Entropy Flow and Exceptional-Point Structure in Two-Mode Squeezed-Bath Dynamics

TL;DR

This paper analyzes how two coupled quantum oscillators driven by squeezed baths exhibit entropy flow and exceptional points, revealing nonlinear entropy generation mechanisms and the conditions for PT symmetry breaking in non-Hermitian dynamics.

Contribution

It provides a comprehensive Gaussian formalism analysis of entropy flow and exceptional points in two-mode squeezed-bath dynamics, highlighting nonlinear entropy generation and PT symmetry conditions.

Findings

Entropy generation occurs at second order in anomalous correlations.

An exceptional-point fan separates PT-unbroken and PT-broken regimes.

PT symmetry is preserved only when reservoirs squeeze opposite quadratures.

Abstract

Squeezed reservoirs provide a powerful means of engineering nonclassical noise and controlling irreversible dynamics in open quantum systems. Here we develop a comprehensive analysis of two coupled harmonic oscillators driven by independent squeezed baths, focusing on the emergence of coherence-driven entropy flow and the structure of exceptional points (EPs) in the corresponding Lindblad dynamics. Working entirely within the Gaussian formalism, we derive closed-form evolution equations for the covariance matrix and show that squeezing induces entropy generation only at *second order* in the anomalous correlations, a nonlinear mechanism absent in thermal environments. This entropy flow is accompanied by a rich non-Hermitian structure: by scanning the squeezing parameters we uncover a characteristic "exceptional-point fan" in the (M1, M2) plane, which separates a narrow PT-unbroken region of oscillatory dynamics from broad PT-broken sectors in which one normal mode becomes purely overdamped. This geometric organization of EPs reveals that PT symmetry survives only when the two reservoirs squeeze opposite quadratures, and is generically broken for in-phase squeezing. Our analysis establishes squeezed reservoirs as a natural setting where information-bearing noise drives irreversible behavior through coherent pathways, and lays the groundwork for experimentally accessible probes of entropy flow and critical mode behavior in more complex open systems.