Does “cooling by heating” protect quantum correlations?

Abstract

The connection between nonequilibrium quantum correlations, such as entanglement and quantum discord, and cooling by heating is investigated for a system composed by two atoms interacting with a single electromagnetic mode of a lossy cavity. This Hamiltonian model is experimentally feasible in the quantum optics domain and presents the occurrence of both nonequilibrium quantum correlations and cooling by heating for a range of parameters. Since in the cooling by heating phenomenon the effective temperature of the system decreases even increasing the environments temperature, it could be expected that quantum correlations could be enhanced. Interestingly, for some parameters we show that, contrary to this expectation, in the case studied here the lowering of the system effective temperature leads to no enhancement in the quantum correlations. In addition, we found that at both zero and finite temperature, depending on the parameters used, quantum correlations can be enhanced even when increasing the damping rates, a somewhat counterintuitive result.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

References

  1. 1.

    Barnett, S.M., Phoenix, S.J.D.: Entropy as a measure of quantum optical correlation. Phys. Rev. A 40, 2404 (1989)

    ADS  MathSciNet  Article  Google Scholar 

  2. 2.

    Almeida, M.P., de Melo, F., Hor-Meyll, M., Salles, A., Walborn, S.P., Souto Ribeiro, P.H., Davidovich, L.: Environment-induced sudden death of entanglement. Science 316, 579 (2007)

    ADS  Article  Google Scholar 

  3. 3.

    Raimond, J.M., Brune, M., Haroche, S.: Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565 (2001)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)

    ADS  Article  Google Scholar 

  5. 5.

    Zheng, S.B.: Quantum-information processing and multiatom-entanglement engineering with a thermal cavity. Phys. Rev. A 66, 060303(R) (2002)

    ADS  Article  Google Scholar 

  6. 6.

    Cardoso, W.B., Avelar, A.T., Baseia, B., de Almeida, N.G.: Entanglement sudden death via two-photon processes in cavity QED. J. Phys. B At. Mol. Opt. Phys. 42, 195507 (2009)

    ADS  Article  Google Scholar 

  7. 7.

    Togan, E., Chu, Y., Trifonov, A.S., Jiang, L., Maze, J., Childress, L., Dutt, M.V.G., Sørensen, A.S., Hemmer, P.R., Zibrov, A.S., Lukin, M.D.: Quantum entanglement between an optical photon and a solid-state spin qubit. Nature 466, 730 (2010)

    ADS  Article  Google Scholar 

  8. 8.

    Chtchelkatchev, N.M., Blatter, G., Lesovik, G.B., Martin, T.: Bell inequalities and entanglement in solid-state devices. Phys. Rev. B 66, 161320(R) (2002)

    ADS  Article  Google Scholar 

  9. 9.

    Martin, I., Shnirman, A., Tian, L., Zoller, P.: Ground-state cooling of mechanical resonators. Phys. Rev. B 69, 125339 (2004)

    ADS  Article  Google Scholar 

  10. 10.

    Sarovar, M., Ishizaki, A., Fleming, G.R., Whaley, K.B.: Quantum entanglement in photosynthetic light-harvesting complexes. Nat. Phys. 6, 462 (2010)

    Article  Google Scholar 

  11. 11.

    Wang, X.: Entanglement in the quantum Heisenberg XY model. Phys. Rev. A 64, 012313 (2001)

    ADS  Article  Google Scholar 

  12. 12.

    Rauschenbeutel, A., Nogues, G., Osnaghi, S., Bertet, P., Brune, M., Raimond, J.M., Haroche, S.: Step-by-step engineered multiparticle entanglement. Science 288, 2024 (2000)

    ADS  Article  Google Scholar 

  13. 13.

    Anteneodo, C., Souza, A.M.C.: Enhancement of thermal entanglement in two-qubit XY models. J. Opt. B Quantum Semiclassical Opt. 5, 73 (2003)

    ADS  Article  Google Scholar 

  14. 14.

    Gu, S.-J., Li, H., Li, Y.-Q., Lin, H.-Q.: Entanglement of the Heisenberg chain with the next-nearest-neighbor interaction. Phys. Rev. A 70, 052302 (2004)

    ADS  Article  Google Scholar 

  15. 15.

    Cao, M., Zhu, S.: Thermal entanglement between alternate qubits of a four-qubit Heisenberg XX chain in a magnetic field. Phys. Rev. A 71, 034311 (2005)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  16. 16.

    Werlang, T., Ribeiro, G.A.P., Rigolin, G.: Interplay between quantum phase transitions and the behavior of quantum correlations at finite temperatures. Int. J. Mod. Phys. B 27, 1345032 (2013)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  17. 17.

