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Kerr nonlinear couples

Gombojav O. Ariunbold, Jan Peřina

Published Mar 13, 2022• 0 citations
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Abstract

Directional nonlinear couplers composed of two Kerr nonlinear waveguides are studied. Quantum consistent solutions of the equations of motion are obtained showing the collapses and revivals of the field mode amplitudes. The approximate method is also adopted for the contradirectional geometry and the switching accompanied by collapses of the modes is revealed. Kerr couplers with varying linear coefficients arc examined and possible controls of the switching of modes, for instance, digital switching and fast switching are demonstrated. The two-mode squeezing of vacuum fluctuations and the generation of pure states are shown.

DOI
10.22353/physics.v11i224.111

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Directional nonlinear couplers composed of two Kerr nonlinear waveguides are studied. Quantum consistent solutions of the equations of motion are obtained showing the collapses and revivals of the field mode amplitudes. The approximate method is also adopted for the contradirectional geometry and the switching accompanied by collapses of the modes is revealed. Kerr couplers with varying linear coefficients arc examined and possible controls of the switching of modes, for instance, digital switching and fast switching are demonstrated. The two-mode squeezing of vacuum fluctuations and the generation of pure states are shown.
Directional nonlinear couplers composed of two Kerr nonlinear waveguides are studied. Quantum consistent solutions of the equations of motion are obtained showing the collapses and revivals of the field mode amplitudes. The approximate method is also adopted for the contradirectional geometry and the switching accompanied by collapses of the modes is revealed. Kerr couplers with varying linear coefficients are examined and possible controls of the switching of modes, for instance, digital switching and fast switching are demonstrated. The two-mode squeezing of vacuum fluctuations and the generation of pure states are shown.
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 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.
The quantum effects in a four-mode Kerr nonlinear directional coupler (NLDC) are investigated using the phase-space representation. The four-mode Kerr NLDC device consists of two closely connected Kerr waveguides where the first channel is traversed by one mode while the second channel is traversed by three modes. The cavity effect on the propagation characteristics of the nonclassical light is also examined. The introduction of a cavity supports amplification of the nonlinearities at the expense of losses in the model. The dynamical quantum behaviour of the system is investigated by integrating the Langevin equations derived in both positive P and Wigner representations numerically. The characteristics of the mean fields and quadrature variances are explored by integrating the stochastic equations numerically over many trajectories. In comparison with a conventional two-mode device, we have found that the cavityless model provides better squeezing and the amplitude oscillation is amplified by controlling the initial state of the coherent light in the first channel. Moreover, the range of squeezing is extended as a result of multimode interaction. In addition, confining the system inside an optical cavity with highly reflective mirrors introduces rapid amplification in the oscillation of the field dynamics.
We investigate both codirectional and contradirectional nonlinear couplers composed of two nonlinear waveguides operating by second-harmonic generation. We take into account possible mismatches inside the waveguides and between them. We calculate the photon number distribution, its factorial moments, quadrature and integrated intensity variances and quadrature uncertainty product taking into account the effects of transmission of light between waveguides. Incident beams are assumed to be coherent, squeezed and mixed with external noise. Second-harmonic modes are assumed to be pumped with strong coherent beams. We show that non-classical behaviour of beams generated by the nonlinear waveguides can be transferred between them and controlled by linear and nonlinear mismatches. In the contradirectional regime of propagation, asymptotic non-classical states can be generated.
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.