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

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.

32 pages, 20 figures

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• Quantum correlations, separability and quantum coherence length in equilibrium many-body systems
• Perspective on new implementations of atomtronic circuits
• Mesoscopic Vortex-Meissner currents in ring ladders
• Coherent phase slips in coupled matter-wave circuits
• Persistent currents in ultracold gases
• Superconductor-insulator transition in Josephson junction chains by quantum Monte-Carlo
• Quantum Phase Slips: from condensed matter to ultracold quantum gases
• Bosonic Double Ring Lattice Under Artificial Gauge Fields
• Single-particle versus many-body phase coherence in an interacting Fermi gas
• Exploring quantum phase slips in 1D bosonic systems
• Geometry-based circulation of local thermal current in quantum harmonic and Bose Hubbard systems
• Sampling algorithms in statistical physics: a guide for statistics and machine learning
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• Emergent electrostatics in planar XY spin models: the bridge connecting topological order with broken $U(1)$ symmetry