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Quantum Electronics and Laser Science Conference

Berry's phase in the degenerate parametric amplifier

Christopher C. Gerry

Published Apr 24, 1989• 0 citations
OpenAlex

Abstract

We discuss the manifestation of Berry’s phase1 in connection with the degenerate parametric amplifier (DPA). Previously,2 Berry’s phase has been discussed in connection with a two-level atom interacting with a resonant electromagnetic field whose phase is varied adiabatically. In the present work we are basically replacirtg the compact system [SU(2) for the two-level atom] by a noncompact system [SU(1,1) for the DPA3].

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We discuss the manifestation of Berry’s phase1 in connection with the degenerate parametric amplifier (DPA). Previously,2 Berry’s phase has been discussed in connection with a two-level atom interacting with a resonant electromagnetic field whose phase is varied adiabatically. In the present work we are basically replacirtg the compact system [SU(2) for the two-level atom] by a noncompact system [SU(1,1) for the DPA3].
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 .