Abstract

Coherence properties are central to quantum systems and are at the heart of phenomena such as superconductivity. Here we study coherence properties of an ultracold Bose gas in a two-dimensional optical lattice across the thermal phase transition [1]. To infer the phase coherence and phase fluctuation profile, we use direct matter-wave imaging [2] of higher Talbot revivals as well as a new phase microscope based on a site-resolved mapping of phase fluctuations to density fluctuations during matter-wave imaging. We observe the algebraic decay of the phase correlations in the superfluid phase and a linear temperature increase of the exponent. These techniques will also allow studying coherence properties in strongly-correlated quantum systems with full spatial resolution.

[1] J. C. Brüggenjürgen, M. S. Fischer, C. Weitenberg, A phase microscope for quantum gases, arXiv:2410.10611 (2024). [2] L. Asteria, H. P. Zahn, M. N. Kosch, K. Sengstock, C. Weitenberg, Quantum gas magnifier for sub-lattice-resolved imaging of 3D quantum systems, Nature 599, 571–575 (2021).