Related papers: Berry phase and the Mandel parameter of the non-degenerate parametric amplifier

Berry phase and the Mandel parameter of the non-degenerate parametric amplifier

URL: http://arxiv.org/abs/2312.15114v2
Date: Mon, 8 Apr 2024 19:22:32 GMT
Title: Berry phase and the Mandel parameter of the non-degenerate parametric amplifier
Authors: J. C. Vega, E. Choreño, D. Ojeda-Guillén, R. D. Mota,
Abstract summary: We write the Hamiltonian of the non-degenerate parametric amplifier problem. By assuming that our Hamiltonian is an explicit function of time we calculate its Mandel Berry phase.
Score: 0.0
License: http://creativecommons.org/publicdomain/zero/1.0/
Abstract: We study the non-degenerate parametric amplifier problem from an algebraic approach of the $SU(1,1)$ group. We write the Hamiltonian of this problem in terms of the boson generators of the $SU(1,1)$ group and the difference operator. We apply the tilting transformation to our results to exactly solve this Hamiltonian and obtain its energy spectrum and eigenfunctions. Then, by assuming that our Hamiltonian is an explicit function of time we calculate its Berry phase. Finally we obtain the Mandel $Q-$parameter of the photon numbers $n_a$ and $n_b$.

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