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

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.