Quantum Information Processing

, Volume 15, Issue 5, pp 2021–2032 | Cite as

Does “cooling by heating” protect quantum correlations?

  • C. J. Villas-Boas
  • W. B. CardosoEmail author
  • A. T. Avelar
  • A. Xuereb
  • N. G. de Almeida


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.


Cooling by heating Quantum correlations Quantum discord Entanglement 



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.


  1. 1.
    Barnett, S.M., Phoenix, S.J.D.: Entropy as a measure of quantum optical correlation. Phys. Rev. A 40, 2404 (1989)ADSMathSciNetCrossRefGoogle 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)ADSCrossRefGoogle 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)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)ADSCrossRefGoogle Scholar
  5. 5.
    Zheng, S.B.: Quantum-information processing and multiatom-entanglement engineering with a thermal cavity. Phys. Rev. A 66, 060303(R) (2002)ADSCrossRefGoogle 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)ADSCrossRefGoogle 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)ADSCrossRefGoogle 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)ADSCrossRefGoogle Scholar
  9. 9.
    Martin, I., Shnirman, A., Tian, L., Zoller, P.: Ground-state cooling of mechanical resonators. Phys. Rev. B 69, 125339 (2004)ADSCrossRefGoogle 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)CrossRefGoogle Scholar
  11. 11.
    Wang, X.: Entanglement in the quantum Heisenberg XY model. Phys. Rev. A 64, 012313 (2001)ADSCrossRefGoogle 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)ADSCrossRefGoogle 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)ADSCrossRefGoogle 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)ADSCrossRefGoogle 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)ADSMathSciNetCrossRefzbMATHGoogle 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)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Zhang, G.-F., Li, S.-S., Liang, J.-Q.: Thermal entanglement in Spin-1 biparticle system. Opt. Commun. 245, 457 (2005)ADSCrossRefGoogle Scholar
  18. 18.
    Osenda, O., Raggio, G.A.: Entanglement in thermal equilibrium states. Phys. Rev. A 72, 064102 (2005)ADSCrossRefGoogle Scholar
  19. 19.
    Canosa, N., Rossignoli, R.: Global entanglement in XXZ chains. Phys. Rev. A 73, 022347 (2006)ADSCrossRefGoogle Scholar
  20. 20.
    Zhang, R., Zhu, S.: Thermal entanglement in a two-dimensional Heisenberg XY model. Phys. Lett. A 348, 110 (2006)ADSMathSciNetCrossRefzbMATHGoogle 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)ADSCrossRefGoogle 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)ADSCrossRefGoogle 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)ADSCrossRefGoogle 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)ADSCrossRefGoogle 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)ADSCrossRefGoogle Scholar
  26. 26.
    Militello, B., Messina, A.: Genuine tripartite entanglement in a spin-star network at thermal equilibrium. Phys. Rev. A 83, 042305 (2011)ADSCrossRefGoogle 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)ADSCrossRefGoogle Scholar
  28. 28.
    Hide, J., Nakata, Y., Murao, M.: Entanglement and the interplay between staggered fields and couplings. Phys. Rev. A 85, 042303 (2012)ADSCrossRefGoogle 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)ADSCrossRefGoogle 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)ADSCrossRefGoogle 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)ADSCrossRefGoogle Scholar
  32. 32.
    Quiroga, L., Rodríguez, F.J., Ramírez, M.E., París, R.: Nonequilibrium thermal entanglement. Phys. Rev. A 75, 032308 (2007)ADSCrossRefGoogle Scholar
  33. 33.
    Sinaysky, I., Petruccione, F., Burgarth, D.: Dynamics of nonequilibrium thermal entanglement. Phys. Rev. A 78, 062301 (2008)ADSCrossRefGoogle 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)ADSCrossRefGoogle Scholar
  35. 35.
    Pumulo, N., Sinayskiy, I., Petruccione, F.: Non-equilibrium thermal entanglement for a three spin chain. Phys. Lett. A 375, 3157 (2011)ADSMathSciNetCrossRefzbMATHGoogle 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)ADSCrossRefGoogle Scholar
  37. 37.
    Cleuren, B., Rutten, B., Van den Broeck, C.: Cooling by heating: refrigeration powered by photons. Phys. Rev. Lett. 108, 120603 (2012)ADSCrossRefGoogle 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)ADSCrossRefGoogle 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)ADSCrossRefGoogle Scholar
  40. 40.
    Hinds, E., Blatt, R.: NOBEL 2012 Physics: manipulating individual quantum systems. Nature 492, 55 (2012). (and references therein)ADSCrossRefGoogle 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)ADSCrossRefGoogle 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)ADSCrossRefGoogle 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)ADSCrossRefGoogle Scholar
  44. 44.
    James, D.F.V.: Quantum computation with hot and cold ions: an assessment of proposed schemes. Fortschr. Phys. 48, 823 (2000)CrossRefGoogle Scholar
  45. 45.
    Tan, S.M.: A computational toolbox for quantum and atomic optics. J. Opt. B Quantum Semiclassical Opt. 1, 424 (1999)ADSCrossRefGoogle 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)ADSCrossRefGoogle Scholar
  47. 47.
    Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRefzbMATHGoogle Scholar
  48. 48.
    Girolami, D., Adesso, G.: Quantum discord for general two-qubit states: analytical progress. Phys. Rev. A 83, 052108 (2011)ADSCrossRefGoogle Scholar
  49. 49.
    Girolami, D., Adesso, G.: Interplay between computable measures of entanglement and other quantum correlations. Phys. Rev. A 84, 052110 (2011)ADSCrossRefGoogle Scholar
  50. 50.
    Girolami, D., Adesso, G.: Observable measure of bipartite quantum correlations. Phys. Rev. Lett. 108, 150403 (2012)ADSCrossRefGoogle Scholar
  51. 51.
    Girolami, D., Tufarelli, T., Adesso, G.: Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. Lett. 110, 240402 (2013)ADSCrossRefGoogle Scholar
  52. 52.
    Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRefGoogle Scholar
  53. 53.
    Asbóth, J.K., Calsamiglia, J., Ritsch, H.: Computable measure of nonclassicality for light. Phys. Rev. Lett. 94, 173602 (2005)ADSCrossRefGoogle Scholar
  54. 54.
    Vogel, W., Sperling, J.: Unified quantification of nonclassicality and entanglement. Phys. Rev. A 89, 052302 (2014)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • C. J. Villas-Boas
    • 1
  • W. B. Cardoso
    • 2
    Email author
  • A. T. Avelar
    • 2
  • A. Xuereb
    • 3
    • 4
  • N. G. de Almeida
    • 2
  1. 1.Departamento de FísicaUniversidade Federal de São CarlosSão CarlosBrazil
  2. 2.Instituto de FísicaUniversidade Federal de GoiásGoiâniaBrazil
  3. 3.Department of PhysicsUniversity of MaltaMsidaMalta
  4. 4.Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and PhysicsQueen’s University BelfastBelfastUK

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