Abstract
The detection of microwave states is complicated by strong thermal noise, which is inevitably introduced by linear amplifiers. We show how to extract from measured data normally or anti-normally ordered moments of photon creation and annihilation operators, the set of which contains complete information on the quantum state of an electromagnetic field. Equations for the evolution of the quantum state are derived in terms of moments. Using this approach, we consider in detail issues of decoherence and thermalization of microwave quantum states. Results are illustrated using the examples of Fock, coherent, squeezed, thermal, and even and odd coherent states (Schrödinger cat states).
Similar content being viewed by others
References
S. Brattke, B. T. N. Varcoe, and H. Walther, Phys. Rev. Lett. 86, 3534 (2001).
A. A. Houck, D. I. Schuster, J. M. Gambetta, J. A. Schreier, B. R. Johnson, J. M. Chow, L. Frunzio, J. Majer, M. H. Devoret, S. M. Girvin, and R. H. Schoelkopf, Nature 449, 328 (2007).
G. Romero, J. J. Garcia-Ripoll, and E. Solano, Phys. Rev. Lett. 102, 173602 (2009).
F. Mallet, M. A. Castellanos-Beltran, H. S. Ku, S. Glancy, E. Knill, K. D. Irwin, G. C. Hilton, L. R. Vale, and K. W. Lehnert, Phys. Rev. Lett. 106, 220502 (2011).
M. A. Castellanos-Beltran, K. D. Irwin, G. C. Hilton, L. R. Vale, and K. W. Lehnert, Nature Physics 4, 929 (2008).
N. Bergeal, R. Vijay, V. E. Manucharyan, I. Siddiqi, R. J. Schoelkopf, S. M. Girvin, and M. H. Devoret, Nature Physics 6, 296 (2010).
E. P. Menzel, F. Deppe, and M. Mariantoni, Phys. Rev. Lett. 105, 100401 (2010).
M. Mariantoni, E. P. Menzel, and F. Deppe, Phys. Rev. Lett. 105, 133601 (2010).
C. Eichler, D. Bozyigit, C. Lang, L. Steffen, J. Fink, and A. Wallraff, Phys. Rev. Lett. 106, 220503 (2011).
R. E. Collin, Foundations for Microwave Engineering (McGraw Hill, New York, 1992).
D. M. Pozar, Microwave Engineering, 3rd. ed. (Wiley, New York, 2005).
M. S. Kim, Phys. Rev. A 56, 3175 (1997).
W. P. Schleich, Quantum Optics in Phase Space, Ed. by V. P. Yakovlev (Wiley-VCH, New York, 2001; Fizmatlit, Moscow, 2005).
M. P. Silva, D. Bozyigit, A. Wallraft, and A. Blais, Phys. Rev. A 82, 043804 (2010).
A. Wunsche, Quantum Opt. J. Europ. Opt. Soc. B 2, 453 (1990).
C. T. Lee, Phys. Rev. A 46, 6097 (1992).
U. Herzog, Phys. Rev. A 53, 2889 (1996).
V. Buzek, G. Adam, and G. Drobny, Phys. Rev. A 54, 804 (1996).
C. M. Caves, Phys. Rev. D 26, 1817 (1982).
S. N. Filippov and V. I. Man’ko, Phys. Rev. A 84, 033827 (2011).
V. V. Dodonov, I. A. Malkin, and V. I. Man’ko, Physica A 72, 597 (1974).
V. V. Dodonov and V. I. Man’ko, Trudy FIAN 183, 182 (1987).
V. V. Dodonov and V. I. Man’ko, J. Mat. Phys. 35, 4277 (1994).
E. Wigner, Phys. Rev. 40, 749 (1932).
J. E. Moyal, Mat. Proc. Cambridge Phil. Soc. 45, 99 (1949).
V. V. Dodonov, S. S. Mizrahi, and A. L. de Souza Silva, J. Opt. 2, 271 (2000).
S. Deleglise, I. Dotsenko, C. Sayrin, J. Bernu, M. Brune, J.-M. Raimond, and S. Haroche, Nature 455, 510 (2008).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S.N. Filippov, V.I. Man’ko, 2012, published in Optika i Spektroskopiya, 2012, Vol. 112, No. 3, pp. 405–413.
Rights and permissions
About this article
Cite this article
Filippov, S.N., Man’ko, V.I. Evolution of microwave quantum states in terms of measurable ordered moments of creation and annihilation operators. Opt. Spectrosc. 112, 365–372 (2012). https://doi.org/10.1134/S0030400X12030083
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0030400X12030083