Representation-free description of light-pulse atom interferometry including non-inertial effects

Abstract

Light-pulse atom interferometers rely on the wave nature of matter and its manipulation with coherent laser pulses. They are used for precise gravimetry and inertial sensing as well as for accurate measurements of fundamental constants. Reaching higher precision requires longer interferometer times which are naturally encountered in microgravity environments such as drop-tower facilities, sounding rockets and dedicated satellite missions aiming at fundamental quantum physics in space. In all those cases, it is necessary to consider arbitrary trajectories and varying orientations of the interferometer set-up in non-inertial frames of reference.Here we provide a versatile representation-free description of atom interferometry entirely based on operator algebra to address this general situation. We show how to analytically determine the phase shift as well as the visibility of interferometers with an arbitrary number of pulses including the effects of local gravitational accelerations, gravity gradients, the rotation of the lasers and noninertial frames of reference. Our method conveniently unifies previous results and facilitates the investigation of novel interferometer geometries.

T 3-Interferometer for atoms

“…In the present Appendix we derive the complete quantum state of the atom consisting of the internal states as well as the center-of-mass in the two exit ports of our interferometer following the procedure outlined in Refs. [32,33,53]. The dynamics in our interferometer consists of the following steps:…”

Representation-free description of atom interferometers in time-dependent linear potentials

“…of F u (t), equation (85), and F l (t), equation (86). In contrast to the average functionsF for the MZ interferometer, equation (59), and the T 3 -interferometer, equation (77), which are constant in the interval 0<t<T, due to the time-dependence of F 1 (t), also the average¯( ) t F is now time-dependent during the interferometer sequence.…”

“…In order to determine the phase and contrast of an atom interferometer, the complete time evolution is usually split into pieces describing the time-evolution resulting from its basic building blocks: beam splitters, mirrors, and free propagation. This is generally the case within the path-integral approach [65], the ABCD formalism [83][84][85], and even in representation-free approaches based on operator methods [80,86].…”

“…Moreover, it is important to highlight that it is the signed area, which is relevant for the calculation of the interferometer phase. For example in the Butterfly geometry [86] the signed area vanishes, and the resulting interferometer phase becomes insensitive toF, assumingF is time-independent. Hence, this device might be used to probe the influence of higher-order effects such as gravity gradients.…”

“…Moreover, we point out that the representation-free approach presented in [86] valid for state-independent gravity gradients and rotations has already been generalized in [82] to state-dependent quadratic potentials. In the future it would be of interest to consider these effects within our simplified treatment.…”