Abstract This book serves as a comprehensive textbook on quantum hydrodynamics and quantum turbulence, focusing on the hydrodynamics of quantum-condensed systems at low temperatures. A defining feature of these systems is the presence of an order parameter, leading to unique phenomena such as inviscid superfluid flow and vortex quantization—characteristics absent in classical hydrodynamics. The turbulence arising in these systems is known as quantum turbulence. This field lies at the intersection of several disciplines, including low-temperature condensed matter physics, fluid dynamics, quantum mechanics, statistical mechanics, and nonlinear and non-equilibrium physics. The primary systems discussed in this book are superfluid 4He, superfluid 3He, and atomic Bose-Einstein condensates (BECs). The study of quantum hydrodynamics began with the discovery of quantum turbulence in superfluid 4He in the 1950s. Superfluid 3He, discovered in 1972, was the first anisotropic superfluid, providing a platform to explore various topological defects. The realization of atomic BECs in 1995 through laser cooling marked a significant breakthrough, offering precise control over condensates and enabling the visualization of quantized vortices. In crafting this book, we aimed to present a unified narrative that emphasizes the common physics underlying these systems, rather than treating them in isolation. The content is tailored for first-year graduate students, ensuring clarity without the need for supplementary references. As both authors are theorists, we have placed a stronger emphasis on theoretical aspects over experimental findings.
Abstract This book serves as a comprehensive textbook on quantum hydrodynamics and quantum turbulence, focusing on the hydrodynamics of quantum-condensed systems at low temperatures. A defining feature of these systems is the presence of an order parameter, leading to unique phenomena such as inviscid superfluid flow and vortex quantization—characteristics absent in classical hydrodynamics. The turbulence arising in these systems is known as quantum turbulence. This field lies at the intersection of several disciplines, including low-temperature condensed matter physics, fluid dynamics, quantum mechanics, statistical mechanics, and nonlinear and non-equilibrium physics. The primary systems discussed in this book are superfluid 4He, superfluid 3He, and atomic Bose-Einstein condensates (BECs). The study of quantum hydrodynamics began with the discovery of quantum turbulence in superfluid 4He in the 1950s. Superfluid 3He, discovered in 1972, was the first anisotropic superfluid, providing a platform to explore various topological defects. The realization of atomic BECs in 1995 through laser cooling marked a significant breakthrough, offering precise control over condensates and enabling the visualization of quantized vortices. In crafting this book, we aimed to present a unified narrative that emphasizes the common physics underlying these systems, rather than treating them in isolation. The content is tailored for first-year graduate students, ensuring clarity without the need for supplementary references. As both authors are theorists, we have placed a stronger emphasis on theoretical aspects over experimental findings.
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.
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.
Abstract In this chapter, we provide an overview of the entire book. After explaining the basic concepts of macroscopic quantum phenomena, superfluidity and quantized vortices, and quantum turbulence, we introduce the quantum fluids that form the stage of this book: superfluid 4He, superfluid 3He, and atomic Bose-Einstein condensates (BECs). Next, we present the theoretical models used in the study of quantum fluid dynamics and quantum turbulence, such as the Gross-Pitaevskii model, the Vortex filament model, and the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model. Finally, we provide a brief overview of the contents from Chapter 2 to Chapter 5.
Quantized vortices appear in low-temperature quantum condensed systems as the direct product of Bose–Einstein condensation. Quantized vortices were first discovered in superfluid 4He in the 1950s, and have since been studied with a primary focus on the quantum hydrodynamics of this system. This chapter reviews and summarizes the current understanding of quantized vortices, bridging superfluid helium and atomic Bose–Einstein condensates. It begins with a basic introduction, which is followed by discussion of modern topics such as quantum turbulence and vortices in unusual cold atom condensates.
The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose-Einstein condensates, which are characterized by quantized vorticity, superfluidity, and, at finite temperatures, two-fluid behavior. This article introduces their basic properties, describes types and regimes of turbulence that have been observed, and highlights similarities and differences between quantum turbulence and classical turbulence in ordinary fluids. Our aim is also to link together the articles of this special issue and to provide a perspective of the future development of a subject that contains aspects of fluid mechanics, atomic physics, condensed matter, and low-temperature physics.
Turbulence in classical fluids has been the subject of scientific study for centuries, yet there is still no complete general theory of classical turbulence connecting microscopic physics to macroscopic fluid flows, and this remains one of the open problems in physics. In contrast, the phenomenon of quantum turbulence in superfluids has well-defined theoretical descriptions, based on first principles and microscopic physics, and represents a realm of physics that can connect the classical and quantum worlds. Studies of quantum turbulence may thus be viewed as a path for progress on the long-standing problem of turbulence.A dilute-gas Bose-Einstein condensate (BEC) is, in most cases, a superfluid that supports quantized vortices, the primary structural elements of quantum turbulence. BECs are particularly convenient systems for the study of vortices, as standard techniques allow the microscopic structure and dynamics of the vortices to be investigated. Vortices in BECs can be created and manipulated using a variety of techniques, hence BECs are potentially powerful systems for the microscopic study of quantum turbulence.This dissertation focuses on quantized vortices in BECs, specifically experimental and numerical studies of their formation, dynamics, and decay, in an effort to understand the microscopic nature of vortices as elements of quantum turbulence. Four main experiments were performed, and are described in the main chapters of this dissertation, after introductions to vortices, experimental methods, and turbulence are presented. These experiments were aimed at understanding various aspects of how vortices are created and behave in a superfluid system. They involved vortex dipole nucleation in the breakdown of superfluidity, persistent current generation from a turbulent state in the presence of energy dissipation, decay of angular momentum of a BEC due to trapping potential impurities, and exploration of the spontaneous formation of vortices during the BEC phase transition. These experiments represent progress towards enhanced understanding of the formation, dynamics, and decay of vortices in BECs and thus may be foundational to more general studies of quantum turbulence in superfluids.