Population control of the Λ-system coupled to a non-Markovian environment

We study population control in a Λ-type three-level quantum emitter coupled to a non-Markovian cavity bath. By engineering the cavity memory kernel, we compute population dynamics across different non-Markovian regimes and establish a quantitative link between control fidelity and environmental memory time. In addition, we show that controlled population retention can deviate qualitatively from free cavity-induced decay, revealing that environmental memory reshapes the control landscape and that controlled and uncontrolled population trends are not necessarily monotonic or dynamically aligned.