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arXiv:2406.03491 · Physical Review Letters

Detecting Phase Coherence of 2D Bose Gases via Noise Correlations

Shinichi Sunami, Vijay Pal Singh, Erik Rydow, Abel Beregi, En Chang, Ludwig Mathey, Christopher J. Foot

Published May 8, 2025• 3 citations
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Abstract

We measure the noise correlations of two-dimensional (2D) Bose gases after free expansion and use them to characterize the in situ phase coherence across the Berezinskii-Kosterlitz-Thouless (BKT) transition. The noise correlation function features a characteristic spatial oscillatory behavior in the superfluid phase, which gives direct access to the superfluid exponent. This oscillatory behavior vanishes above the BKT critical point, as we demonstrate for both single-layer and decoupled bilayer 2D Bose gases. Our Letter establishes noise interferometry as an important general tool to probe and identify many-body states of quantum gases, extending its application to previously inaccessible correlation properties in multimode systems.

DOI
10.1103/physrevlett.134.183407

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We measure the noise correlations of two-dimensional (2D) Bose gases after free expansion and use them to characterize the in situ phase coherence across the Berezinskii-Kosterlitz-Thouless (BKT) transition. The noise correlation function features a characteristic spatial oscillatory behavior in the superfluid phase, which gives direct access to the superfluid exponent. This oscillatory behavior vanishes above the BKT critical point, as we demonstrate for both single-layer and decoupled bilayer 2D Bose gases. Our Letter establishes noise interferometry as an important general tool to probe and identify many-body states of quantum gases, extending its application to previously inaccessible correlation properties in multimode systems.
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 η and find the critical value η_{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.
The understanding of nonequilibrium dynamics in many-body quantum systems is a fundamental issue in statistical physics. Experiments that probe universal properties of these systems can address such foundational questions. In this study, we report the measurement of universal dynamics triggered by a quench from the superfluid to normal phase across the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional (2D) Bose gas. We reduced the density by splitting the 2D gas in two, realizing a quench across the critical point. The subsequent relaxation dynamics were probed with matter-wave interferometry to measure the local phase fluctuations. We show that the time evolution of both the phase correlation function and vortex density obeys universal scaling laws. This conclusion is supported by classical-field simulations and interpreted by means of real-time renormalization group theory.
Fluctuations are an intrinsic feature of many-body systems, and their full statistical distributions reveal a wealth of information about the underlying physics. Of particular interest are non-Gaussian, extreme-value statistics that arise when nontrivial correlations and criticality dominate over the central limit theorem. Strikingly, in two-dimensional (2D) quantum fluids, such effects have been predicted to manifest in the order parameter distribution in the Berezinskii-Kosterlitz-Thouless (BKT) superfluid phase, which approaches a universal extreme-value form in the low-temperature limit. Here, we measure the order parameter statistics of 2D Bose gases across the BKT critical point using matter-wave interferometry. This allows us to confirm the predicted convergence of the observed statistics to a universal Gumbel distribution at low temperatures, to the 0.1% level of the probability density. Furthermore, the intrinsic precision of the atom interferometer allows the robust extraction of higher-moment observables such as skewness and kurtosis; in particular, we report direct measurements of the Binder cumulant which allows us to precisely identify the onset of the phase transition. Extending this approach to the investigation of non-equilibrium systems, we probe vortex unbinding dynamics following a quench across the BKT critical point and identify parameter-independent scaling behaviour of higher moments.
We analyze density-density correlations of expanding clouds of weakly interacting two-dimensional Bose gases below and above the Berezinskii-Kosterlitz-Thouless transition, with particular focus on short-time expansions. During time-of-flight expansion, phase fluctuations of the trapped system translate into density fluctuations, in addition to the density fluctuations that exist in situ. We calculate the correlations of these fluctuations both in real space and in momentum space and derive analytic expressions in momentum space. Below the transition, the correlation functions show an oscillatory behavior, controlled by the scaling exponent of the quasicondensed phase, due to constructive interference. We argue that this can be used to extract the scaling exponent of the quasicondensate experimentally. Above the transition, the interference is rapidly suppressed when the atoms travel an average distance beyond the correlation length. This can be used to distinguish the two phases qualitatively.
Long-range and anisotropic dipolar interactions induce complex order in quantum systems, particularly interesting in 2D where superfluidity emerges via the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. We observe a superfluid phase with algebraically decaying correlation in a quasi-2D dipolar Bose gas of erbium atoms and further identify the superfluid phase transition by monitoring extended coherence. We also measure equations of state with tunable dipolar interactions. Our findings show a transition point shift due to dipole orientation, aligning with BKT transition with effective short-range interaction. However, we observe that in-plane tilted dipoles show nonlocal effects in the superfluid regime, preventing the effective short-range interaction from revealing universal behavior near the BKT critical point. We also measure anisotropic atom number fluctuations in the superfluid regime, highlighting its dipolar nature. Our results provide a foundation for understanding dipolar bosons in 2D and pave the way for investigating complex orders in dipolar superfluids.
We prepare and study strongly interacting two-dimensional Bose gases in the superfluid, the classical Berezinskii-Kosterlitz-Thouless (BKT) transition, and the vacuum-to-superfluid quantum critical regimes. A wide range of the two-body interaction strength 0.05 < g < 3 is covered by tuning the scattering length and by loading the sample into an optical lattice. Based on the equations of state measurements, we extract the coupling constants as well as critical thermodynamic quantities in different regimes. In the superfluid and the BKT transition regimes, the extracted coupling constants show significant down-shifts from the mean-field and perturbation calculations when g approaches or exceeds one. In the BKT and the quantum critical regimes, all measured thermodynamic quantities show logarithmic dependence on the interaction strength, a tendency confirmed by the extended classical-field and renormalization calculations.