# Symmetry-restoring quantum phase transition in a two-dimensional spinor condensate

## TL;DR

This paper demonstrates a quantum phase transition in a two-dimensional spinor Bose-Einstein condensate from a polar phase to a symmetric singlet phase by tuning particle density, revealing a novel symmetry-restoring transition.

## Contribution

It introduces a new quantum phase transition in 2D spinor condensates driven by density, leading to a stable molecular singlet phase, expanding understanding of quantum phase behavior.

## Key findings

- Quantum phase transition from polar to singlet phase achieved by density tuning.
- Identification of a stable molecular singlet phase in 2D spinor condensates.
- Continuous deformation of the symmetric phase into a molecular Bose-Einstein condensate.

## Abstract

Bose Einstein condensates of spin-1 atoms are known to exist in two different phases, both having spontaneously broken spin-rotation symmetry, a ferromagnetic and a polar condensate. Here we show that in two spatial dimensions it is possible to achieve a quantum phase transition from a polar condensate into a singlet phase symmetric under rotations in spin space. This can be done by using particle density as a tuning parameter. Starting from the polar phase at high density the system can be tuned into a strong-coupling intermediate-density point where the phase transition into a symmetric phase takes place. By further reducing the particle density the symmetric phase can be continuously deformed into a Bose-Einstein condensate of singlet atomic pairs. We calculate the region of the parameter space where such a molecular phase is stable against collapse.