    Zhang, G.-F., Li, S.-S., Liang, J.-Q.: Thermal entanglement in Spin-1 biparticle system. Opt. Commun. 245, 457 (2005)

    ADS  Article  Google Scholar 

  18. 18.

    Osenda, O., Raggio, G.A.: Entanglement in thermal equilibrium states. Phys. Rev. A 72, 064102 (2005)

    ADS  Article  Google Scholar 

  19. 19.

    Canosa, N., Rossignoli, R.: Global entanglement in XXZ chains. Phys. Rev. A 73, 022347 (2006)

    ADS  Article  Google Scholar 

  20. 20.

    Zhang, R., Zhu, S.: Thermal entanglement in a two-dimensional Heisenberg XY model. Phys. Lett. A 348, 110 (2006)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  21. 21.

    Hartmann, L., Dür, W., Briegel, H.-J.: Steady-state entanglement in open and noisy quantum systems. Phys. Rev. A 74, 052304 (2006)

    ADS  Article  Google Scholar 

  22. 22.

    Sun, Z.-Y., Yao, K.-L., Yao, W., Zhang, D.-H., Liu, Z.-L.: Finite-temperature entanglement for low-dimensional quantum spin chains. Phys. Rev. B 77, 014416 (2008)

    ADS  Article  Google Scholar 

  23. 23.

    Souza, A.M., Reis, M.S., Soares-Pinto, D.O., Oliveira, I.S., Sarthour, R.S.: Experimental determination of thermal entanglement in spin clusters using magnetic susceptibility measurements. Phys. Rev. B 77, 104402 (2008)

    ADS  Article  Google Scholar 

  24. 24.

    Wang, H., Liu, S., He, J.: Thermal entanglement in two-atom cavity QED and the entangled quantum Otto engine. Phys. Rev. E 79, 041113 (2009)

    ADS  Article  Google Scholar 

  25. 25.

    Guo, J.-L., Mi, Y.-J., Zhang, J., Song, H.-S.: Thermal quantum discord of spins in an inhomogeneous magnetic field. J. Phys. B At. Mol. Opt. Phys. 44, 065504 (2011)

    ADS  Article  Google Scholar 

  26. 26.

    Militello, B., Messina, A.: Genuine tripartite entanglement in a spin-star network at thermal equilibrium. Phys. Rev. A 83, 042305 (2011)

    ADS  Article  Google Scholar 

  27. 27.

    Li, S.-S., Ren, T.-Q., Kong, X.-M., Liu, K.: Thermal entanglement in the Heisenberg XXZ model with Dzyaloshinskii–Moriya interaction. Physica A 391, 35 (2012)

    ADS  Article  Google Scholar 

  28. 28.

    Hide, J., Nakata, Y., Murao, M.: Entanglement and the interplay between staggered fields and couplings. Phys. Rev. A 85, 042303 (2012)

    ADS  Article  Google Scholar 

  29. 29.

    Rojas, O., Rojas, M., Ananikian, N.S., de Souza, S.M.: Thermal entanglement in an exactly solvable Ising-XXZ diamond chain structure. Phys. Rev. A 86, 042330 (2012)

    ADS  Article  Google Scholar 

  30. 30.

    Xu, Y.-L., Wang, L.-S., Kong, X.-M.: Thermal entanglement between non-nearest-neighbor spins on fractal lattices. Phys. Rev. A 87, 012312 (2013)

    ADS  Article  Google Scholar 

  31. 31.

    Zhou, L., Song, H.S., Guo, Y.Q., Li, C.: Enhanced thermal entanglement in an anisotropic Heisenberg XYZ chain. Phys. Rev. A 68, 024301 (2003)

    ADS  Article  Google Scholar 

  32. 32.

    Quiroga, L., Rodríguez, F.J., Ramírez, M.E., París, R.: Nonequilibrium thermal entanglement. Phys. Rev. A 75, 032308 (2007)

    ADS  Article  Google Scholar 

  33. 33.

    Sinaysky, I., Petruccione, F., Burgarth, D.: Dynamics of nonequilibrium thermal entanglement. Phys. Rev. A 78, 062301 (2008)

    ADS  Article  Google Scholar 

  34. 34.

    Huang, X.-L., Guo, J.-L., Yi, X.-X.: Nonequilibrium thermal entanglement in a three-qubit XX model. Phys. Rev. A 80, 054301 (2009)

    ADS  Article  Google Scholar 

  35. 35.

    Pumulo, N., Sinayskiy, I., Petruccione, F.: Non-equilibrium thermal entanglement for a three spin chain. Phys. Lett. A 375, 3157 (2011)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  36. 36.

