Researchers Demonstrate Universal 2D Superfluid Order Parameter Statistics with 0.1% Precision

Scientists have long sought to understand the subtle statistical fingerprints of quantum phase transitions in many-body systems. Abel Beregi, En Chang, and Erik Rydow, alongside colleagues at institutions including Christopher J Foot and Shinichi Sunami, now demonstrate universal non-Gaussian statistics in the order parameter of two-dimensional superfluids. Their research, utilising matter-wave interferometry to probe Bose gases, confirms theoretical predictions of a Gumbel distribution at low temperatures with remarkable precision , to within 0.1% of the probability density. This is significant because it reveals a universal behaviour near the Berezinskii-Kosterlitz-Thouless transition, and the team’s precise measurements of higher-order statistical moments, like the Binder cumulant, offer new insights into critical phenomena and non-equilibrium dynamics following rapid changes to the system.

1% level of probability density. Researchers utilized matter-wave interferometry, a technique leveraging the intrinsic precision and robustness against noise, to measure fluctuations in the 2D Bose gases with large statistics. Furthermore, the ability to extract higher-order moments, such as skewness and kurtosis, provides a more complete picture of the fluctuations and their evolution near the critical point, offering insights beyond traditional mean-field approaches. They discovered parameter-independent scaling behaviour in the higher moments of the contrast distribution, indicating universal dynamics governed by real-time renormalization group theory.

This finding suggests that the system’s response to the quench is independent of specific details, highlighting the robustness of the underlying physics and opening avenues for exploring non-equilibrium phenomena in other systems. The research establishes a powerful new method for investigating the statistical properties of 2D superfluids, with implications for understanding critical phenomena and non-equilibrium dynamics in a wide range of physical systems. This work paves the way for future investigations into the role of fluctuations and correlations in shaping the emergent properties of many-body systems, potentially impacting fields ranging from condensed matter physics to cosmology.

Bose Gas Statistics via Matter-Wave Interferometry

Researchers prepared two independent, identical 2D Bose gases and harnessed matter-wave interferometry to transform relative-phase fluctuations into detectable interference patterns. These patterns were then subjected to a rigorous analysis protocol to quantify the statistical distribution of the interferometric contrast. Experiments employed absorption imaging. Crucially, the high-momentum region of the Fourier spectrum of the integrated density profiles allowed for reconstruction of intrinsic noise statistics, enabling a comprehensive analysis and correction of systematic effects within the protocol.

Over 1000 samples were obtained from more than 200 experimental repeats to ensure robust statistical power. The squared contrast observable was defined as C2 = 1/N1N2 ∫Ω dr1dr2 ψ†1(r1) ψ1(r2) ψ2(r1) ψ†2(r2), where ψ(†)i represent the bosonic annihilation (creation) operators and Ni is the particle number. Within the classical field approximation, the interference contrast simplified to C = 1/N ∫Ω dr n(r)ei(φ1(r)−φ2(r)), where n(r) is the mean density and φi(r) are the phases of the individual layers. This approach establishes a direct correspondence between the measured contrast and the magnetisation in the 2D XY model, allowing for quantitative comparison with theoretical predictions. This innovative approach enables the detailed characterisation of higher-moment observables, previously inaccessible in 2D quantum gases, and provides a powerful tool for exploring non-equilibrium dynamics in strongly correlated systems.

BKT Transition Verified via Gumbel Statistics

Experiments revealed that the intrinsic precision of the atom interferometer enabled robust extraction of higher-moment observables, including skewness and kurtosis, providing detailed insight into the system’s behaviour. Results demonstrate that the squared contrast observable, associated with the interference of two 2D bosonic fields, is given by C² = 1/N₁N₂ ∫Ω dr₁dr₂ ψ†₁(r₁)ψ₁(r₂)ψ₂ (r₁)ψ†₂(r₂), where ψ(†) represent the bosonic annihilation (creation) operators and N is the number of particles. The integration region Ω is defined by the thickness of the repumping light sheet and the image post-processing width. For identical Bose gases in the quasicondensate regime, the equation simplifies to C = 1/N ∫Ω dr n(r)ei(φ₁(r)−φ₂(r)), where n(r) is the mean density and φ(r) are the phases of the individual layers.

Data shows that the interference contrast depends solely on the relative phase, mirroring the order parameter of a single 2D Bose gas, differing only by a prefactor of 2, establishing a clear link to the 2D XY model. Contrast values were normalised by their root-mean-squared value, fixing the mean to unity and highlighting the shifts in distribution shape. The team obtained over 1000 samples from more than 200 experimental repeats, allowing for detailed analysis. Measurements confirm that empirical cumulative distributions and survival functions collapse onto a universal curve over several orders of magnitude, with the shaded area representing the 99% confidence interval for the highest phase-space density dataset. Furthermore, the high-momentum region of the spectrum allowed reconstruction of intrinsic noise statistics of the imaging process, enabling a comprehensive analysis of systematic effects. Analysis of data within the universal regime (phase-space density D between 14 and 21), containing over 7500 contrast values, revealed a histogram closely matching kernel density estimates and Monte Carlo simulations, even when accounting for imaging noise.

Gumbel Statistics Confirm 2D Quantum Gas Behaviour

This innovative approach confirms the emergence of a universal extreme-value distribution, specifically aligning with the predicted Gumbel distribution, deep within the superfluid regime with exceptional accuracy, to within 0.1% of the probability density. They observed parameter-independent scaling behaviour in higher-order moments during this relaxation, suggesting a universal description extends to dynamical processes and prompting the need for a corresponding theoretical framework. The authors acknowledge limitations in fully capturing the complex dynamics, particularly the absence of a plateau in skewness and kurtosis, which indicates differing scaling behaviour between equilibrium and out-of-equilibrium conditions. Future research could focus on developing a theory to account for these observed dynamics and exploring applications to prethermalized states, phase-ordering dynamics, quantum critical points, and Bose glass phases, leveraging this precise full-distribution measurement technique as a powerful tool for understanding two-dimensional quantum fluids.