Impact of quantum noise on Ramsey spectroscopy

We investigate the impact of quantum noise on Ramsey spectroscopy involving a single probe qubit.Considering the impossibility of a full reset of the quantum bath after each measurement shot, we show how the entanglement between system and bath adversely affects the accuracy of frequency estimation in a Ramsey experiment. Our findings are rooted in exact formulas for the expectation values of qubit observables interacting with a bosonic bath, assuming a general zero-mean Gaussian stationary pure dephasing process. These formulas were derived using a cumulant expansion technique, which offers an efficient avenue for the analytical study of non-Markovian open quantum systems. Furthermore, we conducted numerical simulations in which the bath comprised a finite number of qubits subject to classical stochastic noise. Consistent with the analytical findings, these simulations demonstrated a significant impact of the quantum bath on the system's measurements. Our analysis sets the stage for a comprehensive characterization and precise control of quantum noise across a range of configurations employed in sensing and estimation applications.