Skip to main content

Atom—Field Correlations in the Weak-Excitation Limit of Absorptive Optical Bistability


We calculate the steady-state and first-order time varying atom—field correlation functions in the weak-excitation limit of absorptive optical bistability from a linearized theory of quantum fluctuations. We formulate a Fokker—Planck equation in the positive P representation following the phase-space analysis in [H. J. Carmichael, Phys. Rev. A 33, 3262 (1986)], which is suitable for the determination of cross-correlations as it does not resort to adiabatic elimination. Special emphasis is placed on the limit of collective strong coupling as attained from a vanishing photon-loss rate. We compare to the cavity-transmission spectrum with reference to experimental results obtained for macroscopic dissipative systems, discussing the role of anomalous correlations arising as distinct nonclassical features.

This is a preview of subscription content, access via your institution.


  1. 1.

    A. Szöke, V. Daneu, J. Goldhar, and N. A. Kurnit, Appl. Phys. Lett. 15, 376 (1969).

    ADS  Article  Google Scholar 

  2. 2.

    F. Casagrande and L. A. Lugiato, Nuovo Cim. B 55, 173 (1980).

    ADS  Article  Google Scholar 

  3. 3.

    D. F. Walls, Nature (London, U.K.) 280, 451 (1979).

    ADS  Article  Google Scholar 

  4. 4.

    R. Bonifacio and L. A. Lugiato, Phys. Rev. Lett. 40, 1023 (1978).

    ADS  Article  Google Scholar 

  5. 5.

    C. M. Bowden and C. C. Sung, Phys. Rev. A 19, 2392 (1979).

    ADS  Article  Google Scholar 

  6. 6.

    G. S. Agarwal, L. M. Narducci, R. Gilmore, and D. H. Feng, Phys. Rev. A 18, 620 (1978).

    ADS  Article  Google Scholar 

  7. 7.

    H. J. Carmichael, Z. Phys. B 42, 183 (1981).

    ADS  Article  Google Scholar 

  8. 8.

    C. M. Savage and H. J. Carmichael, IEEE J. Quantum Electron. 24, 1495 (1988).

    ADS  Article  Google Scholar 

  9. 9.

    P. Alsing and H. J. Carmichael, J. Eur. Opt. Soc., Part B 3, 13 (1991).

    Article  Google Scholar 

  10. 10.

    M. A. Armen, A. E. Miller, and H. Mabuchi, Phys. Rev. Lett. 103, 173601 (2009).

    ADS  Article  Google Scholar 

  11. 11.

    G. Rempe, R. J. Thompson, R. J. Brecha, W. D. Lee, and H. J. Kimble, Phys. Rev. Lett. 67, 1727 (1991).

    ADS  Article  Google Scholar 

  12. 12.

    S. L. Mielke, G. T. Foster, and L. A. Orozco, Phys. Rev. Lett. 80, 3948 (1998).

    ADS  Article  Google Scholar 

  13. 13.

    G. T. Foster, S. L. Mielke, and L. A. Orozco, Phys. Rev. A 61, 053821 (2000).

    ADS  Article  Google Scholar 

  14. 14.

    S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, Phys. Rev. Lett. 99, 213601 (2007).

    ADS  Article  Google Scholar 

  15. 15.

    F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, Nature (London, U.K.) 450, 268 (2007).

    ADS  Article  Google Scholar 

  16. 16.

    H. Gothe, T. Valenzuela, M. Cristiani, and J. Eschner, Phys. Rev. A 99, 013849 (2019).

    ADS  Article  Google Scholar 

  17. 17.

    A. Dombi, A. Vukics, and P. Domokos, J. Phys. B: At., Mol. Opt. Phys. 46, 224010 (2013).

    ADS  Article  Google Scholar 

  18. 18.

    D. Hagenmüller, S. Schütz, G. Pupillo, and J. Schachenmayer, Phys. Rev. A 102, 013714 (2020).

    ADS  Article  Google Scholar 

  19. 19.

    H. J. Carmichael, Phys. Rev. A 33, 3262 (1986).

    ADS  Article  Google Scholar 

  20. 20.

    P. D. Drummond and C. W. Gardiner, J. Phys. A 13, 2353 (1980).

    ADS  MathSciNet  Article  Google Scholar 

  21. 21.

    H. J. Carmichael, J. S. Satchell, and S. Sarkar, Phys. Rev. A 34, 3166 (1986).

    ADS  Article  Google Scholar 

  22. 22.

    H. J. Carmichael, Statistical Methods in Quantum Optics 2: Non-Classical Fields (Springer, Berlin, 2008).

    Book  Google Scholar 

  23. 23.

    M. G. Raizen, R. J. Thompson, R. J. Brecha, H. J. Kimble, and H. J. Carmichael, Phys. Rev. Lett. 63, 240 (1989).

    ADS  Article  Google Scholar 

  24. 24.

    H. J. Carmichael, D. F. Walls, P. D. Drummond, and S. S. Hassan, Phys. Rev. A 27, 3112 (1983).

    ADS  Article  Google Scholar 

Download references


I am grateful to Prof. H.J. Carmichael for instructive discussions and guidance.

Author information



Corresponding author

Correspondence to Th. K. Mavrogordatos.

Additional information


I acknowledge the support of the Swedish Research Council (VR) alongside the Knut and Alice Wallenberg foundation (KAW).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mavrogordatos, T.K. Atom—Field Correlations in the Weak-Excitation Limit of Absorptive Optical Bistability. Jetp Lett. 112, 274–282 (2020).

Download citation