Classical field simulation of vortex lattice melting in a two-dimensional fast rotating Bose gas

TL;DR

This study uses classical field simulations to analyze the thermal melting process of vortex lattices in a rotating Bose gas, highlighting finite-size effects and identifying the phases involved.

Contribution

It provides a numerical analysis of vortex lattice melting in a 2D Bose gas, extending experimental findings with detailed phase characterization and finite-size effect insights.

Findings

Identification of the two-step melting scenario.

Finite-size effects influence defect proliferation.

Characterization of crystalline, hexatic, and liquid phases.

Abstract

We present a classical field simulation study of the thermal melting of a two-dimensional vortex lattice in a rotating Bose gas, focusing on the role of finite-size effects on the melting temperature. This work constitutes a numerical continuation of the recent experimental investigation reported in [Physical Review Letters 133, 143401 (2024)], which addressed the thermal melting of a vortex lattice in a quasi-two-dimensional Bose gas. Using the stochastic projected Gross-Pitaevskii equation in a harmonic plus quartic trap, we simulate the finite-temperature equilibrium state and extract vortex configurations from density snapshots. Clear signatures of the two-step Kosterlitz--Thouless--Halperin--Nelson--Young melting scenario are identified. Our simulations enable a detailed characterization of the crystalline, hexatic, and liquid phases through correlation functions quantifying the translational and orientational order and through defect statistics. Finite-size effects are shown to play a crucial role at lower rotation frequencies, affecting the proliferation of lattice defects.