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arXiv:2512.11436 · Symmetry

Nonreciprocal flow of fluctuations, populations and correlations between doubly coupled bosonic modes

Zbigniew Ficek

quant-phSubmitted Dec 12, 2025• Announced Dec 15, 2025• 0 citations• Revised Jan 26, 2026 (v2)
v1 · Dec 12, 2025v2 · Jan 26, 2026
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Abstract

Interesting new correlation and unidirectional properties of two bosonic modes under the influence of environment appear when the modes are mutually coupled through the simultaneously applied linear mode-hopping and nonlinear squeezing interactions. Under such double coupling, it is found that while the Hamiltonian of the system is clearly Hermitian the dynamics of the quadrature components of the field operators can be attributed to non-Hermicity of the system. It is manifested in an asymmetric coupling between the quadrature components which then leads to a variety of remarkable features. In particular, we identify how the emerging exceptional point controls the conversion of thermal states of the modes into single-mode classically or quantum squeezed states. Furthermore, for reservoirs being in squeezed states, we find that the two-photon correlations present in these reservoirs are responsible for unidirectional flow of populations and correlations among the modes and the flow can be controlled by appropriate tuning of the mutual orientation of the squeezed noise ellipses. In the course of analyzing these effects we find that the flow of the population creates the first-order coherence between the modes which, on the other hand rules out an enhancement of the two photon correlations responsible for entanglement between the modes. These results suggest new alternatives for the creation of single mode squeezed fields and the potential applications for controlled unidirectional transfer of population and correlations in bosonic chains.

Journal reference
Symmetry 18, 214 (2026)
DOI
10.3390/sym18020214
Comments
published version

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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.
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Squeezing the quantum fluctuations of the two-mode light due to the nonstationary coupling between the quadrature components q1{q}_{1}q1​ and q2{q}_{2}q2​ is examined. The \ensuremath{\delta}- and step-function mode couplings are considered. The conditions of weak and strong step-function coupling are distinguished, the latter being the condition of the instability for the classical counterpart of the quantum system under study. Under the conditions of weak coupling the quadrature squeezing is established in both a two-mode electromagnetic noise in thermal equilibrium (the thermal state) and a two-mode correlated coherent state (CCS). Squeezing in the thermal state is suppressed at a high temperature. The photon distribution function (PDF) in the thermal state reveals oscillatory behavior for both high and low temperature, the oscillations decrease while the temperature increases. The PDF in the CCS can be either oscillatory or smooth, whereas the photon statistics is essentially non-Poissonian. The nonclassical intermode photon-number correlations in the CCS are briefly studied.
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