Observation of the BKT Transition in a 2D Bose Gas via Matter-Wave Interferometry

TL;DR

This study experimentally observes the BKT transition in a 2D Bose gas by measuring phase fluctuations and vortex density using matter-wave interferometry, supported by Monte Carlo simulations.

Contribution

It provides the first direct measurement of the BKT transition in a trapped 2D Bose gas through phase correlation and vortex density analysis.

Findings

Phase correlation function changes from algebraic to exponential decay at transition.

Critical BKT exponent $ta_c$ determined as 0.17(3).

Vortex density exhibits scale-invariant behavior across the transition.

Abstract

We probe local phase fluctuations of trapped two-dimensional (2D) Bose gases using matter-wave interferometry. This enables us to measure the phase correlation function, which changes from an algebraic to an exponential decay when the system crosses the Berezinskii-Kosterlitz-Thouless (BKT) transition. We determine the temperature dependence of the BKT exponent $\eta$ and find the critical value $\eta_c = 0.17(3)$ for our trapped system. Furthermore, we measure the local vortex density as a function of the local phase-space density, which shows a scale-invariant behaviour across the transition. Our experimental investigation is supported by Monte Carlo simulations and provides a comprehensive understanding of the BKT transition in a trapped system.