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Physical Review A

SU(2) and SU(1,1) time-dependent coherence-preserving Hamiltonians and generation of antibunched radiation in laser-plasma scattering

G. Dattoli, Francesco Paolo Orsitto, A. Torre

Published Sep 1, 1986• 14 citations
Publisher

Abstract

In this work we discuss the problems underlying the time evolution of states driven by SU(2) and SU(1,1) coherence-preserving Hamiltonians, using the Wei-Norman algebraic procedure. We also solve the problem of finding the explicit time evolution of a quantum system whose Hamiltonian is a time-dependent linear combination of the SU(1,1) group generators and those of the Weyl-Heisenberg algebra. The relevance of this Hamiltonian to the generation of antibunched radiation in a laser-plasma scattering experiment is also briefly analyzed.

DOI
10.1103/physreva.34.2466

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In this work we discuss the problems underlying the time evolution of states driven by SU(2) and SU(1,1) coherence-preserving Hamiltonians, using the Wei-Norman algebraic procedure. We also solve the problem of finding the explicit time evolution of a quantum system whose Hamiltonian is a time-dependent linear combination of the SU(1,1) group generators and those of the Weyl-Heisenberg algebra. The relevance of this Hamiltonian to the generation of antibunched radiation in a laser-plasma scattering experiment is also briefly analyzed.
We study the time evolution of a quantum system with Hamiltonian consisting of time-dependent linear combination of SU(1,1) and SU(2) generators. A proper hermitian invariant operator has been found to obtain not only closed formulas for the time evolution of quantum states but also the time evolution operators for both the SU(1, 1) and SU(2) systems. The time evolution operators have been used to investigate the time-dependent two photons and SU(2) squeezing states and squeezing properties of the time-dependent SU(1,1) coherent states.
We study the time evolution of a class of exactly solvable time-dependent quantum systems with a time-dependent Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators with the help of the invariant Hermitian operator. The exact common solutions of the Schrödinger equations for both the SU(1,1) and SU(2) systems are obtained in terms of eigenstates of the invariant operator. The adiabatic and non-adiabatic Berry phases are calculated with the exact solutions. Moreover, we derive an explicit time-evolution operator which is used to investigate the time-dependent two-photon squeezing states and SU(2) squeezing states. The squeezing properties of the time-dependent SU(1,1) coherent states are also discussed.