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Journal of Electromagnetic Waves and Applications

Single- and compound-mode squeezing in nonlinear coupler with frequency mismatch

Rafael Julius, Mansoor Zahirzai, Abdel-Baset M.A. Ibrahim, Hichem Eleuch, P. K. Choudhury

Published Dec 12, 2019• 8 citations
Publisher

Abstract

The properties of squeezing, in relation to the different interaction frequencies of the input modes in three-mode Kerr nonlinear coupler consisting of two linearly-coupled Kerr waveguides, were explored. Utilizing the exact representation of a set of noisy-stochastic equations, an investigation was made of the first-order properties of squeezing for two- and three-mode interactions with frequency mismatch. It was observed that enhanced squeezing could be obtained under certain conditions of interactions.

DOI
10.1080/09205071.2019.1702591

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The properties of squeezing, in relation to the different interaction frequencies of the input modes in three-mode Kerr nonlinear coupler consisting of two linearly-coupled Kerr waveguides, were explored. Utilizing the exact representation of a set of noisy-stochastic equations, an investigation was made of the first-order properties of squeezing for two- and three-mode interactions with frequency mismatch. It was observed that enhanced squeezing could be obtained under certain conditions of interactions.
In this paper, we investigate the single-mode quantum properties of the codirectional Kerr nonlinear coupler when the frequency mismatch is involved and a condition for an exact solution of equations of motion is fulfilled. Particularly, we investigate quadrature and principal squeezing, Wigner function, quadrature distribution, phase distribution and phase variance. We show that the quadrature squeezing and the phase variance can exhibit collapse–revival and collapse–revival–subrevival phenomena, respectively, based on the values of the detuning parameter. Furthermore, we analytically demonstrate that the system can generate cat states, in particular, Yurke–Stoler states.
Abstract Squeezed states of light in a three-channel nonlinear coupler with second-order nonlinearity using the phase space method and the analytical perturbative method is reported in this paper. The system is studied under the frequency mismatch condition, where the frequencies of the pump mode are not common. The effect of frequency mismatch on the generated squeezed states is investigated. We have found that the frequency mismatch does significantly affect the behavior of the generated squeezed states only at higher values of linear coupling between the waveguides. By increasing the frequency mismatch, the squeezing pattern also evolves from a collapses-revivals-like squeezing into a constant oscillation.
The effects of squeezing have been of great importance in quantum computing [1], as evidenced in the studies of squeezed light presented in the literature [2]. The present work discusses on the possibility of enhancing squeezing using nonlinear coupler utilizing different operating frequencies of the input modes. In our two-channel model, one of the channels contains the fundamental mode, whereas the other one confines the next two higher-order modes. Here we examine numerically the effect of frequency mismatch on the dynamics of the generated squeezed light.
Abstract In this work, we examine the quantum features of a multi-waveguide nonlinear coupler exploiting the second-and third-order nonlinearities. The considered system contains four identical channels, each with a single fundamental transverse mode. The essence of this type of nonlinear coupler is to examine the effect of two or more competing nonlinearities on the generated nonclassical features in this class of devices. Here, we consider the case of second harmonic generation, wherein the fundamental harmonic (FH) fields are up-converted in pairs to double-frequency second harmonic (SH) fields, which are then evanescently coupled with the fields from other Kerr nonlinear waveguides. Using the positive P representation of the phase space, the time-evolution of the density matrix could be mapped to the corresponding Fokker–Planck equation of a classical quasiprobability distribution. Using Langevin stochastic equation, an exact representation of the system in phase space led to the demonstration of sub-Poissonian property, squeezing, and entanglement. With more effective squeezing achieved in all channel waveguides, the present system with χ(2)–χ(3) interaction can be a more efficient alternative to other versions of nonlinear couplers such as the quantum optical dimer (QOD) and Kerr nonlinear coupler (KNC). Furthermore, such a structure offers more flexibility in coupled-mode interactions in the form of correlation between the modes in different waveguides. This provides a better mechanism for the generation of enhanced nonclassical effects.
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.
In this paper, we investigate the single mode quantum properties of the codirectional Kerr nonlinear coupler when the frequency mismatch is involved and a condition for an exact solution of equations of motion is fulfilled. Particularly, we investigate quadrature and principal squeezing, Wigner function, quadrature distribution, phase distribution and phase variance. We show that the quadrature squeezing and the phase variance can exhibit collapse-revival and collapse-revivalsubrevival phenomena, respectively, based on the values of the detuning parameter. Furthermore, we analytically demonstrate that the system can generate cat states, in particular, Yurke-Stoler states. PACS numbers: 42.50Dv,42.60.Gd