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arXiv:2506.16300

Effect of linear and nonlinear coupling processes on correlation properties of bosonic modes

Bembenek, Jakub, Z. Ficek

Published Jun 19, 2025• 0 citations
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Abstract

We study the influence of the linear and nonlinear coupling processes on the correlation properties of a system composed of two bosonic modes. The coupling processes are treated as Gaussian while the modes are assumed to experience damping and fluctuations that are due to their coupling to independent squeezed vacua. We investigate under what circumstances a given type of coupling causes the creation of the first-order correlations and which causes the creation of the two-photon correlations. Distinctly different results are obtained for the linear and nonlinear couplings, especially when there are two-photon correlations present in the modes. In particular, the linear coupling process can generate the inter-mode correlations only when there are differences between the modes either in populations or two-photon correlations. The varying with the coupling strength a population difference is shown to be responsible for generation of the first-order correlations while the varying asymmetry in the two-photon correlations is found to be responsible for the generation of the inter-mode two-photon correlations. In the case of the nonlinear coupling the generation of the inter-mode correlations is insensitive to any difference between the modes. The varying with the coupling strength amplification of the population of the modes is found to be responsible for generation of the inter-mode two photon correlations while the varying amplification of the two-photon correlations results in the first-order correlations between the modes. Furthermore, in the strong coupling limit the linear coupling tends to destroy all of the inter-mode correlations, and simultaneously turns the states of the modes to be identical, either thermal or equally squeezed states. In the case of nonlinear coupling process the modes are turned to be perfectly coherent.

DOI
10.48550/arxiv.2506.16300

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We study the influence of the linear and nonlinear coupling processes on the correlation properties of a system composed of two bosonic modes. The coupling processes are treated as Gaussian while the modes are assumed to experience damping and fluctuations that are due to their coupling to independent squeezed vacua. We investigate under what circumstances a given type of coupling causes the creation of the first-order correlations and which causes the creation of the two-photon correlations. Distinctly different results are obtained for the linear and nonlinear couplings, especially when there are two-photon correlations present in the modes. In particular, the linear coupling process can generate the inter-mode correlations only when there are differences between the modes either in populations or two-photon correlations. The varying with the coupling strength a population difference is shown to be responsible for generation of the first-order correlations while the varying asymmetry in the two-photon correlations is found to be responsible for the generation of the inter-mode two-photon correlations. In the case of the nonlinear coupling the generation of the inter-mode correlations is insensitive to any difference between the modes. The varying with the coupling strength amplification of the population of the modes is found to be responsible for generation of the inter-mode two photon correlations while the varying amplification of the two-photon correlations results in the first-order correlations between the modes. Furthermore, in the strong coupling limit the linear coupling tends to destroy all of the inter-mode correlations, and simultaneously turns the states of the modes to be identical, either thermal or equally squeezed states. In the case of nonlinear coupling process the modes are turned to be perfectly coherent.
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.
Interesting coherence and correlations appear between superpositions of two bosonic modes when the modes are parametrically coupled to a third intermediate mode and are also coupled to external modes which are in thermal states of unequal mean photon numbers. Under such conditions, it is found that one of linear superpositions of the modes, which is effectively decoupled from the other modes, can be perfectly coherent with the other orthogonal superposition of the modes and can simultaneously exhibit anticoherence with the intermediate mode, which can give rise to entanglement between the modes. It is shown that the coherence effects have a substantial effect on the population distribution between the modes, which may result in lowering the population of the intermediate mode. This shows that the system can be employed to cool modes to lower temperatures. Furthermore, for appropriate thermal photon numbers and coupling strengths between the modes, it is found that entanglement between the directly coupled superposition and the intermediate modes may occur in a less restricted range of the number of the thermal photons such that the modes could be strongly entangled, even at large numbers of the thermal photons.
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We study the problem of the influence of one-sided different noisy channels to the quantum correlations decay in a symmetric bosonic system. We concentrate on one type of these correlations—the entanglement. The system under consideration is composed of two nonlinear oscillators coupled by two-boson interactions and externally driven by a continuous coherent field. Our low-dimensional system can be treated as 2-qutrit one. Two different noisy channels (the amplitude and the phase-damping reservoirs) are applied to both of the system’s modes. We show that there is a noticeable difference in the quantum entanglement in 2-qubit subspaces of the whole system decrease after swapping the reservoirs between the modes of the considered symmetric system. It appears also that the degree of obtained entanglement depends crucially on the position of the appropriate type of reservoir. The origin of the observed asymmetry is also explained.
We describe the generation of quantum correlations (entanglement, discord and steering) in a system composed of two coupled non-resonant bosonic modes immersed in a common thermal reservoir, in the framework of the theory of open systems. We show that for separable initial squeezed thermal states entanglement generation may take place, for definite values of squeezing parameter, average photon numbers, temperature of the thermal bath, dissipation constant and strength of interaction between the two bosonic modes. We also show that for initial uni-modal squeezed states Gaussian discord can be generated for all non-zero values of the strength of interaction between the modes. Likewise, for an initial separable state, a generation of Gaussian steering may take place temporarily, for definite values of the parameters characterizing the initial state and the thermal environment, and the strength of coupling between the two modes.
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