General model of counterpropagating continuous-variable entangled states in lossy waveguides

Abstract

We present a general theoretical approach to model an integrated source of counterpropagating continuous-variable entangled states in lossy waveguides pumped by a classical pulsed source incident from above the waveguide. We use a backward Heisenberg approach to model the generation of the entangled state and then solve the adjoint master equation to model the propagation of the state in the lossy waveguide. We employ a numerical method to implement the Schmidt decomposition method for the biphoton wave function rather than pursuing analytical methods. This approach allows us to model a wide variety of waveguide systems and pump configurations. We apply our model to the nonlinear generation and propagation of continuous-variable entangled states in a coupled resonator optical waveguide under a variety of different pump conditions and derive the optimal pumping conditions for our system.