Quantum Gases Show Turbulence Via Vortices, Waves, and Sound

Researchers are leveraging the uniquely controllable environment of ultracold gases to study turbulence, a phenomenon typically defined by chaotic behavior. In 1995, the observation of Bose-Einstein condensation in dilute atomic gases realized a long-predicted phase of matter with macroscopic quantum coherence. Unlike classical fluids, which rely on viscosity and the Reynolds number, quantum gases depend on quantized circulation, compressibility, and sound emission and interaction to understand turbulence because an ideal superfluid has no classical viscosity. These gases are routinely prepared close to their many-body ground state, allowing a direct connection between microscopic wave function dynamics and observed turbulence, as detailed in work from Ashton S. Bradley of the University of Otago, and colleagues.

This achievement wasn’t merely a confirmation of theory; it established a uniquely controllable environment for exploring turbulence, a notoriously complex phenomenon. An ideal superfluid possesses no classical viscosity, rendering standard turbulence analysis inadequate. The ability to study turbulence in this manner stems from the unique properties of Bose-Einstein condensation (BEC), observed in 1995, where circulation around closed loops is quantized, a consequence recognized by Onsager in a footnote. This quantization fundamentally alters how vorticity manifests, localizing it on vortex lines or points rather than allowing continuous distribution as in classical fluids. The compressibility inherent in these quantum gases introduces another layer of complexity; the size of a quantum-vortex core is determined by the healing length, balancing kinetic energy with interaction energy. This interplay between vortices and density waves is central to understanding quantum turbulence, and is why the Gross-Pitaevskii equation became a foundational tool for identifying turbulent regimes. Experiments have shifted the field from simple observation, aiming for quantitative tests of transport phenomena and a microscopic understanding of nonequilibrium processes within these quantum fluids.

Brian P. Anderson and colleagues at the University of Arizona contributed to experiments that have shifted the field from the observation of vortices and turbulent-looking states toward quantitative tests of transport. A fundamental challenge lies in the fact that standard turbulence theory, governed by the Reynolds number, doesn’t directly apply to superfluids. Instead of focusing on damping forces, researchers investigate how energy cascades through quantized vortices and density waves, elements absent in classical fluids. This precision allows for quantitative tests of transport phenomena, and recent experiments have enabled a direct link between theoretical predictions and experimental results. This detailed analysis promises a deeper understanding of turbulence at a fundamental level, potentially reshaping our understanding of fluid dynamics itself.

The study of turbulence within quantum fluids is rapidly evolving beyond classical descriptions, offering potential insights into energy transfer at scales previously inaccessible. Unlike traditional fluid dynamics governed by the Reynolds number, these ultracold gases exhibit behavior dictated by their superfluid nature. A key feature of these quantum fluids is their topological nature; the single-valuedness of the wave function restricts phase winding around closed contours to integer multiples, meaning circulation is quantized. Classical fluids allow continuously distributed vorticity, but quantum gases localize vorticity on vortex lines or point vortices. This topological constraint, first recognized by Onsager, fundamentally alters the dynamics. The inherent compressibility of these gases, where the size of a vortex core is balanced by interaction energy, means vortices and density waves are inextricably linked, influencing the development of hydrodynamic theories like the Gross-Pitaevskii equation.

The seemingly simple act of swirling a fluid reveals profound differences at the quantum scale. This interplay is elegantly captured by the Gross-Pitaevskii equation (GPE), a nonlinear wave equation that incorporates vortices, sound, and density changes within a single framework. The authors note that the GPE’s importance lies in its ability to model these interconnected phenomena, conserving total particle number and energy, with parameters like the healing length and speed of sound becoming key physical parameters of a compressible quantum fluid that play a central role in quantum fluid dynamics and quantum turbulence. Through the Madelung transformation, the GPE transitions into a form resembling classical hydrodynamics, but with crucial quantum corrections. Experiments have shifted the field from the observation of vortices and turbulent-looking states toward quantitative tests of these predictions, moving beyond mere observation to controlled microscopic studies of nonequilibrium processes within these unique quantum systems.

Experimental Advances in Atomic Gas Turbulence

Recent experimental work has moved beyond simply observing turbulence in ultracold atomic gases, now focusing on rigorous quantitative testing of theoretical predictions. Researchers are no longer limited to visualizing turbulent states; they are actively probing transport properties within these uniquely controllable quantum fluids. Advances in techniques like box traps, programmable optical potentials, and in situ imaging are central to this development, enabling detailed measurements of forcing, dissipation, momentum distributions, and vortex statistics. A key development lies in the ability to compare experimental results with predictions from both the Gross-Pitaevskii equation and wave-kinetic theory. The GPE, describing the evolution of the condensate’s order parameter, contains vortices, sound, density depletion, and their mutual conversion, providing a foundational framework for understanding the interplay between these elements.

Experiments are now designed to resolve these interactions, moving towards a microscopic understanding of nonequilibrium processes. The work demonstrates a growing capacity to engineer quantum fluids and measure their response to external stimuli with unprecedented precision. The focus on compressibility, and the role of sound emission and interaction, further distinguishes these quantum systems from their classical counterparts. The ultimate goal, as the paper states, is to turn cascade phenomenology into a controlled microscopic nonequilibrium process, offering a new window into the fundamental physics of turbulence.

Crucially, the Madelung representation reveals how the single-valued nature of the superfluid phase enforces quantized circulation; this contrasts sharply with classical fluids, which permit continuous circulation values. This interaction scale also defines the speed of sound within the superfluid, demonstrating that vortices and density waves are intrinsically connected. By applying the Madelung transformation, the Hamiltonian becomes interpretable, with the kinetic energy term often analyzed in quantum turbulence due to its role in scale-local cascades.