Quantum Fisher information of a cosmic qubit undergoing non-Markovian de Sitter evolution

We revisit the problem of thermalization process for an Unruh-DeWitt (UDW) detector in de Sitter space. We derive the full dynamics of the detector in the context of open quantum system, neither using Markovian or RWA approximations. We utilize quantum Fisher information (QFI) for Hubble parameter estimation, as a process function to distinguish the thermalization paths in detector Hilbert space, determined by its local properties, e.g., detector energy gap and its initial state preparation, or global spacetime geometry. We find that the non-Markovian contribution in general reduces the QFI comparing with Markovian approximated solution. Regarding to arbitrary initial states, the late-time QFI would converge to an asymptotic value. In particular, we are interested in the background field in the one parameter family of $\alpha$-vacua in de Sitter space. We show that for general $\alpha$-vacuum choices, the asymptotic values of converged QFI are significantly suppressed, comparing to previous known results for Bunch-Davies vacuum.