Abstract
Using the Lie-algebraic approach, we develop the theory of generation of squeezed states of light in nonstationary parametric processes of the light interaction with a medium with the quadratic and quartic nonlinearities. The exact solution for the variance of the quadrature component of the field strength is obtained in the case of the quadratic parametric process with the SU(1, 1) dynamical symmetry. We show that decay of the field mode in this processes may have strong impact on squeezing. The solution for the standard deviation of the field strength in the case of the quartic parametric process with the approximated \({\mathcal{L}}_{5}\) dynamical symmetry is obtained in the first order of smallness with respect to the nonlinearity parameter.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Stoler, Phys. Rev. D, 4, 2309 (1971).
H. P. Yuen, Phys. Rev. A, 13, 2226 (1976).
V. V. Dodonov, A. B. Klimov, V. I. Man’ko, Phys. Lett. A, 149, 225 (1990).
U. L. Andersen, T. Gehring, C. Marquardt, and G. Leuchs, Phys. Scr., 91, 05300 (2016).
F. T. Hioe, Phys. Rev. A, 32, 2824 (1985).
G. Campolieti and B. C. Sanctuary, J. Chem. Phys., 81, 2108 (1989).
S. V. Prants, J. Russ. Laser Res., 17, 539 (1996).
S. V. Prants, J. Russ. Laser Res., 18, 69 (1997).
A. R. P. Rau, G. Selvaraj, and D. Uskov, Phys. Rev. A, 71, 062316 (2005).
P. Adam, V. A. Andreev, M. A. Man’ko, et al., Symmetry, 12, 1099 (2020).
L. E. Kon’kov and S. V. Prants, JETP Lett., 65, 833 (1997).
S. V. Prants and L. E. Kon’kov, Phys. Lett. A, 225, 33 (1997).
S. V. Prants, L. E. Kon’kov, and I. L. Kirilyuk, Phys. Rev. E, 60, 335 (1999).
S. V. Prants and L. E. Kon’kov, JETP Lett., 73, 1801 (2001).
S. V. Prants and M. Yu. Uleysky, Phys. Lett. A, 309, 357 (2003).
I. A. Malkin and V. I. Man’ko, Dynamic Symmetries and Coherent States of Quantum Systems [in Russian], Nauka, Moscow (1979).
R. W. Brockett, “Lie algebras and Lie groups in control theory,” in: Mathematical Methods in Systems Theory, Mir, Moscow (1979), pp. 174–220.
J. Wei and E. Norman, J. Math. Phys., 4, 575 (1963).
I. A. Zhelobenko and A. I. Stern, Representations of Lie Groups, Nauka, Moscow (1983).
W. H. Louisell, Radiation and Noise in Quantum Electronics, McGrow Hill Book Company, New York (1964).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Prants, S.V. Dynamical Symmetry and Generation of Squeezed States of Light. J Russ Laser Res 45, 155–161 (2024). https://doi.org/10.1007/s10946-024-10198-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-024-10198-2