New Simulations Show Quantum Turbulence Forms Via Kibble-Zurek Mechanism

Researchers have, through numerical simulations, begun to unravel the origins of spontaneous quantum turbulence, revealing a connection to a well-established principle governing phase transitions. Seong-Ho Shinn, among others, modeled the formation of a Bose-Einstein condensate in two spatial dimensions, observing the proliferation of quantum vortices, tiny, swirling defects, as the condensate formed via a thermal quench. The researchers propose that the Kibble-Zurek mechanism (KZM) drives this spontaneous turbulence, suggesting a fundamental link between seemingly disparate areas of physics. The vortex count at equilibration time versus quench time demonstrates the Kibble-Zurek power-law scaling, establishing the nonequilibrium universality of SQT through the Kibble-Zurek and Kolmogorov scaling of the incompressible kinetic energy. This work offers insight into a long-standing unsolved problem with broad applications ranging from biology to weather prediction.

Numerical simulations are revealing a surprising link between established theories of phase transitions and the chaotic world of quantum turbulence. This suggests a previously understood mechanism governs this complex quantum phenomenon. The team utilized simulations of the stochastic projected Gross-Pitaevskii equation in two spatial dimensions, with Seong-Ho Shinn among the authors, modeling the formation of a BEC populated by quantum vortices. This setup allowed observation of vortex proliferation, a key characteristic of quantum turbulence. The simulations revealed that the density of vortices formed scales predictably with the speed of the thermal quench, aligning with predictions from the KZM. Specifically, the vortex count at equilibration time versus quench time demonstrates the Kibble-Zurek power-law scaling. This alignment with the KZM suggests that SQT isn’t merely a consequence of the BEC formation, but a predictable outcome governed by universal critical dynamics, offering a new avenue for exploring turbulence across different scales and physical systems.

Numerical modeling is increasingly employed to dissect the complex behavior of quantum fluids, particularly the emergence of turbulence at extremely low temperatures. Researchers from the University of Luxembourg, Christ University, and the Donostia International Physics Center are now leveraging the stochastic projected Gross-Pitaevskii equation to simulate the formation of Bose-Einstein condensates (BECs) and the resulting proliferation of quantum vortices, offering insights previously inaccessible through direct experimentation. These simulations, conducted in two spatial dimensions, allow for detailed observation of the processes governing spontaneous quantum turbulence (SQT). The researchers propose that spontaneous quantum turbulence (SQT) is generated via the Kibble-Zurek mechanism (KZM) during Bose-Einstein condensation induced by a thermal quench. Specifically, the vortex count at equilibration time versus quench time demonstrates the Kibble-Zurek power-law scaling. Data averaged over 1000 realizations, with error bars indicating one standard deviation, support this finding. This detailed analysis, combined with the simulation’s two-dimensional setup, provides a powerful tool for understanding the fundamental physics of quantum turbulence and its potential applications in fields ranging from atomtronics to astrophysics.

Quantum Turbulence Emerges in Superfluids and BECs

Researchers at the University of Luxembourg, the Center for Quantum Technologies and Complex Systems (CQTCS), Christ University, and the Donostia International Physics Center are employing advanced numerical simulations to dissect the origins of spontaneous quantum turbulence (SQT) within Bose-Einstein condensates (BECs). Their work centers on understanding how turbulence arises not from continuous energy input, but spontaneously during the BEC formation process itself, a phenomenon driven by a rapid thermal quench. This approach is often too violent, complicating the study of QT due to the generation of a variety of excitations. A key finding connects this SQT to the well-established Kibble-Zurek mechanism (KZM), a theory predicting defect formation during continuous phase transitions. The researchers propose that SQT can emerge through the KZM. The vortex count at equilibration time versus quench time demonstrates the Kibble-Zurek power-law scaling.

Specifically, the vortex count at equilibration time versus quench time demonstrates the Kibble-Zurek power-law scaling. Data averaged over 1000 realizations, with error bars indicating one standard deviation, support this finding. The researchers establish the nonequilibrium universality of SQT through the Kibble-Zurek and Kolmogorov scaling of the incompressible kinetic energy. This scaling confirms that despite operating in the quantum realm, the turbulence exhibits behavior analogous to its classical counterpart, offering a new avenue for exploring the fundamental nature of turbulent flows. The team reports demonstrating this scaling across a range of quench times, solidifying the connection between the KZM and the observed turbulence.

Defining Quantum Turbulence: Diagnostic Tools & Challenges

Establishing definitive diagnostic tools for quantum turbulence remains a complex undertaking, mirroring challenges faced in classical fluid dynamics where multiple, inequivalent definitions of chaos exist. Researchers are employing a diversity of approaches, including analysis of energy spectra, velocity autocorrelations, and circulation statistics, to fully characterize this quantum phenomenon. Initial investigations into quantum turbulence stemmed from low-temperature physics studies of superfluid helium, but the advent of Bose-Einstein condensates in the mid-1990s provided a significantly more controllable experimental platform. A defining characteristic of a superfluid is its quantized circulation, a consequence of the macroscopic wavefunction’s single-valued nature; this is expressed mathematically as 𝒗​(𝒓) = ℏ∇θ​(𝒓)/m. Unlike classical eddies, quantum vortices possess conserved and quantized circulation, contributing to their enhanced stability.

Simulations, conducted in two spatial dimensions with researchers including Seong-Ho Shinn of the University of Luxembourg, Matteo Massaro, Mithun Thudiyangal, and Adolfo del Campo, are proving invaluable in observing the proliferation of these vortices, a key signature of turbulent flow. The researchers propose that spontaneous quantum turbulence arises via the Kibble-Zurek mechanism, a theory predicting the formation of topological defects during continuous phase transitions. The vortex count at equilibration time versus quench time demonstrates the Kibble-Zurek power-law scaling. Data averaged over 1000 realizations, with error bars indicating one standard deviation, support this finding. Understanding the nuances of turbulence, they note, has broad applications spanning biology, medicine, industry, and weather prediction, highlighting the far-reaching implications of this fundamental research.

