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Acta Physica Polonica A

Quantum Correlations in System of Kerr Nonlinear Coupler

Vinh Le Duc, Joanna K. Kalaga, W. Leoński

Published May 1, 2021• 0 citations
Publisher

Abstract

We consider a system composed of two linearly mutually interacting, identical Kerr-like nonlinear oscillators.Assuming that the system initially is in a coherent state, we discuss the system's dynamics and concentrate on the field's mutual correlations.As a measure of such correlations, we apply the normalized first-and second-order coherence functions.We derive the analytical formulas for such functions showing that their time-evolution strongly depends on the linear coupling parameter.

DOI
10.12693/aphyspola.139.532

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We consider a system composed of two linearly mutually interacting, identical Kerr-like nonlinear oscillators.Assuming that the system initially is in a coherent state, we discuss the system's dynamics and concentrate on the field's mutual correlations.As a measure of such correlations, we apply the normalized first-and second-order coherence functions.We derive the analytical formulas for such functions showing that their time-evolution strongly depends on the linear coupling parameter.
Quantum statistical properties of interacting optical fields in Kerr nonlinear couplers may be regarded as one of the most fundamental problems yet to be solved in quantum optics. As an analytical solution to this system is not always possible, a semi-analytic or direct numerical solution must be employed in order to obtain a more complete description of their evolution. This study investigates the quantum properties of four-mode couplers composed of two and four Kerr nonlinear waveguides, both with and without cavity set up via phase space representation. In these systems, the electromagnetic fields are described by their Hamiltonians, while the time-evolution of the systems are described by the Von-Neumann equation. Following standard techniques, the master equations for the density matrices of the systems are obtained and further converted to the corresponding classical Fokker- Planck equations using both positive P and Wigner representations. The corresponding set of Langevin Stochastic equations is then obtained from the Fokker-Planck equations by means of Ito rules. Finally, the systems are integrated numerically and averaged over many trajectories to get the relevant information. The effects of self-action nonlinearity, cross-action coupling and the initial energy of the coherent light on the evolution of the field quadrature variances are investigated. Furthermore, the influences of multimode interaction on the dynamics of the squeezed states are discussed. In this research, we show that the system may produce squeezed states in both quadrature variances for all calculated parameters. The multimode two channel model can provide better squeezing in contrast to the conventional device. The amplitude oscillation of maximal squeezing may be amplified by manipulation of the initial state of the coherent light in the first mode, and the range may be extended through multimode interaction. When the model is contained in a cavity, the system is able to generate better amplitude oscillations and squeezing range with leaf-revival-collapse-like behaviour; with the whole oscillation able to evolute below the standard quantum limit Regular photon transition and self trapping effects of the interacting modes in the four channels model are simulated, and squeezing is predicted for various initial intensities of the coherent field and nonlinear coupling parameter g. The cavity setup caused the system to undergo fluctuation amplification and the potential for different types of squeezing to be generated is observed. Depending on how we choose the interaction parameter values, the system may generate better squeezing in comparison to the cavity-less model.
A two-level atom interacting with two nonlinear Kerr oscillators pumped by an optical parametric process is studied. An analytical solution for the dynamical evolution of an interaction between Su(1,1) and Su(2)-systems is derived. The role of intrinsic damping, detuning, and Kerr-like medium on the entanglement evolution, quantum correlation, and coherence is elucidated. It is shown that the intrinsic decoherence leads to the sudden death and sudden birth entanglement, while the detuning eradicates these effects. The quantum coherence growth can be controlled by the detuning and the Kerr-like medium.
We investigate a codirectional nonlinear coupler composed of two Kerr nonlinear waveguides. Unlike the conventional device, the linear coupling between the guides is supposed to be a variable function of the propagation distance. We calculate quantum statistical and dynamical properties of the Kerr nonlinear coupler with a coherent input and analyse the influence of coupling variation on oscillations in mean photon number. The possibility to control the switching characteristics and principal squeezing effect by adjusting the form of coupling function is shown.
Quantum statistical properties of interacting optical fields in Kerr nonlinear coupler can be regarded as one of the most fundamental problems in quantum optics. As the analytical solution to these systems is not always possible, a semi-analytic or direct numerical solution has to be employed to obtain more complete description of their evolution. This paper investigates the quantum properties of a four-mode coupler composed of two Kerr nonlinear waveguides via phase-space representation. In this system, the electromagnetic field is described by its Hamiltonian and the time evolution of the system is described by Von-Neumann equation. Following the standard techniques, the master equation for the density matrix of the system is obtained and converted to the corresponding classical Fokker-Planck equation using both positive-P and Wigner representations. The corresponding set of Langevin Stochastic equations are then obtained from the Fokker-Planck equation using Ito rules. Finally, the system is integrated numerically and averaged over many trajectories to get the relevant information. The dynamics of the mean fields, the effects of self-action nonlinearity, cross-action coupling and initial energy of the coherent light on the evolution of the field quadrature variances are investigated. Further, the influences of multimode interaction on the dynamics of the squeezed states are discussed. We show that the system can produce squeezed states in both quadrature variances for all calculated parameters. In addition, the multimode interaction extends the range of squeezing at the expense of its amplitude.
We discuss a model comprising two coupled nonlinear oscillators (Kerr-like nonlinear coupler) with one of them pumped by an external coherent excitation. Applying the method of nonlinear quantum scissors we show that the quantum evolution of the coupler can be closed within a finite set of n -photon Fock states. Moreover, we show that the system is able to generate Bell-like states and, as a consequence, the coupler discussed behaves as a two-qubit system. We also analyse the effects of dissipation on entanglement of formation parametrized by concurrence.