Limitations of a multi-Raman-pulse atom interferometry acceleration sensor

Given that atom interferometry has been the most successful quantum sensing application, ways to increase the sensitivity is a current topic of interest. One way to increase the sensitivity is an increase in the momentum axis by providing a larger momentum to the atom cloud. This has been done through increasing the number of central Raman π − pulses. In this approach, a longer stay in the intermediate high energy state, which is often neglected through adiabatic elimination due to large optical detuning, causes a higher chance of undesired spontaneous decay. The loss of quantum information of the atomic states due to this undesired spontaneous decay will add an additional error to the atom interferometer. In this work, we consider an open quantum system using the Lindblad master equation to devise a model for the atomic state dynamics that incorporates the undesired spontaneous decay. We formulate a noise model and combined it with the mean-value-deviation to analyze our figure of merit error in the measurement of local acceleration. Our theoretical results show the measurement error will be dominated by the inverse square noise dependence on the number of Raman pulses in low numbers of Raman pulses, while that in the high numbers of Raman pulses will be dominated by the loss of quantum information through the undesired spontaneous decay in the intermediate high energy state.