Stanford University Team Models Many-Body Effects for Turbulent Quantum Hydrodynamics

Scientists led by Sayak Bhattacharjee at Stanford University, in collaboration with the Indian Institute of Technology, Stockholm University, University of Connecticu, are presenting a new understanding of quantum turbulence in superfluids. The study moves beyond traditional mean-field theories to explore many-body effects at extremely low temperatures, offering a condensed-matter perspective on turbulent hydrodynamics. This research focuses on systems like ultracold atoms and holds potential implications for the development of quantum computing platforms. The findings address fundamental questions about quantum turbulence and propose avenues for utilising modern quantum many-body techniques to understand these phenomena, potentially advancing knowledge of quantum critical points and superfluidity.

Turbulent quantum behaviour observed at temperatures above established theoretical boundaries

Hydrodynamic descriptions of quantum systems are now extending to previously inaccessible regimes, shifting focus from simplified mean-field theory to incorporating many-body quantum effects. Traditionally, the behaviour of fluids has been modelled using classical hydrodynamics, which assumes a continuous fluid description. However, at the quantum level, this breaks down due to the discrete nature of particles and the inherent uncertainty in their positions and momenta. Calculations previously faced limitations when quantum fluctuations became significant, rendering standard perturbative approaches ineffective. The analysis reveals turbulent behaviour now extends to regimes exceeding a critical temperature of approximately 0.1 times the Bose-Einstein condensation temperature, a threshold previously insurmountable due to the limitations of mean-field approximations. This represents a substantial advancement, allowing for the investigation of turbulent behaviour at temperatures closer to those achievable in laboratory experiments.

Weakly-interacting superfluids are now open to investigation of quantum turbulence, often modelled by a mean-field theory governed by the Gross-Pitaevskii equation. The Gross-Pitaevskii equation is a nonlinear partial differential equation that describes the quantum mechanical evolution of a macroscopic wave function for a Bose-Einstein condensate. While successful in many scenarios, it neglects the effects of quantum fluctuations and particle interactions beyond the mean-field level. Modelling now considers many-body quantum effects in turbulent hydrodynamics, particularly near zero temperature, with examples including bosons confined in low-dimensional periodic potentials and ultracold-atom systems used in quantum computing. These systems provide a highly controllable environment for studying quantum phenomena. Spatial correlation analysis indicates a power-law scaling, mirroring behaviour observed in classical fluids, although the precise exponent requires further investigation. The observed power-law scaling suggests a degree of universality between classical and quantum turbulence, despite the fundamentally different underlying physics. Such findings open avenues for studying these systems and exploring examples where these effects may be uncovered, such as at the quantum critical point of the superfluid-insulator transition, a phase transition where the superfluid loses its ability to flow without resistance.

Quantum turbulence modelling necessitates reconciling fluid dynamics with many-body quantum

Researchers at Stanford University and collaborating institutions are attempting to reconcile two distinct areas of physics: the behaviour of turbulent fluids and the intricacies of quantum mechanics. For a long time, hydrodynamic models have described fluid flow, traditionally relying on approximations that smooth over the individual behaviour of countless particles. This approach, however, breaks down when considering the subtle effects of quantum fluctuations, particularly at extremely low temperatures where quantum behaviour dominates. Classical turbulence is characterised by a cascade of energy from large scales to small scales, resulting in the formation of vortices and chaotic flow patterns. Quantum turbulence, however, exhibits unique features arising from the quantum nature of the fluid, such as the formation of quantized vortices, topological defects in the superfluid flow.

Explicitly accounting for the impact of numerous interacting quantum particles is key to understanding systems like bosons confined within low-dimensional spaces and the superfluid-insulator transition, a change in a fluid’s flow properties, which are identified as promising systems for observation using current ultracold atom and quantum computing technologies. Low-dimensional systems, such as those confined to one or two dimensions, exhibit enhanced quantum fluctuations and are therefore particularly susceptible to many-body effects. The superfluid-insulator transition represents a dramatic change in the system’s behaviour, from a state where the fluid flows without resistance to a state where it is effectively insulating. Fully capturing quantum effects within turbulent systems presents a formidable challenge given the vast number of interacting particles involved. The computational complexity of solving the many-body Schrödinger equation for such systems is immense, requiring the development of sophisticated numerical techniques and approximations. Nevertheless, this Stanford-led work offers valuable insights into quantum many-body systems exhibiting turbulence, like ultracold atoms and potential quantum computing applications. Ultracold atoms, cooled to temperatures near absolute zero, provide a clean and controllable platform for studying quantum phenomena. Applying techniques from condensed matter physics to quantum fluids broadens the scope of turbulent hydrodynamics, allowing for a more detailed examination of the underlying mechanisms driving these complex phenomena. This interdisciplinary approach could lead to a deeper understanding of both fundamental physics and the development of novel quantum technologies, potentially influencing the design and optimisation of future quantum devices.

The research detailed a study of turbulence in quantum fluids, focusing on the behaviour of superfluids and the impact of quantum effects. Understanding these effects is crucial because it allows for a more accurate description of systems like bosons in low dimensions and the superfluid-insulator transition, both of which are relevant to ultracold atom and quantum computing platforms. Researchers applied condensed matter physics techniques to explore these complex systems, offering insights into the many-body interactions governing turbulent flow. The authors identified open questions that can be addressed using modern quantum many-body techniques, furthering the field’s understanding of these phenomena.