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Journal of the Optical Society of America B

Raman-induced compound-mode squeezing in a nonlinear coupler implementing Wigner representation and the analytical method

Mohd Syafiq M. Hanapi, Abdel-Baset M.A. Ibrahim, Rafael Julius, P. K. Choudhury

Published Dec 19, 2024• 1 citation
Publisher

Abstract

We investigate the generation of compound-mode squeezing in a Raman nonlinear coupler using both the analytical perturbative (AP) method and the Wigner phase-space representation. While the AP approach is rooted in the Heisenberg picture, the Wigner representation employs the Schrödinger picture, enabling a detailed comparison of the two frameworks. The temporal evolution of compound-mode squeezing is rigorously analyzed across different mode combinations, revealing an oscillatory behavior within a specific time window that depends on key system parameters. The optimal point within this window offers insights into maximizing squeezing under precise conditions. Both methods yield consistent results, providing robust insights into the dynamics of squeezing. This study advances the understanding of compound-mode squeezing in Raman nonlinear systems, with unique applications in quantum metrology, secure quantum communication, and advanced quantum sensing technologies.

DOI
10.1364/josab.543931

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We investigate the generation of compound-mode squeezing in a Raman nonlinear coupler using both the analytical perturbative (AP) method and the Wigner phase-space representation. While the AP approach is rooted in the Heisenberg picture, the Wigner representation employs the Schrödinger picture, enabling a detailed comparison of the two frameworks. The temporal evolution of compound-mode squeezing is rigorously analyzed across different mode combinations, revealing an oscillatory behavior within a specific time window that depends on key system parameters. The optimal point within this window offers insights into maximizing squeezing under precise conditions. Both methods yield consistent results, providing robust insights into the dynamics of squeezing. This study advances the understanding of compound-mode squeezing in Raman nonlinear systems, with unique applications in quantum metrology, secure quantum communication, and advanced quantum sensing technologies.
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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.
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Two-mode squeezing is central to entangled-photon generation and nonlinear interferometry, yet standard perturbative low-gain treatments and Gaussian formalisms can obscure the interference of photon-number amplitudes, especially in nonlinear interferometers and at high gain. Here we derive a closed-form Fock-basis expression for the action of the two-mode squeezing operator on arbitrary number states, enabling the direct analysis of nonlinear interferometers in the photon-number basis at arbitrary squeezing strength. Within this framework, we provide intuitive physical interpretations of several known quantum-interference effects and identify a new multi-photon interference phenomenon in a four-crystal geometry that could readily be observed in laboratories. Our work provides a compact analytic toolkit and explicit design rules for engineering multi-photon interference, with applications in quantum sensing, precision metrology, and quantum state generation.