Entanglement produced by pairs of superposed two-mode coherent and subharmonic cavity light beams.

We examined a two-mode coherent and subharmonic light beam within a cavity that is coupled to a two-mode vacuum reservoir through a single port mirror. Utilizing the solutions of the quantum Langevin equations, we developed Q-functions for the two-mode coherent and subharmonic cavity light beams. Subsequently, we calculated the Q-function for the superposed two-mode light beams in question. By leveraging the relevant Q-functions for the superposed cavity light beams, we investigated the quadrature statistics and entanglement. To conduct our analysis, we focused on a quantum system characterized by Gaussian operators with a zero mean. We have identified that the superposed two-mode coherent and subharmonic cavity light beams are in a squeezed state, with the squeezing occurring in the plus quadrature. Moreover, our analysis revealed that at steady state and at threshold, the superposed two-mode coherent and subharmonic light beams exhibit a maximum squeezing of 25% below the two-mode vacuum-state level. We have also clearly illustrated, using continuous variable entanglement criteria, that the superposed two-mode cavity light beams are entangled at both steady-state and threshold, with the entanglement being manifested in the highly correlated squeezed photons, which show a 75% degree of entanglement. Our analysis, applying Cauchy-Schewarz, Hillary-Zubiary, and Logarithmic Negativity entanglement criteria, further confirmed that the superposed cavity light beams in question are entangled. The Logarithmic Negativity criteria validated the entanglement of the superposed light, indicating a 50% degree of entanglement.