Abstract
The Jaynes-Cummings (JC) model is presented based on quantized counterpropagating waves, characteristic of a ring resonator. This model, in addition to the Hamiltonian and the operator of the number of excitations, includes an interference operator whose eigenvalues imitate the term cos 2kz of the classical picture of the field. The average number of photons, dispersion, the Mandel parameter Q, and atomic-photon entanglement in states with certain excitations are considered. The collapses and revivals are revealed, which in the standard JC model are present only in states with an indefinite number of excitations. It is shown that photons at the boundary energy levels are antibunched (with Q ≈ –1/2) regardless of the system’s parameters, and photons of other energy levels are grouped to the degree that grows with the total number of photons.
REFERENCES
Jaynes, E.T. and Cummings, F.W., Proc IEEE, 1963, vol. 51, p. 89.
Shore, B.W. and Knight, P.L., J. Mod. Opt., 1993, vol. 40, p. 1195.
Allen, L. and Eberly, J.H., Optical Resonance and Two-Level Atoms. New York: Dover, 1987.
Gerry, C.C. and Knight, P.L., Introductory Quantum Optics. Cambridge: Cambridge University Press, 2005.
Walls, D.F. and Milburn, G.J., Quantum Optics. Berlin: Springer-Verlag, 2008.
Grynberg, G., Aspect, A., and Fabre, C., Introduction to Quantum Optics. New York: Cambridge University Press, 2010.
Haroche, S. and Kleppner, D., Physics Today, 1989, vol. 42, p. 24.
Reiserer, A. and Rempe, G., Rev. Mod. Phys., 2015, vol. 87, p. 1379.
Greentree, A.D., Koch, J., and Larson, J., J. Phys. B, 2013, vol. 46, p. 220201.
Larson, J. and Mavrogordatos, T., arXiv:2202.00330v1 (2022).
Shore, B.W., Meystre, P., and Stenholm, S., J. Opt. Soc. Am., 1991, vol. 8, p. 903.
Muradyan, A.Zh. and Muradyan, G.A., J. Phys. B, 2002, vol. 35, p. 3995.
Tavis, M. and Cummings, F.W., Phys. Rev., 1968, vol. 170, p. 379.
Arimondo, E., Bambini, A., and Stenholm, S., Phys. Rev. A, 1981, vol. 24, p. 898.
Muradyan, A.Zh., Izv. NAS of Armenia, Physics, 1995, vol. 30, p. 114 [In Russian].
Karlov, N.V., Lectures on Quantum Electronics. CRC Press Inc, 1992.
Funding
The work was supported by the Science Committee of the Ministry of Education, Science, Culture and Sports of the Republic of Armenia at the Laboratory for Research and Modeling of Quantum Phenomena at Yerevan State University.
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Translated by V. Musakhanyan
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Muradyan, A.Z. Jaynes-Cummings Model in Counter Propagating Waves Basis: Large Numbers of Excitations. J. Contemp. Phys. 58, 134–139 (2023). https://doi.org/10.1134/S1068337223020159
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DOI: https://doi.org/10.1134/S1068337223020159