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

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Abstract

We present the results of a study of the two-time correlation functions of a dichotomously driven two-level system in contact with a thermal bath by using corrections beyond the quantum regression theorem. In the strong system-environment coupling regime, it is found that the noise parameters could be tuned to control the magnitude of corrections at low environmental temperatures. Motional averaging and narrowing effect of the external noise were observed on the absorption and emission spectra of the two-state system. Furthermore, effects similar to the destruction of tunneling and noise enhancement of transport are observed in the dynamics of the two-time correlations.

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References

  1. Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997)

    Book  Google Scholar 

  2. Carmichael, H.J.: Statistical Methods in Quantum Optics. Springer Press, USA (1999)

    Book  MATH  Google Scholar 

  3. Gardiner, C.W., Zoller, P.: Quantum Noise. Springer, USA (2000)

    Book  MATH  Google Scholar 

  4. Li, J., Silveri, M.P., Kumar, K.S., Pirkkalainen, J.M., Vepsäläinen, A., Chien, W.C., Tuorila, J., Sillanpää, M.A., Hakonen, P.J., Thuneberg, E.V., Paraoanu, G.S.: Motional averaging in a superconducting qubit. Nat. commun. 4, 1420 (2013)

    Article  ADS  Google Scholar 

  5. Li, L., Hall, M.J.W., Wisemanv, H.M.: Concepts of quantum non-markovianity: a hierarchy. Phys. Rep. 759, 1–51 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. de Vega, I., Alonso, D.: Dynamics of non-markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  7. Berthelot, A., Favero, I., Cassabois, G., Voisin, C., Delalande, C., Roussignol, Ph, Ferreira, R., Gérard, J.M.: Unconventional motional narrowing in the optical spectrum of a semiconductor quantum dot. Nat. Phys. 2, 759–764 (2006)

    Article  Google Scholar 

  8. Winger, M., Volz, T., Tarel, G., Portolan, S., Badolato, A., Hennessy, K.J., Hu, E.L., Beveratos, A., Finley, J., Savona, V., Imamoğlu, A.: Explanation of photon correlations in the far-off-resonance optical emission from a quantum-dot-cavity system. Phys. Rev. Lett. 103, 207403 (2009)

    Article  ADS  Google Scholar 

  9. Ulrich, S.M., Ates, S., Reitzenstein, S., Löffler, A., Forchel, A., Michler, P.: Dephasing of triplet-sideband optical emission of a resonantly driven \(\rm InAs{ GaAs}\) quantum dot inside a microcavity. Phys. Rev. Lett. 106, 247402 (2011)

    Article  ADS  Google Scholar 

  10. Jørgensen, M.R., Pollock, F.A.: A discrete memory-kernel for multi-time correlations in non-markovian quantum processes. Phys. Rev. A 102, 052206 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  11. Brixner, T., Stenger, J., Vaswani, H.M., Cho, M., Blankenship, R.E., Fleming, G.R.: Two-dimensional spectroscopy of electronic couplings in photosynthesis. Nature 434, 625–628 (2005)

    Article  ADS  Google Scholar 

  12. Onsager, L.: Reciprocal relations in irreversible processes. i. Phys. Rev. 37, 405 (1931)

    Article  ADS  MATH  Google Scholar 

  13. Lax, M.: Formal theory of quantum fluctuations from a driven state. Phys. Rev. 129, 2342–2348 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  14. Alonso, D., de Vega, I.: Multiple-time correlation functions for non-markovian interaction: beyond the quantum regression theorem. Phys. Rev. Lett. 94, 200403 (2005)

    Article  ADS  Google Scholar 

  15. de Vega, I., Alonso, D.: Non-markovian reduced propagator, multiple-time correlation functions, and master equations with general initial conditions in the weak-coupling limit. Phys. Rev. A 73, 022101 (2006)

    MathSciNet  Google Scholar 

  16. Alonso, D., de Vega, I.: Hierarchy of equations of multiple-time correlation functions. Phys. Rev. A 75, 052108 (2007)

    Article  ADS  Google Scholar 

  17. Budini, A.A.: Operator correlations and quantum regression theorem in non-markovian lindblad rate equations. J. Stat. Phys. 131, 51–78 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Goan, H.S., Chen, P.W., Jian, C.C.: Non-markovian finite-temperature two-time correlation functions of system operators: Beyond the quantum regression theorem. J. Chem. Phys. 134, 124112 (2011)

    Article  ADS  Google Scholar 

  19. Chen, P.W., Jian, C.C., Goan, H.S.: Non-markovian dynamics of a nanomechanical resonator measured by a quantum point contact. Phys. Rev. B 83, 115439 (2011)

    Article  ADS  Google Scholar 

  20. Goan, H.S., Jian, C.C., Chen, P.W.: Non-markovian finite-temperature two-time correlation functions of system operators of a pure-dephasing model. Phys. Rev. A 82, 012111 (2010)

    Article  ADS  Google Scholar 

  21. McCutcheon, D.P.S.: Optical signatures of non-markovian behavior in open quantum systems. Phys. Rev. A 93, 022119 (2016)

    Article  ADS  Google Scholar 

  22. de Vega, I., Alonso, D.: Emission spectra of atoms with non-markovian interaction: Fluorescence in a photonic crystal. Phys. Rev. A 77, 043836 (2008)

    Article  ADS  Google Scholar 

  23. Jin, J., Karlewski, C., Marthaler, M.: Non-markovian correlation functions for open quantum systems. New J. Phys. 18, 083038 (2016)

