Noisy Coherent Population Trapping: Applications to Noise Estimation and Qubit State Preparation

TL;DR

This paper investigates how stochastic classical noise affects coherent population trapping in quantum systems, deriving a master equation to estimate noise parameters and optimize qubit state initialization fidelity.

Contribution

It introduces a time-convolutionless master equation for systems with classical noise, linking spectral features to noise parameters and optimizing qubit initialization.

Findings

Spectral dips correlate with noise decay parameters.

Noise impacts qubit initialization fidelity.

Optimal Rabi frequencies improve dark state preparation.

Abstract

Coherent population trapping is a well-known quantum phenomenon in a driven $\Lambda$ system, with many applications across quantum optics. However, when a stochastic bath is present in addition to vacuum noise, the observed trapping is no longer perfect. Here we derive a time-convolutionless master equation describing the equilibration of the $\Lambda$ system in the presence of additional temporally correlated classical noise, with an unknown decay parameter. Our simulations show a one-to-one correspondence between the decay parameter and the depth of the characteristic dip in the photoluminescence spectrum, thereby enabling the unknown parameter to be estimated from the observed spectra. We apply our analysis to the problem of qubit state initialization in a $\Lambda$ system via dark states and show how the stochastic bath affects the fidelity of such initialization as a function of the desired dark-state amplitudes. We show that an optimum choice of Rabi frequencies is possible.