Noisy Coherent Population Trapping: Qubit Dark State Initialization in a Driven Λ system.

Coherent Population Trapping (CPT) is a known quantum phenomenon in a driven Λ system with many applications. However, when a stochastic bath is present, the observed trapping is no longer perfect. We derive a time-convolutionless master equation describing the equilibration of the Λ system in the presence of additional temporally correlated noise, with an unknown decay parameter. Our simulations show a one-to-one correspondence between the decay parameter and the depth of the CPT dip in the photoluminescence spectrum, thereby enabling the unknown parameter to be estimated from the observed spectra. Finally, we apply our results to the problem of qubit state initialization in a Λ system via dark states and show how the stochastic bath affects the fidelity as a function of the desired dark state amplitudes. This means that dissipative state preparation becomes informed, and combined with a minimum fidelity requirement, certain dark states are eliminated from consideration. We show that an optimum choice of Rabi frequencies is possible.