Metastable Quantum Phase Transitions in a Periodic One-dimensional Bose Gas: Mean-Field and Bogoliubov Analyses

TL;DR

This paper extends the concept of quantum phase transitions to metastable states in finite one-dimensional Bose gases, revealing two distinct phases including a novel soliton phase with continuous angular momentum.

Contribution

It introduces a new perspective on quantum phase transitions for metastable states in finite systems, supported by mean-field and Bogoliubov analyses.

Findings

Existence of two topologically distinct quantum phases in a finite 1D Bose gas

Identification of a new soliton phase with broken symmetry and continuous angular momentum

Consistency between mean-field and Bogoliubov methods in the weakly interacting regime

Abstract

We generalize the concept of quantum phase transitions, which is conventionally defined for a ground state and usually applied in the thermodynamic limit, to one for \emph{metastable states} in \emph{finite size systems}. In particular, we treat the one-dimensional Bose gas on a ring in the presence of both interactions and rotation. To support our study, we bring to bear mean-field theory, i.e., the nonlinear Schr\"odinger equation, and linear perturbation or Bogoliubov-de Gennes theory. Both methods give a consistent result in the weakly interacting regime: there exist \emph{two topologically distinct quantum phases}. The first is the typical picture of superfluidity in a Bose-Einstein condensate on a ring: average angular momentum is quantized and the superflow is uniform. The second is new: one or more dark solitons appear as stationary states, breaking the symmetry, the average angular momentum becomes a continuous quantity, and the phase of the condensate can be continuously wound and unwound.