Title: Error analysis in large area multi-Raman pulse atom interferometry due to undesired spontaneous decay

Abstract: Despite the fact that atom interferometry has been a successful application of quantum sensing, a major topic of interest is the further improvement of the sensitivity of these devices. In particular, the area enclosed by the interferometer (which controls the sensitivity) can be increased by providing a larger momentum kick to the atom cloud, increasing the extent of the momentum axis. One such atom optics technique involves increasing the number of central $\pi-$Raman pulses. This technique, while providing the prerequisite additional momentum boost, also causes the atom to remain in the intermediate high energy state for longer periods of time. This additional length of time is often neglected in many treatments due to the adiabatic elimination of the higher energy state enabled by the large optical detuning. The increased time in the intermediate high energy state results in a higher probability of undesired spontaneous decay and a loss of quantum information, thereby adding 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 includes the undesired spontaneous decay from the intermediate high energy state. We formulate an error figure of merit to analyze limitations of an atom interferometer configured for acceleration measurements. Our theoretical results show the error figure of merit will be dominated by a $N_{R}^{-2}$ scaling factor for low numbers of $\pi-$Raman pulses, but will be dominated by a monotonic increase in error for high number of $\pi-$Raman pulses. We determined the number of $\pi$-Raman pulses that accomplishes maximal momentum transfer with a the minimal error, depending on major system parameters.