# Al'tshuler-Aronov-Spivak oscillations of bosonic matter-wave beams in the presence of interaction

## TL;DR

This paper investigates how weak interactions in a Bose-Einstein condensate affect Al'tshuler-Aronov-Spivak oscillations in a disordered Aharonov-Bohm ring, revealing a transition from localization to anti-localization behaviors.

## Contribution

It demonstrates analytically and numerically that very weak atom-atom interactions invert the oscillations, indicating a shift from weak localization to weak anti-localization in bosonic matter waves.

## Key findings

- Weak interactions invert Al'tshuler-Aronov-Spivak oscillations.
- Numerical simulations show oscillation washing out with increased interaction.
- Weak anti-localization signature appears at very low interaction strengths.

## Abstract

We theoretically study the propagation of a guided atom laser across an Aharonov-Bohm ring which is exposed to a synthetic gauge field. The presence of disorder within the ring gives rise to Al'tshuler-Aronov-Spivak oscillations, seen in the disorder average of the transmission as a function of the effective gauge flux that is contained within the ring. Those oscillations are induced by coherent backscattering and represent a manifestation of weak localization. Through analytical and numerical calculations that are based on the mean-field Gross-Pitaevskii approximation for the propagating Bose-Einstein condensate, we show that the presence of a very weak atom-atom interaction within the ring leads to an inversion of the Al'tshuler-Aronov-Spivak oscillations, in a very similar manner as for the coherent backscattering of Bose-Einstein condensates within two-dimensional disorder potentials. Numerical simulations based on the Truncated Wigner method reveal that this signature of weak antilocalization becomes washed out if the interaction strength is increased.