Two approaches in the theory of atom interferometry

TL;DR

This paper compares two theoretical approaches to atom interferometry phase calculations, showing they agree up to second order in Planck's constant when including the Q-term.

Contribution

It demonstrates the equivalence of the path integral and Wigner density matrix approaches for atom interferometry phases up to second order in , emphasizing the importance of the Q-term.

Findings

The two approaches yield coinciding phase expressions up to ^2 order.

Including the Q-term is essential for the agreement.

The methods are consistent when the Q-term is considered.

Abstract

We compare expressions for the atom interferometer phase obtained using the path integral approach and the approach based on the density matrix equation in the Wigner representation. The power series of these expressions over the Planck constant, truncated to the $\hbar ^{2}$ term, coincide. This coincidence is achieved only after the $Q-$term is included.