Observation of scale invariance and universality in two-dimensional Bose gases (1009.0016v2)

Abstract: The collective behavior of a many-body system near a continuous phase transition is insensitive to the details of its microscopic physics[1]. Characteristic features near the phase transition are that the thermodynamic observables follow generalized scaling laws[1]. The Berezinskii-Kosterlitz-Thouless (BKT) phase transition[2,3] in two-dimensional (2D) Bose gases presents a particularly interesting case because the marginal dimensionality and intrinsic scaling symmetry[4] result in a broad fluctuation regime which manifests itself in an extended range of universal scaling behavior. Studies on BKT transition in cold atoms have stimulated great interest in recent years[5-10], clear demonstration of a critical behavior near the phase transition, however, has remained an elusive goal. Here we report the observation of a scale-invariant, universal behavior of 2D gases through in-situ density and density fluctuation measurements at different temperatures and interaction strengths. The extracted thermodynamic functions confirm a wide universal region near the BKT phase transition, provide a sensitive test to the universality prediction by classical-field theory[11,12] and quantum Monte Carlo (MC) calculations[13], and point toward growing density-density correlations in the fluctuation region. Our assay raises new perspectives to explore further universal phenomena in the realm of classical and quantum critical physics.

Observation of Scale Invariance and Universality in Two-Dimensional Bose Gases

The paper enlightens our understanding of critical phenomena by presenting empirical evidence on the scale invariance and universality of two-dimensional (2D) Bose gases, especially in the context of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. The authors provide comprehensive experimental verification of the theoretical predictions surrounding critical behavior, specifically the manifestation of universal scaling laws near continuous phase transitions in 2D systems.

In their experimental investigation, the authors utilize an optical trap to confine cesium Bose gases in a quasi-two-dimensional geometry. This setup allows an exploration of the scale invariance and universality across varying temperatures and interaction strengths, leveraging in-situ density and density fluctuation measurements. The experimental approach is robustly designed to ensure negligible disruption from vertical excitations, thus preserving the intended 2D environment.

Key outcomes are derived from examining the dimensionless scaling of density and fluctuation parameters: the phase-space density ($\tilde{n}$) and scaled fluctuation ($\delta\tilde{n}^2$), as functions of scaled chemical potential ($\tilde{\mu}$). The paper observes that both density and fluctuation demonstrate universal scaling behavior across a wide spectrum, encompassing the fluctuation region, while deviations occur from simple mean-field predictions in this domain. The acquiring of these results hinges on fine-tuned manipulation of atomic interactions using Feshbach resonances, underscoring the role of weak coupling in sustaining scale invariance across the normal, fluctuation, and superfluid phases.

The authors correlate the crossover feature in density fluctuations ($\delta\tilde{n}^2$) and compressibility with the BKT transition, accurately determining the critical phase-space density and chemical potentials. The universality prediction is subjected to rigorous experimental tests by collapsing density profiles for varying interaction limits into a singular universal function, which conforms to expectations from the classical-field and quantum Monte Carlo calculations. This trait is notably expressed in the crossover regime, affirming the core tenet of universality in these gases.

Returns of the paper are notably significant in aligning empirical data substantially with theoretical models, distinguishing the paper as a pivotal reference for density-density correlations in critical phenomena. It opens discussions on utilizing fluctuation-dissipation frameworks to infer correlations, with implications highlighted by systematic deviations between fluctuation and compressibility measurements in the fluctuation and superfluid regimes, marking an interactive course between experimental data and theoretical predictions.

This work grants experimentalists a refined toolkit to probe critical phenomena in low-dimensional quantum systems, promising expansions in the landscape of critical physics and phase transitions. Future directions could encompass deeper explorations into correlation effects and the intricate dynamics within fluctuation regions, with potential to unveil further insights into the quantum behavior unique to 2D Bose gases and their transitions.