# Collisions of solitary waves in condensates beyond mean-field theory

## TL;DR

This paper investigates how quantum decoherence affects the collision behavior of bright solitary waves in Bose-Einstein condensates, revealing a transition from mean-field to quantum-dominated dynamics that explains experimental observations.

## Contribution

It demonstrates that phase diffusion causes decoherence of solitary waves, leading to predominantly repulsive collisions beyond mean-field theory, aligning with experimental results.

## Key findings

- Decoherence due to phase diffusion alters collision dynamics.
- Collisions become predominantly repulsive after decoherence.
- Mean-field theory fails to describe post-decoherence collisions.

## Abstract

Bright solitary waves in a Bose-Einstein condensate contain thousands of identical atoms held together despite their only weakly attractive contact interactions. They nonetheless behave like a compound object, staying whole in collisions, with their collision properties strongly affected by inter-soliton quantum coherence. We show that separate solitary waves decohere due to phase diffusion, dependent on their effective ambient temperature, after which their initial mean-field relative phases are no longer well defined or relevant for collisions. In this situation, collisions occur predominantly repulsively and can no longer be described within mean field theory. When considering the time-scales involved in recent solitary wave experiments where non-equilibrium phenomena play an important role, these features could explain the predominantly repulsive collision dynamics observed in most condensate soliton train experiments.