Beyond the semiclassical approximation in atom interferometry

• URL: http://arxiv.org/abs/2410.08040v2
• Date: Mon, 13 Jan 2025 22:43:29 GMT
• Title: Beyond the semiclassical approximation in atom interferometry
• Authors: W. LaRow, M. Edwards, C. A. Sackett,
• Abstract summary: We describe a quantum perturbative approach to evaluating the phase shift of an atom interferometer in a weakly anharmonic trap. We find that the form of the semi-classical approximation remains valid to first order in the anharmonic perturbation. We provide analytical results for one-dimensional perturbations of power three through six in the position coordinate.
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• Abstract: We describe a quantum perturbative approach to evaluating the phase shift of an atom interferometer in a weakly anharmonic trap. This provides a simple way to evaluate quantum corrections to the standard semi-classical approximation. The calculation benefits from the use of generalized coherent states for a basis. We find that the form of the semi-classical approximation remains valid to first order in the anharmonic perturbation, but that phase differences arise because the trajectory of a quantum wave packet will generally deviate from that of a classical particle. The quantum correction to the phase is a factor $\ell^2/A^2$ smaller than the semi-classical perturbation itself, where $\ell$ is the quantum harmonic oscillator length scale and $A$ is the classical amplitude of the motion. We provide analytical results for one-dimensional perturbations of power three through six in the position coordinate.

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