Unlike the complex conditions of helium studies, BECs offer researchers the ability to tune and manipulate quantum fluids with unprecedented precision, opening new avenues for understanding this elusive phenomenon. The experimental measurement of quantized vortices in BECs proved crucial in confirming their superfluid character, and has since become a cornerstone of QT research. Researchers at the University of Luxembourg, the Center for Quantum Technologies and Complex Systems (CQTCS), Christ University, and the Donostia International Physics Center are now leveraging BECs to test fundamental theories about the origins of turbulence itself. The vortex count at equilibration time versus quench time demonstrates the Kibble-Zurek power-law scaling. Data averaged over 1000 realizations, with error bars indicating one standard deviation, support this finding. This scaling establishes the nonequilibrium universality of SQT through the Kibble-Zurek and Kolmogorov scaling, suggesting that despite operating in the quantum realm, the turbulence exhibits behavior analogous to its classical counterpart.

Macroscopic Wavefunction & Quantized Circulation in Superfluids

The very nature of a superfluid hinges on a concept central to understanding its unusual properties. This wavefunction, described mathematically as Ψ(𝒓) = ρ(𝒓)eiθ(𝒓), dictates that the superfluid velocity, v(𝒓) = ℏ∇θ(𝒓)/m, is directly linked to the gradient of its phase. Consequently, circulation, the line integral of velocity around a closed loop, is not continuous but quantized, a direct result of maintaining the single-valued character of this macroscopic wavefunction. This quantization of circulation is a defining feature, ensuring the stability of vortices within the superfluid, unlike their classical counterparts. Researchers are increasingly focused on how turbulence manifests in these quantum fluids, differing significantly from classical turbulence due to the presence of these quantized vortices. While classical turbulence in three dimensions involves energy cascading to smaller scales, two-dimensional turbulence exhibits an inverse cascade, with energy flowing to larger scales.

Notably, in 2D quantum turbulence, enstrophy, a measure of vorticity, may not be conserved, potentially leading to a direct energy cascade, as observed in both numerical simulations and experiments with Bose-Einstein condensates. The researchers propose that spontaneous quantum turbulence (SQT) can emerge through the Kibble-Zurek mechanism (KZM), a paradigm for describing universal critical dynamics.

Two-Dimensional Turbulence: Enstrophy and Energy Cascades

The study of turbulence continues to challenge physicists across multiple scales, with implications extending from biological systems to weather forecasting. Recent numerical simulations, however, are beginning to illuminate the distinct characteristics of turbulence in two dimensions, revealing behaviors markedly different from those observed in three-dimensional flows. Unlike the energy cascade from large to small scales seen in 3D turbulence, two-dimensional systems are governed by enstrophy, a measure of vorticity, leading to an inverse cascade where energy flows from smaller to larger scales. Researchers observed that in 2D quantum turbulence, enstrophy conservation can lead to the clustering of vortices into larger structures, a phenomenon previously predicted theoretically and experimentally in BECs and exciton-polariton superfluids. This clustering is particularly evident when examining condensate density and phase profiles at equilibration time, revealing the complex interplay of vortices with opposing topological charges.

The vortex count at equilibration time versus quench time demonstrates the Kibble-Zurek power-law scaling. Data averaged over 1000 realizations, with error bars indicating one standard deviation, support this finding. The researchers propose the generation of spontaneous quantum turbulence (SQT) via the Kibble-Zurek mechanism (KZM) during Bose-Einstein condensation induced by a thermal quench. By establishing the nonequilibrium universality of SQT through the Kibble-Zurek and Kolmogorov scaling of the incompressible kinetic energy, researchers at the University of Luxembourg, Christ University, and Donostia International Physics Center are employing advanced numerical simulations to dissect the origins of spontaneous quantum turbulence (SQT) within Bose-Einstein condensates (BECs). This approach diverges from typical turbulence studies which are often too violent, complicating the study of QT due to the generation of a variety of excitations. Several protocols are used to induce QT in a superfluid sample, but their approach, a finite-time thermal quench, offers a cleaner pathway to study SQT, minimizing extraneous excitations.

The team’s simulations, conducted in two spatial dimensions, model a thermal quench, a swift change in temperature, inducing BEC formation and the subsequent proliferation of quantum vortices. A key finding centers on the scaling relationship between vortex count and quench time. The vortex count at equilibration time versus quench time demonstrates the Kibble-Zurek power-law scaling. Data averaged over 1000 realizations, with error bars indicating one standard deviation, support this finding.

Simulations reveal that quantum turbulence can arise naturally during the formation of a Bose-Einstein condensate via a process known as spontaneous quantum turbulence (SQT), driven by finite-time symmetry breaking. This differs from typical methods that are often too violent, complicating the study of QT due to the generation of a variety of excitations. Researchers at the University of Luxembourg, the Christ University, and the Donostia International Physics Center are now focusing on understanding how SQT emerges as topological defects during a continuous phase transition, leveraging the Kibble-Zurek mechanism (KZM) as a foundational paradigm. The researchers propose the generation of SQT via the KZM during Bose-Einstein condensation induced by a thermal quench. The vortex count at equilibration time versus quench time demonstrates the Kibble-Zurek power-law scaling. Data averaged over 1000 realizations, with error bars indicating one standard deviation, support this finding. The researchers establish the nonequilibrium universality of SQT through the Kibble-Zurek and Kolmogorov scaling of the incompressible kinetic energy.