Dynamics of pulsed SU(1,1) coherent states
- 1 June 1989
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 39 (11), 5717-5724
- https://doi.org/10.1103/physreva.39.5717
Abstract
In this paper we consider the time evolution of SU(1,1) coherent states driven by a coherence-preserving Hamiltonian containing periodic or quasiperiodic pulsing terms. This is a generalization of a system consisting of a two-level atom subjected to quasiperiodic pulsing that was recently studied by Milonni, Ackerhalt, and Goggin [Phys. Rev. A 35, 1714 (1987)]. The time-evolution operator in our case is given by a product of two finite group transformations of SU(1,1). Assuming an initial SU(1,1) coherent state, we determine the equivalent classical motion generated by a Poincaré map that is a Möbius transformation on the Lobachevski plane, the interior of the unit circle in the complex plane. The quantum-mechanical evolution of the state vector is calculated exactly and in closed form even though the Hilbert space is infinite dimensional. We also study the autocorrelation function which, as in the work of Milonni, Ackerhalt, and Goggin, is found to decay in the case of quasiperiodic pulsing that may possibly be associated with a manifestation of chaos in a quantum-mechanical system.Keywords
This publication has 14 references indexed in Scilit:
- Quantum Suppression of Irregularity in the Spectral Properties of the Kicked RotatorPhysical Review Letters, 1988
- Application of SU(1,1) coherent states to the interaction of squeezed light in an anharmonic oscillatorPhysical Review A, 1987
- Quasiperiodically kicked quantum systemsPhysical Review A, 1987
- Chaotic Rabi oscillations under quasiperiodic perturbationPhysical Review Letters, 1986
- Generalized Coherent States and Their ApplicationsPublished by Springer Science and Business Media LLC ,1986
- Dynamics of SU(1,1) coherent statesPhysical Review A, 1985
- Coherent states, squeezed fluctuations, and the SU(2) am SU(1,1) groups in quantum-optics applicationsJournal of the Optical Society of America B, 1985
- Quantum dynamics of a nonintegrable systemPhysical Review A, 1984
- Quantum dynamics and nonintegrabilityPhysical Review A, 1983
- Stochastic Behavior in Classical and Quantum Hamiltonian SystemsLecture Notes in Physics, 1979