quantum telecloning of optical coherent states. Phys. Rev. Lett. 96, 060504 (2006)

51.

Ollivier, H., Zurek, W.H.: Quantum discord: A measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)

52.

Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A: Math. Gen. 34(35), 6899 (2001)ADSMathSciNetMATHCrossRef

53.

Ferraro, A., Aolita, L., Cavalcanti, D., Cucchietti, F.M., Acín, A.: Almost all quantum states have nonclassical correlations. Phys. Rev. A 81, 052318 (2010)

54.

Rana, S., Parashar, P.: Entanglement is not a lower bound for geometric discord. Phys. Rev. A 86, 030302 (2012)

55.

Dakić, B., Vedral, V., Brukner, I..C..V.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)ADSMATHCrossRef

56.

Dakić, B., Lipp, Y.O., Ma, X., Ringbauer, M., Kropatschek, S., Barz, S., Paterek, T., Vedral, V., Zeilinger, A., Brukner, Č, et al.: Quantum discord as resource for remote state preparation. Nat. Phys. 8(9), 666–670 (2012)CrossRef

57.

Tufarelli, T., Girolami, D., Vasile, R., Bose, S., Adesso, G.: Quantum resources for hybrid communication via qubit-oscillator states. Phys. Rev. A 86, 052326 (2012)

58.

Chaves, R., de Melo, F.: Noisy one-way quantum computations: the role of correlations. Phys. Rev. A 84, 022324 (2011)ADSCrossRef

59.

Yao, Y., Li, H.W., Zou, X.B., Huang, J.Z., Zhang, C.M., Yin, Z.Q., Chen, W., Guo, G.C., Han, Z.F.: Quantum discord in quantum random access codes and its connection to dimension witnesses. Phys. Rev. A 86, 062310 (2012)

60.

Giampaolo, S.M., Streltsov, A., Roga, W., Bruß, D., Illuminati, F.: Quantifying nonclassicality: Global impact of local unitary evolutions. Phys. Rev. A 87, 012313 (2013)

61.

Laha, P., Lakshmibala, S., Balakrishnan, V.: Nonclassical effects in optomechanics: dynamics and collapse of entanglement. J. Opt. Soc. Am. B 36(3), 575–584 (2019)ADSCrossRef

62.

Barnett, S.M., Jeffers, J.: The damped Jaynes-Cummings model. J. Mod. Opt. 54(13–15), 2033–2048 (2007)ADSMATHCrossRef

63.

Di Fidio, C., Vogel, W., Khanbekyan, M., Welsch, D.G.: Photon emission by an atom in a lossy cavity. Phys. Rev. A 77, 043822 (2008)

64.

Di Fidio, C., Vogel, W.: Entanglement signature in the mode structure of a single photon. Phys. Rev. A 79, 050303 (2009)

65.

Di Fidio, C., Vogel, W.: Entanglement evolution in a cascaded system with losses. Physica E 42(3), 369–373 (2010)ADSCrossRef

66.

Baghshahi, H.R., Tavassoly, M.K., Behjat, A.: Entanglement of a damped non-degenerate \(\diamond \)-type atom interacting nonlinearly with a single-mode cavity. Eur. Phys. J. Plus 131(4), 80 (2016)CrossRef

67.

Mohamed, A.B.A.: Bipartite non-classical correlations for a lossy two connected qubit-cavity systems: trace distance discord and Bell’s non-locality. Quantum Inf. Process. 17(4), 1–18 (2018)MathSciNetMATHCrossRef

68.

Alqahtani, M.M.: Multiphoton process in cavity QED photons for implementing a three-qubit quantum gate operation. Quantum Inf. Process. 19(1), 1–15 (2020)MathSciNetCrossRef

69.

Liao, J.Q., Nori, F.: Photon blockade in quadratically coupled optomechanical systems. Phys. Rev. A 88, 023853 (2013)

70.

Xie, H., Lin, G.W., Chen, X., Chen, Z.H., Lin, X.M.: Single-photon nonlinearities in a strongly driven optomechanical system with quadratic coupling. Phys. Rev. A 93, 063860 (2016)

71.

Xie, H., Liao, C.G., Shang, X., Ye, M.Y., Lin, X.M.: Phonon blockade in a quadratically coupled optomechanical system. Phys. Rev. A 96, 013861 (2017)

72.

Zhang, J.S., Li, M.C., Chen, A.X.: Enhancing quadratic optomechanical coupling via a nonlinear medium and lasers. Phys. Rev. A 99, 013843 (2019)

73.

Wang, D.Y., Bai, C.H., Liu, S., Zhang, S., Wang, H.F.: Photon blockade in a double-cavity optomechanical system with nonreciprocal coupling. New J. Phys. 22(9), 093006 (2020)

74.

Eleuch, H.: Photon statistics of light in semiconductor microcavities. J. Phys. B: At. Mol. Opt. Phys. 41(5), 055502 (2008)

75.

Mohamed, A.B., Eleuch, H.: Non-classical effects in cavity QED containing a nonlinear optical medium and a quantum well: Entanglement and non-Gaussanity. Eur. Phys. J. D 69(8), 191 (2015)ADSCrossRef

76.

Altintas, F.: Geometric measure of quantum discord in non-Markovian environments. Opt. Commun. 283(24), 5264–5268 (2010)ADSCrossRef

77.

Lecocq, F., Teufel, J.D., Aumentado, J., Simmonds, R.W.: Resolving the vacuum fluctuations of an optomechanical system using an artificial atom. Nat. Phys. 11(8), 635–639 (2015)CrossRef

78.

Altintas, F., Eryigit, R.: Creation of quantum correlations between two atoms in a dissipative environment from an initial vacuum state. Phys. Lett. A 376(22), 1791–1796 (2012)ADSCrossRef

79.

Altintas, F., Eryigit, R.: Dissipative dynamics of quantum correlations in the strong-coupling regime. Phys. Rev. A 87, 022124 (2013)

80.

Gamel, O., James, D.F.V.: Time-averaged quantum dynamics and the validity of the effective hamiltonian model. Phys. Rev. A 82, 052106 (2010)

Title: Geometric discord in a dissipative double-cavity optomechanical system
Authors: Hamid Reza Baghshahi
Mohammad Haddad
Mohammad Javad Faghihi
Publication date: 01-07-2021
Publisher: Springer US
Published in: Quantum Information Processing / Issue 7/2021
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-021-03166-1

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 7/2021

Towards designing quantum reversible ternary multipliers

Quantum secure multi-party summation protocol based on blind matrix and quantum Fourier transform

Implementation of efficient quantum search algorithms on NISQ computers

An improved quantum algorithm for support matrix machines

Quantum key distribution with PRF(Hash, Nonce) achieves everlasting security

Rectangular surface code under biased noise