Normal Order Non-Classical Criteria In Non-Degenerate Four-Wave Mixing Process: Quantum Entanglement, Squeezing And Anti-Bunching.

Four-wave mixing process (FWM) in the non-degenerate category can be produced by the interaction of the radiation field with the third-order nonlinear optical media. In our present paper, to describe the non-degenerate four-wave mixing process we have used the fully quantum mechanical bosonic Hamiltonian. Heisenberg’s equations of motion for various modes involving pump, signal and idler are constructed. The corresponding differential equations are coupled and nonlinear. Due to non-linearity, the solution of these equations in closed set analytical form is not possible. To solve these coupled nonlinear differential equations we use the Sen-Mandal perturbative technique. Interestingly, this approach provides a broader and more general set of solutions that may be applicable across a wider range of conditions. The Sen-Mandal perturbative technique allows a more general solution that can result in a more accurate and general representation of the system that is more advantageous than the well-known short-time approximation method. The obtained solutions have been used to study the intermodal entanglement, normal order anti-bunching and normal order squeezing for various modes under the non-degenerate four-wave mixing process. The non-degenerate FWM is one of the processes for generating entanglement, squeezing and anti-bunching etc. [ABSTRACT FROM AUTHOR]