At low temperature Quantum Physics can manifest itself at the macroscopic scale in many spectacular ways. Some of its most remarkable features occur when a fluid is stirred. Indeed, as a consequence of the existence of a macroscopic wave-function describing the system, a quantum fluid cannot sustain rigid body rotation by contrast with a classical fluid. Rather, the stirring generates quantized vortices. The recent observation of novel quantum fluids formed by ultra-cold atomic gases allows us to revisit the properties of vortex systems, and to address pending questions of condensed matter physics.
At low temperature Quantum Physics can manifest itself at the macroscopic scale in many spectacular ways. Some of its most remarkable features occur when a fluid is stirred. Indeed, as a consequence of the existence of a macroscopic wave-function describing the system, a quantum fluid cannot sustain rigid body rotation by contrast with a classical fluid. Rather, the stirring generates quantized vortices. The recent observation of novel quantum fluids formed by ultra-cold atomic gases allows us to revisit the properties of vortex systems, and to address pending questions of condensed matter physics.
Quantum fluids are able to flow past obstacles without creating drag and through channels without any resistance. This superfluidity is a consequence of Bose–Einstein condensation, a process in which all the particles gather in the same, lowest-energy quantum state. At low flow velocities, energy exchanges between the obstacle and the fluid are forbidden because of the twin requirements of energy and momentum conservation. As the flow speed is increased, however, the superfluidity breaks down at some critical velocity above which excitations in the fluid can occur. These excitations can be phonons (i.e. quantized vibrations), vortices or, in the case of superfluid liquid helium, rotons (see Rotons: a low-temperature puzzle by Russell Donnelly Physics World February 1997 p25)
Since its realization in dilute bosonic atomic gases [], [], Bose-Einstein condensation of alkali atoms and hydrogen has been produced and studied extensively in the laboratory [], and has permitted an intriguing glimpse into the macroscopic quantum world. In view of potential applications [], [], [], the study of quantized vortices, which are well-known signatures of superfluidity, is one of the key issues. In fact, bulk superfluids are distinguished from normal fluids by their ability to support dissipationless flow. Such persistent currents are intimately related to the existence of quantized vortices, which are localized phase singularities with integer topological charge []. The superfluid vortex is an example of a topological defect that is well known in superconductors [] and in liquid helium []. The occurrence of quantized vortices in superfluids has been the focus of fundamental theoretical and experimental work []. Different research groups have obtained quantized vortices in Bose-Einstein condensates (BECs) experimentally, e.g., the JILA group [], [], the ENS group [] and the MIT group [], []. Currently, there are at least two typical ways to generate quantized vortices from a BEC ground state: (i) impose a laser beam rotating with an angular velocity on the magnetic trap holding the atoms to create a harmonic anisotropic potential [], [], []; or (ii) add to the stationary magnetic trap a narrow, moving Gaussian potential, representing a far-blue detuned laser [], [], [], [], [], [].
Fluid turbulence remains an open problem in contemporary physics. In gases or liquids encountered in daily life, turbulence is comprised of swirling vortices of varying sizes, shapes and strengths. The impossibility of making detailed predictions of turbulent flows comes, in part, from the complicated nature of these vortices. Turbulence in quantum mechanical superfluids, on the other hand, is comparatively simple. When stirred, a superfluid produces well-defined, discretised vortex lines, and hence turbulence in these fluids is much more straightforward to interpret. As such, there is hope that the study of vortices in superfluids may hold the key to unlocking the mysteries of turbulence.
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'.
Bose-Einstein condensation is a quantum statistical phase transition which was theoretically predicted almost a hundred years ago. After years of seminal research, physicists realized the first almost ideal Bose-Einstein condensates in ultracold dilute atomic gases in 1995. Since then, the theoretical and experimental methods concerning such systems have been developing rapidly, and many fascinating phenomena have been found in these novel quantum systems.\n\nBose-Einstein condensation occurs in a system consisting of massive bosons when a single quantum state becomes macroscopically occupied as the temperature is lowered below the transition temperature. In general, condensates consisting of repulsively interacting bosons exhibit superfluidity: Particle currents can flow in the system without dissipation and viscosity. Moreover, the velocity fields of condensates have to be irrotational, which severely restricts the rotational characteristics of these systems. Apart from the center of mass motion, the system may carry angular momentum in the form of elementary excitations or so-called quantized vortices.\n\nThis Thesis is a theoretical study of subjects related to stability and dynamics of quantized vortices in dilute atomic Bose-Einstein condensates. The precession and instability of off-centered vortices in trapped condensates is investigated both in the zero-temperature limit and at finite temperatures. Dynamical stability of multiply quantized vortices and vortex clusters is studied in axisymmetric trap geometries. Splitting of energetically and dynamically unstable multiply quantized vortices into singly quantized vortices is also studied. Finally, as a separate subject, tunneling of a condensate through a potential barrier is investigated. Majority of this work relies on numerical methods for solving the Gross-Pitaevskii and Bogoliubov equations, which are of central importance in the study of dilute atomic Bose-Einstein condensates.
In the previous chapter we described quantized vortex lines, which are one of the characteristic features of superfluids. In a classical fluid, the circulation of vortex lines is not quantized and, in addition, vortex lines decay because of viscous processes. Another feature of a superfluid, the lack of response to rotation for a small enough angular velocity, was also demonstrated. This is analogous to the Meissner effect for superconductors. One characteristic common to superfluids and superconductors is the ability to carry currents without dissipation. Such current-carrying states are not the lowest-energy state of the system. They are metastable states, the existence of which is intimately connected to the nature of the low-lying elementary excitations. The word ‘superfluidity’ does not refer to a single property of the system, but it is used to describe a variety of different phenomena (see Ref. [1]). Historically, the connection between superfluidity and the existence of a condensate, a macroscopically occupied quantum state, dates back to Fritz London's suggestion in 1938, as we have described in Chapter 1. However, the connection between Bose–Einstein condensation and superfluidity is a subtle one. A Bose–Einstein condensed system does not necessarily exhibit superfluidity, an example being the ideal Bose gas for which the critical velocity vanishes, as demonstrated in Sec. 10.1 below. Also lower-dimensional systems may exhibit superfluid behaviour in the absence of a true condensate, as we shall see in Chapter 15.