We probe local phase fluctuations of trapped two-dimensional 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 behavior 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.

中文翻译：

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通过物质波干涉观测二维玻色气体中的 Berezinskii-Kosterlitz-Thouless 跃迁

我们使用物质波干涉法探测捕获的二维玻色气体的局部相位波动。这使我们能够测量相位相关函数，当系统穿过 Berezinskii-Kosterlitz-Thouless (BKT) 跃迁时，该函数从代数衰减变为指数衰减。我们确定 BKT 指数的温度依赖性$\eta$并找到临界值${\eta }_C=0.17(3)$对于我们被困的系统。此外，我们将局部涡旋密度测量为局部相空间密度的函数，这显示了过渡过程中的尺度不变行为。我们的实验研究得到了蒙特卡罗模拟的支持，并提供了对被困系统中 BKT 转变的全面理解。