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In this paper we derive the quantum statistical and dynamical properties of nonlinear optical couplers composed of two nonlinear waveguides operating by the second subharmonic generation, which are coupled linearly through evanescent waves and nonlinearly through nondegenerate optical parametric interaction. Main attention is paid to generation and transmission of nonclassical light, based on a discussion of squeezing phenomenon, normalized second-order correlation function, and quasiprobability distribution functions. Initially coherent, number and thermal states of optical beams are considered. In particular, results are discussed in dependence on the strength of the nonlinear coupling relatively to the linear coupling. We show that if the Fock state $|1>$ enters the first waveguide and the vacuum state $|0>$ enters the second waveguide, the coupler can serve as a generator of squeezed vacuum state governed by the coupler parameters. Further, if thermal fields enter initially the waveguides the coupler plays similar role as a microwave Josephson-junction parametric amplifier to generate squeezed thermal light.
Following the concept of $mathcal{PT}$-symmetric couplers, we propose a linearly coupled system of nonlinear waveguides, made of positive- and negative-index materials, which carry, respectively, gain and loss. We report novel bi- and multi-stability
We present some numerical results for nonlinear quantum walks (NLQWs) studied by the authors analytically cite{MSSSS18DCDS, MSSSS18QIP}. It was shown that if the nonlinearity is weak, then the long time behavior of NLQWs are approximated by linear qu
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective parts of t
A time crystal is a macroscopic quantum system in periodic motion in its ground state, stable only if isolated from energy exchange with the environment. For this reason, coupling separate time crystals is challenging, and time crystals in a dynamic
We investigate the influence of a weakly nonlinear Josephson bath consisting of a chain of Josephson junctions on the dynamics of a small quantum system (LC oscillator). Focusing on the regime where the charging energy is the largest energy scale, we