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Acta Physica Polonica A

Squeezed States Generation in a Three-Mode System of Nonlinear Quantum Oscillators

Joanna K. Kalaga

Published Nov 1, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.12693/aphyspola.144.289

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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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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 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.