Skip to main content

Advertisement

Springer Nature Link
Log in

Perturbative dissipation dynamics of a weakly driven cavity QED system: generalized microscopic master equation

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We generalize a microscopic master equation method to study the dissipation dynamics of Jaynes–Cummings two-level system with a weak external driving. Using perturbative analysis to extend the damping bases theory, we derive the corrected Rabi oscillation and vacuum Rabi splitting analytically. The evolution of the decoherence factor of the weakly driven system reveals that the off-diagonal density matrix elements are oscillating at a frequency dependent on the driving strength and the initial population inversion. For highly inverted systems at the weak-driving limit, this frequency reduces to twice the value for the non-driven system, showing the dissipation dynamics unable to be discovered using more conventional approaches.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Jaynes, E.T., Cummings, F.W.: Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE 51, 89–109 (1963)

    Article  Google Scholar 

  2. Raimond, J.M., Brune, M., Haroche, S.: Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565–582 (2001)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  3. Bermudez, A., Martin-Delgado, M.A., Solano, E.: Exact mapping of the 2+1 Dirac oscillator onto the Jaynes–Cummings model: Ion-trap experimental proposal. Phys. Rev. A 76, 041801–041804 (2007)

    Article  ADS  Google Scholar 

  4. Wallraff, A., Schuster, D.I., Blais, A., Frunzio, L., Huang, R.S., Majer, J., Kumar, S., Girvin, S.M., Schoelkopf, R.J.: Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004)

    Article  ADS  Google Scholar 

  5. Majer, J., Chow, J.M., Gambetta, J.M., Koch, J., Johnson, B.R., Schreier, J.A., Frunzio, L., Schuster, D.I., Houck, A.A., Wallraff, A., Blais, A., Devoret, M.H., Girvin, S.M., Schoelkopf, R.J.: Coupling superconducting qubits via a cavity bus. Nature 449, 443–447 (2007)

    Article  ADS  Google Scholar 

  6. Devoret, M.H., Schoelkopf, R.J.: Superconducting circuits for quantum information: an outlook. Science 339, 1169–1174 (2013)

    Article  ADS  Google Scholar 

  7. DiVincenzo, D.: The physical implementation of quantum computation. Fortschr. Phys. 48, 771–783 (2000)

    Article  MATH  Google Scholar 

  8. Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119–130 (1976)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  9. Davies, E.B.: Markovian master equations. Commun. Math. Phys. 39, 91–110 (1974)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  10. Spohn, H., Lebowitz, J.L.: Irreversible thermodynamics for quantum systems weakly coupled to thermal reservoirs. Adv. Chem. Phys. 38, 109–142 (1978)

    Google Scholar 

  11. Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford Press, Oxford (2002)

    MATH  Google Scholar 

  12. Scala, M., Militello, B., Messina, A., Piilo, J., Maniscalco, S.: Microscopic derivation of the Jaynes–Cummings model with cavity losses. Phys. Rev. A 75, 013811–013818 (2007)

    Article  ADS  MATH  Google Scholar 

  13. Chen, C., Gao, Y.B.: Quantum decoherence of charge qubit coupled to nonlinear nanomechanical resonator. Commun. Theor. Phys. 60, 531–534 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  14. Xiao, X., Zhao, M.Y., Yu, S.M., Gao, Y.B.: Temporal behavior of Rabi oscillation in nanomechanical qed system with a nonlinear resonator. Commun. Theor. Phys. 65, 273–277 (2016)

    Article  ADS  MATH  Google Scholar 

  15. Gao, Y.B., Yang, S., Liu, Y.X., Sun, C.P., Nori, F.: Probing nano-mechanical QED effects (2009). arXiv:0902.2512

  16. Eberly, J.H., Narozny, N.B., Sanchez-Mondragon, J.J.: Periodic spontaneous collapse and revival in a simple quantum model. Phys. Rev. Lett. 44, 1323–1326 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  17. Narozny, N.B., Sanchez-Mondragon, J.J., Eberly, J.H.: Coherence versus incoherence: collapse and revival in a simple quantum model. Phys. Rev. A 23, 236–247 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  18. Rempe, G., Walther, H., Klein, N.: Observation of quantum collapse and revival in a one-atom maser. Phys. Rev. Lett. 58, 353–356 (1987)

    Article  ADS  Google Scholar 

  19. Briegel, H.J., Englert, B.G.: Quantum optical master equations: the use of damping bases. Phys. Rev. A 47, 3311–3329 (1993)

    Article  ADS  Google Scholar 

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

    Book  MATH  Google Scholar 

  21. Leggett, A.J., Chakravarty, S., Dorsey, A.T., Fisher, M.P.A., Garg, A., Zwerger, W.: Dynamics of the dissipative two-state system. Rev. Mod. Phys. 59, 1–85 (1987)

    Article  ADS  Google Scholar 

  22. Sun, C.P.: Quantum dynamical model for wave-function reduction in classical and macroscopic limits. Phys. Rev. A 48, 898–906 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  23. Cucchietti, F.M., Paz, J.P., Zurek, W.H.: Decoherence from spin environments. Phys. Rev. A 72, 052113–052120 (2005)

    Article  ADS  Google Scholar 

  24. Wen, P.Y., Kockum, A.F., Ian, H., Chen, J.C., Nori, F., Hoi, I.-C.: Reflective amplification without population inversion from a strongly driven superconducting qubit (2017). arXiv:1707.06400

Download references

Acknowledgements

Y. B. Gao acknowledges the support of the National Natural Science Foundation of China under Grant No. 11674017. H. I. acknowledges the support of FDCT Macau under grants 013/2013/A1 and 065/2016/A2, the University of Macau under grant MYRG2014-00052-FST and the National Natural Science Foundation of China under Grant No. 11404415.

Author information

Authors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, Beijing, 100124, China

    Shumin Yu & Yibo Gao

  2. Institute of Applied Physics and Materials Engineering, University of Macau, Macau, China

    Hou Ian

  3. UMacau Research Institute, Zhuhai, Guangdong, China

    Hou Ian

Authors
  1. Shumin Yu
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Yibo Gao
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Hou Ian
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Yibo Gao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yu, S., Gao, Y. & Ian, H. Perturbative dissipation dynamics of a weakly driven cavity QED system: generalized microscopic master equation. Quantum Inf Process 16, 283 (2017). https://doi.org/10.1007/s11128-017-1732-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-017-1732-6

Keywords