Interesting new correlations and unidirectional properties of two bosonic modes under the influence of the 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 the non-Hermicity of the system. This manifests through 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 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 the controlled unidirectional transfer of population and correlations in bosonic chains.
Zbigniew Ficek (Fri,) studied this question.