Limitations of a large momentum atom interferometer acceleration sensor due to spontaneous emission

Atom interferometry has been a successful quantum sensing application. Recently ways to increase the sensitivity has become a current topic of interest. One way to increase the sensitivity is an increase in the momentum of the atom cloud. This has been done through increasing the number of 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. Another way is by implementing Bragg scattering pulses which also can bring in spontaneous emission due to increased interaction time. 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 use the Lindblad master equation to devise a model for the atomic state dynamics that incorporates the undesired spontaneous decay. We determine an error figure of merit to analyze the error in the measurement of local acceleration. Our theoretical results show the noise will be dominated by the inverse square dependence on the number of Raman or Bragg pulses in low numbers of pulses, while the measurement error in the high numbers of pulses will be dominated by the loss of quantum information through the undesired spontaneous decay. Our figure of merit reaches a minimum at a specific pulse number depending on the Raman or Bragg pulses used before the error starts to increase.