Optimizing precision in quantum metrology through engineered environments

This manuscript investigates the enhancement of parameter-estimation precision (P-EP) in photonic systems subjected to pure dephasing within Markovian and non-Markovian environments. We employ the quantum Fisher information (QFI) to quantify precision and analyze its dynamics in a system where a single photon's polarization interacts with a structured frequency environment. This environment is engineered using a Fabry-Pérot cavity and characterized by parameters such as the tilt angle, spectral width, and refractive index difference. Our results demonstrate that for specific configurations, particularly at certain angles, the system exhibits pronounced non-Markovian behavior, leading to oscillatory revivals in QFI, which signify periods of enhanced P-EP. Furthermore, we find that narrower spectral widths and smaller refractive index differences amplify these effects, prolonging periods of high QFI and improving estimation precision. These findings are corroborated by von Neumann entropy analysis, which reveals corresponding oscillations in quantum purity. Our study highlights the potential of engineered environments to improve the precision of quantum measurements despite environmental interactions, offering a promising strategy for advancing quantum technologies.