Quantum state generation in a four-mode Kerr nonlinear directional coupler

Abstract

The quantum effects in a four-mode Kerr nonlinear directional coupler (NLDC) are investigated using the phase-space representation. The four-mode Kerr NLDC device consists of two closely connected Kerr waveguides where the first channel is traversed by one mode while the second channel is traversed by three modes. The cavity effect on the propagation characteristics of the nonclassical light is also examined. The introduction of a cavity supports amplification of the nonlinearities at the expense of losses in the model. The dynamical quantum behaviour of the system is investigated by integrating the Langevin equations derived in both positive P and Wigner representations numerically. The characteristics of the mean fields and quadrature variances are explored by integrating the stochastic equations numerically over many trajectories. In comparison with a conventional two-mode device, we have found that the cavityless model provides better squeezing and the amplitude oscillation is amplified by controlling the initial state of the coherent light in the first channel. Moreover, the range of squeezing is extended as a result of multimode interaction. In addition, confining the system inside an optical cavity with highly reflective mirrors introduces rapid amplification in the oscillation of the field dynamics.