Some statistical properties for the interaction between SU(1, 1) and SU(2) quantum systems

Abstract

In this paper we introduce a Hamiltonian model which represents the interaction between SU(1, 1) and SU(2) quantum systems. The Heisenberg equations of motion are invoked to derive the exact time-dependent dynamical operators. The phenomena of the collapse and revival are observed for the intermediate states, however, for a large value of the excitation number m. It is also shown that the phenomenon of squeezing is observed in the intermediate state. Moreover, it is sensitive to the variation in the coupling parameter λ, the detuning parameter Δ, as well as in the Bargmann index k. The examination of the correlation function shows that the system displays anti-bunching for all periods of time except for a large value of the excitation number when k = 3/4. Our discussion for the variance squeezing also shows that the phenomenon of squeezing is pronounced in the quadrature variances for the odd parity case when the detuning parameter is large.