Theoretical study of optical rectification of a nanostructure inside an ideal photonic crystal cavity

Abstract

A theoretical method is applied to calculate the optical rectification (OR) in a cavity-quantum dot system based on open quantum systems theory. This method allows studying the linear and non-linear optical response of a nanostructure found within an ideal photonic crystal cavity by solving a Born–Markov master equation in the Lindblad form, including spontaneous emission processes and dephasing due to interaction with the environment. For a quantum dot (QD) interacting with non-classical light in a very high-quality factor cavity, an analytical expression for the OR was found when the average number of photons n¯ is small, which explicitly depends on the quantum dot-cavity system’s initial state. The expression found was applied to a nanostructure constituted by a cylindrical quantum dot (CQD) of GaAs/Ga0.6Al0.4As with a donor impurity inside. It was found that the OR in nanostructures that interact with a quantum field of light exhibits an absorption peak at lower frequencies than in the case of interaction with classical light. The physical reason for this behavior is attributed to the number of quantum states involved in the optical transitions and, therefore, to the number of photons involved in the transitions.