Exact dynamics and squeezing in two harmonic modes coupled through angular momentum

TL;DR

This paper provides an exact analytical study of two harmonic oscillators coupled via angular momentum, revealing how entanglement and squeezing emerge near instability and under weak coupling conditions.

Contribution

It derives the exact solutions for the system's dynamics and explores the conditions for stability, entanglement, and squeezing in different coupling regimes.

Findings

Near instability, significant entanglement and squeezing occur.

Weak coupling results in small entanglement with alternating squeezing.

Exact solutions enable precise analysis of dynamical stability and quantum correlations.

Abstract

We investigate the exact dynamics of a system of two independent harmonic oscillators coupled through their angular momentum. The exact analytic solution of the equations of motion for the field operators is derived, and the conditions for dynamical stability are obtained. As application, we examine the emergence of squeezing and mode entanglement for an arbitrary separable coherent initial state. It is shown that close to instability, the system develops considerable entanglement, which is accompanied with simultaneous squeezing in the coordinate of one oscillator and the momentum of the other oscillator. In contrast, for weak coupling away from instability, the generated entanglement is small, with weak alternating squeezing in the coordinate and momentum of each oscillator. Approximate expressions describing these regimes are also provided.