    Article  ADS  MATH  Google Scholar 

  24. Ford, G.W., O’Connell, R.F.: There is no quantum regression theorem. Phys. Rev. Lett. 77, 798–801 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Ford, G.W., O’Connell, R.F.: Calculation of correlation functions in the weak coupling approximation. Ann. Phys. 276, 144–151 (1999)

    Article  ADS  MATH  Google Scholar 

  26. Ford, G.W., O’Connell, R.F.: Driven systems and the lax formula. Opt. Commun. 179, 451–461 (2000)

    Article  ADS  Google Scholar 

  27. Blanter, YaM, Büttiker, M.: Shot noise in mesoscopic conductors. Phys. Rep. 336, 1–166 (2000)

    Article  ADS  Google Scholar 

  28. Cosacchi, M., Cygorek, M., Ungar, F., Barth, A.M., Vagov, A., Axt, V.M.: Path-integral approach for nonequilibrium multitime correlation functions of open quantum systems coupled to markovian and non-markovian environments. Phys. Rev. B 98, 125302 (2018)

    Article  ADS  Google Scholar 

  29. Shao, J., Makri, N.: Iterative path integral formulation of equilibrium correlation functions for quantum dissipative systems. J. Chem. Phys. 116, 507 (2002)

    Article  ADS  Google Scholar 

  30. Pollock, F., Rodriguez-Rosario, C.A., Frauenheim, T., Paternostro, M., Modi, K.: Non-markovian quantum processes: complete framework and efficient characterization. Phys. Rev. A 97, 012127 (2018)

    Article  ADS  Google Scholar 

  31. Jørgensen, M.R., Pollock, F.A.: Exploiting the causal tensor network structure of quantum processes to efficiently simulate non-markovian path integrals. Phys. Rev. Lett. 123, 240602 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  32. Guarnieri, G., Smirne, A., Vacchini, B.: Quantum regression theorem and non-markovianity of quantum dynamics. Phys. Rev. A 90, 022110 (2014)

    Article  ADS  Google Scholar 

  33. Chen, P.-W., Ali Md., M.: Investigating leggett-garg inequality for a two level system under decoherence in a non-markovian dephasing environment. Sci. Rep. 4, 6165 (2014)

    Article  Google Scholar 

  34. Ali Md., M., Lo, P.Y., Tu, T.W.Y., Zhang, W.M.: Non-markovianity measure using two-time correlation functions. Phys. Rev. A 92, 062306 (2015)

    Article  ADS  Google Scholar 

  35. Kurt, A.: Non-markovian corrections to quantum regression theorem for the strong coupling spin-boson model. SAUJS 24, 596–604 (2020)

    Google Scholar 

  36. Jang, S.J., Benedetta, M.: Delocalized excitons in natural light-harvesting complexes. Rev. Mod. Phys. 90, 035003 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  37. Goychuk, I.A., Petrov, E.G., May, V.: Dynamics of the dissipative two-level system driven by external telegraph noise. Phys. Rev. E 52, 2392–2400 (1995)

    Article  ADS  Google Scholar 

  38. Pashkin, YuA, Astafiev, O., Yamamoto, T., Nakamura, Y., Tsai, J.S.: Josephson charge qubits: a brief review. Quantum Inf. Proc. 8, 55–80 (2009)

    Article  Google Scholar 

  39. Panev, N., Pistol, M.-E., Jeppesen, S., Evtikhiev, V.P., Katznelson, A.A., Kotelnikov, EYu.: Spectroscopic studies of random telegraph noise in InAs quantum dots in GaAs. J. Appl. Phys. 92, 12 (2002)

    Article  Google Scholar 

  40. Zhou, D., Lang, A., Joynt, R.: Disentanglement and decoherence from classical non-Markovian noise: random telegraph noise. Quantum Inf. Proc. 9, 727–747 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  41. de Vega, I., Alonso, D.: Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  42. Kurt, A., Eryiğit, R.: Noise-induced non-Markovianity. Phys. Rev. A 98, 042125 (2018)

    Article  ADS  Google Scholar 

  43. Garg, A., Onuchic, J.N., Ambegaokar, V.J.: Effect of friction on electron transfer in biomolecules. J. Chem. Phys. 83, 4491–4503 (1985)

    Article  ADS  Google Scholar 

  44. Bourret, R.C., Frisch, U., Pouquet, A.: Browian motion of harmonic oscillator with stochastic frequency. Physica 65, 303–320 (1973)

    Article  ADS  Google Scholar 

  45. Shapiro, V.E., Loginov, V.M.: Formulae of differentiation and their use for solving stochastic equations. Phys. A 91, 563 (1978)

    Article  MathSciNet  Google Scholar 

  46. Magazzù, L., Hänggi, P., Spagnolo, B., Valenti, D.: Quantum resonant activation. Phys. Rev. E 95, 042104 (2017)

    Article  ADS  Google Scholar 

  47. Berry, M.: Two-state quantum asymptotics. Ann. N. Y. Acad. Sci. 755, 303 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  48. Rebentrost, P., Mohseni, M., Kassal, I., Lloyd, S., Aspuru-Guzik, A.: Environment-assisted quantum transport. New J. Phys. 11, 033003 (2009)

    Article  ADS  Google Scholar 

  49. Wang, X.R., Zheng, Y.S., Sun, Y.: Spin relaxation and decoherence of two-level systems. Phys. Rev. B 72, 121303 (2005)

    Article  ADS  Google Scholar 

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Acknowledgements

The author would like to acknowledge many useful comments and discussions with Prof. Dr. Resul Eryiğit.

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Correspondence to Arzu Kurt.

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Kurt, A. Two-time correlation functions beyond quantum regression theorem: effect of external noise. Quantum Inf Process 20, 238 (2021). https://doi.org/10.1007/s11128-021-03153-6

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