Since the idea of quantum turbulence was first proposed by Feynman and later realized in experiments of superfluid helium and Bose-Einstein condensates, much emphasis has been put on finding signatures that distinguish quantum turbulence from its classical counterpart. Here we show that quantum turbulence in rotating condensates is fundamentally different from the classical case. While rotating quantum turbulence develops a negative temperature state with self-organization of the kinetic energy in quantized vortices, it also displays an anisotropic dissipation mechanism and a different, non-Kolmogorovian, scaling of the energy at small scales. This scaling is compatible with Vinen turbulence and also has been found in recent simulations of condensates with multicharged vortices. An elementary explanation for the scaling is presented in terms of disorder in the vortices positions.
Since the idea of quantum turbulence was first proposed by Feynman and later realized in experiments of superfluid helium and Bose-Einstein condensates, much emphasis has been put on finding signatures that distinguish quantum turbulence from its classical counterpart. Here we show that quantum turbulence in rotating condensates is fundamentally different from the classical case. While rotating quantum turbulence develops a negative temperature state with self-organization of the kinetic energy in quantized vortices, it also displays an anisotropic dissipation mechanism and a different, non-Kolmogorovian, scaling of the energy at small scales. This scaling is compatible with Vinen turbulence and also has been found in recent simulations of condensates with multicharged vortices. An elementary explanation for the scaling is presented in terms of disorder in the vortices positions.
Quantum turbulence is recently one of the most important topics in low temperature physics. Physics of quantum turbulence and quantized vortices have been studied chiefly in superfluid helium. The realization of atomic Bose-Einstein condensation has allowed us to study quantized vortives in the fascinating systems too. Generally there are two kinds of cooperative phenomena comprised of quantized vortices, from the research history of superfluid helium. Lots of studies in atomic Bose-Einstein condensates (BECs) are devoted mainly to the issues of vortex lattices under rotation. However, another important state on quantized vortices, namely quantum turbulence, has been never studied in atomic BECs. In this work, we address for the first time quantum turbulence in atomic BECs theoretically and numerically. After reviewing shortly the recent developments on quantum turbulecne, we propose how to make quantum turbulence in a trapped BEC by combining rotation around two axes, and confirm the Kolmogorov spectra by the Gross-Pitaevskii model.
This article reviews recent developments in quantum fluid dynamics and quantum turbulence (QT) for superfluid helium and atomic Bose–Einstein condensates. Quantum turbulence was discovered in superfluid 4He in the 1950s, but the field moved in a new direction starting around the mid-1990s. Quantum turbulence is comprised of quantised vortices that are definite topological defects arising from the order parameter appearing in Bose–Einstein condensation. Hence, QT is expected to yield a simpler model of turbulence than does conventional turbulence. A general introduction to this issue and a brief review of the basic concepts are followed by a description of vortex lattice formation in a rotating atomic Bose–Einstein condensate, typical of quantum fluid dynamics. Then we discuss recent developments in QT of superfluid helium such as the energy spectra and dissipative mechanisms at low temperatures, QT created by vibrating structures, and the visualisation of QT. As an application of these ideas, we end with a discussion of QT in atomic Bose–Einstein condensates.
This paper reviews recent developments in the physics of quantum turbulence (QT). QT was discovered in superfluid (4)He in the 1950s, while the research has taken a new direction since the middle of the 1990s. QT is comprised of quantized vortices that are definite topological defects and expected to give a prototype of turbulence much simpler than usual classical turbulence. We give a general introduction and brief review of classical turbulence followed by a description of the dynamics of quantized vortices. After mentioning the modern research trends in QT, we discuss the energy spectra, the energy cascade and the possible dissipation mechanism of QT at very low temperatures. The last part is devoted to QT in atomic Bose-Einstein condensates.
We present a study on the development of rotating turbulence in Bose-Einstein condensates with a dissipative Gross-Pitaevskii model. Turbulence is generated by driving the lattice of quantized vortices in a harmonic potential with a random forcing potential. As the turbulence progressed, the initial alignment of vortices underwent slight disruptions, thereby increasing the high-wavenumber components of the kinetic energy. In the turbulent state, the distribution of incompressible kinetic energy exhibits milder anisotropy than that in the initial lattice state and demonstrates a scaling behavior of kz−2.5 in the direction parallel to the rotation axis. In contrast, the compressible kinetic energy exhibits an isotropic scaling behavior at high wavenumbers.
Quantum turbulence shares many similarities with classical turbulence in the isotropic and homogeneous case, despite the inviscid and quantized nature of its vortices. However, when quantum fluids are subjected to rotation, their turbulent dynamics depart significantly from the classical expectations. We explore the phenomenology of rotating quantum turbulence, emphasizing how rotation introduces new regimes with no classical analogues. We review recent theoretical, experimental and numerical developments, and present new numerical results that map out distinct dynamical regimes arising from the interplay of rotation, quantization, nonlinearities and condensed matter regimes. In particular, we show the importance of distinguishing the dynamics of rotating quantum fluids in the slowly rotating, rapidly rotating and low Landau level regimes. The findings have implications for the dynamics of liquid helium, atomic Bose-Einstein condensates and neutron stars, and show how rotating quantum fluids can serve as a unique platform bridging turbulence theory and condensed matter physics, revealing novel states of out-of-equilibrium quantum matter. This article is part of the theme issue 'Frontiers of turbulence and statistical physics'.
Abstract Chapter 5 delves into quantum turbulence in superfluid helium and atomic Bose-Einstein condensates (BECs). The foundation of quantum turbulence research lies in classical fluid dynamics and turbulence, which is why we begin by covering essential concepts like the Reynolds number and Kolmogorov’s -5/3 power law in the energy spectrum. These principles are crucial for understanding quantum turbulence. We then explore the shared aspects of quantum turbulence in superfluid helium and atomic BECs, such as the differences in vortex configurations compared to classical turbulence, energy spectra, cascades, and the distinction between quasiclassical (Kolmogorov) and ultraquantum (Vinen) turbulence, focusing on their decay behaviors. In superfluid helium, we emphasize experimental studies in thermal counterflow and numerical simulations using the Vortex Filament Model (VFM). The advent of visualization experiments in the mid-2000s was transformative, allowing the observation of normal fluid velocity profiles and accelerations via tracer particles, which led to more accurate simulations coupling the VFM with normal fluid dynamics. Another significant topic is the energy spectrum of quantum turbulence, and whether it mirrors classical turbulence remains a key question. In addition to thermal counterflow, localized quantum turbulence generated by oscillating objects has been a major area of study. We present research showing how quantized vortices grow and evolve into turbulence. Superfluid 3He-B also provides a platform for quantum turbulence, with advancements in microfabrication bringing MEMS and NEMS into focus for studying quantum hydrodynamics at micro- and nanoscale, influenced by boundary conditions. In atomic BECs, confined by potentials, turbulence is induced through techniques like shaking or moving potentials. A unique aspect of BECs is two-dimensional quantum turbulence, featuring inverse energy cascades, Onsager vortices, and negative temperature states. Finally, atomic BECs, being compressible, serve as a platform for both vortex and wave turbulence. Multicomponent BECs, such as spinor BECs, introduce spin turbulence, further diversifying the field.