Quantum optical diode based on Lyapunov control in a superconducting system

Abstract

In this paper, we show how to use Lyapunov control theory to realize the unidirectional transmission of photons. We construct a quantum diode in a two-cavity system that includes two coplanar waveguide resonators connected by a superconducting quantum interference device, and the coupling strength can be adjusted by a magnetic flux. We utilize the Lyapunov control theory to design the shape of the coupling coefficient so that the dynamic evolution of the system can be effectively controlled. Moreover, we select the more stable and feasible control scheme by comparing and analyzing two control methods. Our scheme can obtain high efficiency of photon transmission in the presence of quantum noise without the need to construct strong nonlinear interactions, thus greatly reducing the difficulty of the experiment.