Revival and fractional revival in the quantum dynamics of SU(1,1) coherent states

We have used a generic two-mode Hamiltonian with two associated time scales to study the evolution of generalized SU(1,1) coherent states, in particular the pair and Perelomov coherent states, which have been realized in many systems such as radiation fields, trapped ions, and phonons. We have found that their dynamics does not depend on the ratio of these time scales but is instead determined crucially by the difference in photon numbers of the two modes. This is in stark contrast to the previously studied harmonic-oscillator coherent states and can be attributed to the different nature of the underlying algebra. We provide analytical results for their revival and fractional revival along with numerical plots of the autocorrelation function and the quadrature distribution and demonstrate the formation of Schrodinger cats. The results are extremely sensitive to the Casimir invariant and the complex parameters characterizing SU(1,1) coherent states.