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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Three-mode system of nonlinear quantum oscillators and quantum correlations

Joanna K. Kalaga, W. Leoński, A. Kowalewska-Kudłaszyk

Published Dec 5, 2014• 1 citation
Publisher

Abstract

We discuss a chain of three nonlinear oscillators excited by an external field. We show that during system’s evolution squeezed states can be generated in all three modes. Such generated squeezing appears simultaneously in all modes but for different quadratures. We show that degree of the squeezing and time of its appearance depend on the values of the parameters determining strengths of external and internal couplings and dumping of the system.

DOI
10.1117/12.2084893

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Three identical, interacting with each other nonlinear oscillators are considered. In addition, they are also externally driven by a coherent field of constant amplitude. The possibility of generating two-mode squeezed states is analyzed in this system. The two-mode principal squeeze variance is used to study the properties of the squeezed states of the system. The time evolution of this variance is analyzed, as well as the effect of the strength of the interaction between the oscillators and the damping strength on the generation of squeezed states.
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In this paper we consider a system with two nonlinear oscillators which are coupled via a nonlinear interaction.In order to excite the system, we use two external coherent fields.Two oscillators have different frequencies.It follows from numerical simulation that evolution of the system is similar to that of a combination of n-photon states.Therefore, the considered system behaves as so-called nonlinear quantum scissor.Nevertheless, evolution of the system generates Bell-like states in several times with very high probability.Because of the nonlinear properties of oscillators and their interaction, the system creates a truncation of optical states, which leads to obtain two-qubit states.It will also be shown that these states appear several times in the qutrit-qutrit system.
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.
We study the influence of the linear and nonlinear coupling processes on the correlation properties of a system composed of two bosonic modes. The coupling processes are treated as Gaussian while the modes are assumed to experience damping and fluctuations that are due to their coupling to independent squeezed vacua. We investigate under what circumstances a given type of coupling causes the creation of the first-order correlations and which causes the creation of the two-photon correlations. Distinctly different results are obtained for the linear and nonlinear couplings, especially when there are two-photon correlations present in the modes. In particular, the linear coupling process can generate the inter-mode correlations only when there are differences between the modes either in populations or two-photon correlations. The varying with the coupling strength a population difference is shown to be responsible for generation of the first-order correlations while the varying asymmetry in the two-photon correlations is found to be responsible for the generation of the inter-mode two-photon correlations. In the case of the nonlinear coupling the generation of the inter-mode correlations is insensitive to any difference between the modes. The varying with the coupling strength amplification of the population of the modes is found to be responsible for generation of the inter-mode two photon correlations while the varying amplification of the two-photon correlations results in the first-order correlations between the modes. Furthermore, in the strong coupling limit the linear coupling tends to destroy all of the inter-mode correlations, and simultaneously turns the states of the modes to be identical, either thermal or equally squeezed states. In the case of nonlinear coupling process the modes are turned to be perfectly coherent.