    Mari, A., Eisert, J.: Cooling by heating: very hot thermal light can significantly cool quantum systems. Phys. Rev. Lett. 108, 120602 (2012)

    ADS  Article  Google Scholar 

  37. 37.

    Cleuren, B., Rutten, B., Van den Broeck, C.: Cooling by heating: refrigeration powered by photons. Phys. Rev. Lett. 108, 120603 (2012)

    ADS  Article  Google Scholar 

  38. 38.

    Rossatto, D.Z., de Almeida, A.R., Werlang, T., Villas-Boas, C.J., de Almeida, N.G.: Cooling by heating in the quantum optics domain. Phys. Rev. A 86, 035802 (2012)

    ADS  Article  Google Scholar 

  39. 39.

    Gleyzes, S., Kuhr, S., Guerlin, C., Bernu, J., Deléglise, S., Hoff, U.B., Brune, M., Raimond, J.-M., Haroche, S.: Quantum jumps of light recording the birth and death of a photon in a cavity. Nature 446, 297 (2007)

    ADS  Article  Google Scholar 

  40. 40.

    Hinds, E., Blatt, R.: NOBEL 2012 Physics: manipulating individual quantum systems. Nature 492, 55 (2012). (and references therein)

    ADS  Article  Google Scholar 

  41. 41.

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

    ADS  Article  Google Scholar 

  42. 42.

    Osnaghi, S., Bertet, P., Auffeves, A., Maioli, P., Brune, M., Raimond, J.M., Haroche, S.: Coherent control of an atomic collision in a cavity. Phys. Rev. Lett. 87, 037902 (2001)

    ADS  Article  Google Scholar 

  43. 43.

    Santos, M.F., Solano, E., de Matos Filho, R.L.: Conditional large Fock state preparation and field state reconstruction in cavity QED. Phys. Rev. Lett. 87, 093601 (2001)

    ADS  Article  Google Scholar 

  44. 44.

    James, D.F.V.: Quantum computation with hot and cold ions: an assessment of proposed schemes. Fortschr. Phys. 48, 823 (2000)

    Article  Google Scholar 

  45. 45.

    Tan, S.M.: A computational toolbox for quantum and atomic optics. J. Opt. B Quantum Semiclassical Opt. 1, 424 (1999)

    ADS  Article  Google Scholar 

  46. 46.

    Zia, R.K.P., Praestgaard, E.L., Mouritsen, O.G.: Getting more from pushing less: negative specific heat and conductivity in nonequilibrium steady states. Am. J. Phys. 70, 384 (2002)

    ADS  Article  Google Scholar 

  47. 47.

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

    ADS  Article  MATH  Google Scholar 

  48. 48.

    Girolami, D., Adesso, G.: Quantum discord for general two-qubit states: analytical progress. Phys. Rev. A 83, 052108 (2011)

    ADS  Article  Google Scholar 

  49. 49.

    Girolami, D., Adesso, G.: Interplay between computable measures of entanglement and other quantum correlations. Phys. Rev. A 84, 052110 (2011)

    ADS  Article  Google Scholar 

  50. 50.

    Girolami, D., Adesso, G.: Observable measure of bipartite quantum correlations. Phys. Rev. Lett. 108, 150403 (2012)

    ADS  Article  Google Scholar 

  51. 51.

    Girolami, D., Tufarelli, T., Adesso, G.: Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. Lett. 110, 240402 (2013)

    ADS  Article  Google Scholar 

  52. 52.

    Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)

    ADS  Article  Google Scholar 

  53. 53.

    Asbóth, J.K., Calsamiglia, J., Ritsch, H.: Computable measure of nonclassicality for light. Phys. Rev. Lett. 94, 173602 (2005)

    ADS  Article  Google Scholar 

  54. 54.

    Vogel, W., Sperling, J.: Unified quantification of nonclassicality and entanglement. Phys. Rev. A 89, 052302 (2014)

    ADS  Article  Google Scholar 

Download references

Acknowledgments

We acknowledge financial support from the Brazilian agency CNPq, CAPES, and FAPEG. C.J.V.-B. also acknowledges financial support from São Paulo Research Foundation (FAPESP)—Grant No. 2013/04162-5. This work was performed as part of the Brazilian National Institute of Science and Technology (INCT) for Quantum Information. A.X. thanks the Universidade Federal de Goiás for its kind hospitality.

Author information

Affiliations

Authors

Corresponding author

Correspondence to W. B. Cardoso.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Villas-Boas, C.J., Cardoso, W.B., Avelar, A.T. et al. Does “cooling by heating” protect quantum correlations?. Quantum Inf Process 15, 2021–2032 (2016). https://doi.org/10.1007/s11128-016-1254-7

Download citation

Keywords

  • Cooling by heating
  • Quantum correlations
  • Quantum discord
  • Entanglement