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

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 $n_b$.

arXiv comment11 pages

References in corpus (8)

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Cited by in corpus (2)

• $SU(1,1)\times SU(2)$ approach and the Mandel parameter to the Hamiltonian of two oscillators with weak coupling
• A Generalization of the Parametric Amplifier with Dunkl Derivative: Spectral and Statistical Properties