Abstract

We treat a $\mathcal{PT}$-symmetric directional coupler with Kerr nonlinearity in both the single-mode waveguides. We investigate the quantum propagation of a coherent state through this device and simplify the appropriate description to a semiclassical one. Through numerical calculation we find that, for lower gain rates, the oscillatory behavior of the coupler changes only a little under the influence of the supplied noise. But for higher gain rates, the noise causes the coupler to behave like above the threshold of the increase of the photon number in one mode. In the coupler without the cross-Kerr interaction, this behavior is more pronounced. In this connection, the first- and second-order correlation functions exhibit a temporary oscillatory behavior for higher gain rates.

© 2019 Optical Society of America

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