Rotating Bose-Einstein condensates with a finite number of atoms confined in a ring potential: Spontaneous symmetry breaking, beyond the mean-field approximation

TL;DR

This paper investigates how a finite number of atoms in a rotating Bose-Einstein condensate confined in a ring potential leads to spontaneous symmetry breaking, surpassing mean-field predictions by considering many-body superpositions.

Contribution

It introduces a general method to analyze finite-atom effects on the lowest energy states, going beyond mean-field approximation by constructing symmetry-breaking many-body states.

Findings

Finite atom number affects the energy states of rotating BECs.

Many-body superpositions lower the energy compared to mean-field states.

The approach aligns with experimental setups involving toroidal traps.

Abstract

Motivated by recent experiments on Bose-Einstein condensed atoms which rotate in annular/toroidal traps we study the effect of the finiteness of the atom number $N$ on the states of lowest energy for a fixed expectation value of the angular momentum, under periodic boundary conditions. To attack this problem, we develop a general strategy, considering a linear superposition of the eigenstates of the many-body Hamiltonian, with amplitudes that we extract from the mean field approximation. This many-body state breaks the symmetry of the Hamiltonian, it has the same energy to leading order in $N$ as the mean-field state and the corresponding eigenstate of the Hamiltonian, however it has a lower energy to subleading order in $N$ and thus it is energetically favorable.