# Phase collapse and revival of a 1-mode Bose-Einstein condensate induced by an off-resonant optical probe field and superselection rules

## TL;DR

This paper explores how an off-resonant optical probe can induce and control phase collapse and revival in a single-mode Bose-Einstein condensate, revealing the influence of superselection rules and measurement effects.

## Contribution

It demonstrates optical control of phase dynamics in a single-mode BEC and examines the role of superselection rules and photo-detection in the condensate's phase behavior.

## Key findings

- Optical interaction affects condensate phase revival time.
- Photo-detection does not provide additional control but allows inference of system statistics.
- Superselection rules influence the physical states of the condensate.

## Abstract

Phase collapse and revival for Bose-Einstein condensates is a nonlinear phenomena appearing due atomic collisions. While it has been observed in a general setting involving many modes, for one-mode condensates its occurrence is forbidden by the particle number superselection rule (SSR), which arises because there is no phase reference available. We consider a single mode atomic Bose-Einstein condensate interacting with an off-resonant optical probe field. We show that the condensate phase revival time is dependent on the atom-light interaction, allowing optical control on the atomic collapse and revival dynamics. Incoherent effects over the condensate phase are included by considering a continuous photo-detection over the probe field. We consider conditioned and unconditioned photo-counting events and verify that no extra control upon the condensate is achieved by the probe photo-detection, while further inference of the atomic system statistics is allowed leading to a useful test of the SSR on particle number and its imposition on the kind of physical condensate state.