Dynamics of a harmonic oscillator coupled with a Glauber amplifier

TL;DR

This paper analytically studies the exact dynamics of a quantum harmonic oscillator coupled with a Glauber amplifier using a time-dependent Hamiltonian, revealing unique physical effects through comparison with standard oscillators.

Contribution

It introduces an exact analytical approach to the dynamics of a coupled oscillator-amplifier system using invariant subspaces and the Jordan-Schwinger map.

Findings

Exact solutions for the system's dynamics under specific scenarios

Identification of peculiar physical effects in the coupled system

Comparison with standard oscillator interactions

Abstract

A system of a quantum harmonic oscillator bi-linearly coupled with a Glauber amplifier is analysed considering a time-dependent Hamiltonian model. The Hilbert space of this system may be exactly subdivided into invariant finite dimensional subspaces. Resorting to the Jordan-Schwinger map, the dynamical problem within each invariant subspace may be traced back to an effective SU(2) Hamiltonian model expressed in terms of spin variables only. This circumstance allows to analytically solve the dynamical problem and thus to study the exact dynamics of the oscillator-amplifier system under specific time-dependent scenarios. Peculiar physical effects are brought to light by comparing the dynamics of such a system with that of two interacting standard oscillators.