From quantum to thermal topological-sector fluctuations of strongly interacting bosons in a ring lattice

TL;DR

This paper explores the topological fluctuations of a one-dimensional Bose field in a ring lattice, revealing a quantum-to-thermal crossover in winding number behavior driven by quantum phase slips and thermal activation.

Contribution

It provides the first detailed analysis of the topological-sector fluctuations in strongly interacting bosons, combining quantum Monte Carlo simulations with experimental relevance.

Findings

Quantum phase slips cause winding number fluctuations at zero temperature.

Susceptibility jumps at the superfluid-Mott insulator transition.

Thermal activation leads to uniform phase twists at finite temperature.

Abstract

Inspired by recent experiments on Bose-Einstein condensates in ring traps, we investigate the topological properties of the phase of a one-dimensional Bose field in the presence of both thermal and quantum fluctuations -- the latter ones being tuned by the depth of an optical lattice applied along the ring. In the regime of large filling of the lattice, quantum Monte Carlo simulations give direct access to the full statistics of fluctuations of the Bose-field phase, and of its winding number $W$ along the ring. At zero temperature the winding-number (or topological-sector) fluctuations are driven by quantum phase slips localized around a Josephson link between two lattice wells, and their { susceptibility} is found to jump at the superfluid-Mott insulator transition. At finite (but low) temperature, on the other hand, the winding number fluctuations are driven by thermal activation of nearly uniform phase twists, whose activation rate is governed by the superfluid fraction. A quantum-to-thermal crossover in winding number fluctuations is therefore exhibited by the system, and it is characterized by a conformational change in the topologically non-trivial configurations, from localized to uniform phase twists, which can be experimentally observed in ultracold Bose gases via matter-wave interference.