# Transition from the mean-field to the bosonic Laughlin state in a rotating Bose-Einstein condensate

## TL;DR

This paper investigates how a rotating Bose-Einstein condensate transitions from a mean-field state to a correlated Laughlin state in harmonic traps, while remaining mean-field in anharmonic traps, through numerical analysis.

## Contribution

It provides a comparative numerical study of the transition behavior in harmonic versus anharmonic traps, highlighting the conditions under which mean-field or correlated states dominate.

## Key findings

- In harmonic traps, the condensate transitions to a Laughlin state at high angular momentum.
- In anharmonic traps, the mean-field approximation remains valid regardless of rotation.
- Numerical results compare mean-field and many-body Hamiltonian approaches for small atom numbers.

## Abstract

We consider a weakly-interacting Bose-Einstein condensate that rotates in either a harmonic, or a weakly-anharmonic trapping potential. Performing numerical calculations, we investigate the behaviour of the gas in these two cases as the angular momentum, or equivalently as the rotational frequency of the trap increases. While in the case of a purely-harmonic potential the gas makes a transition from the mean-field regime to the correlated, "Laughlin", regime, in the case of anharmonic confinement the mean-field approximation remains always valid. We compare our derived results in these two cases, using both the mean-field approximation, as well as the diagonalization of the many-body Hamiltonian considering a small atom number.