This paper provides a brief description of recent experiments measuring the fluid circulation in 3He. In the B phase, the circulation around a 16 ~m diameter wire is found to be quantized in units of h/2m~. Possible future experiments are also described. It is widely believed that quantized circulation is a fundamental property of any superfluid system [1]. The fluid circulation must be quantized in units of h/nm, where m is the mass of the individual atoms in the fluid and n is an integer that depends on the microscopic process responsible for the macroscopic quantum state. For the case of 4He, the interacting atoms experience a Bose condensation into the superfluid state and n = 1. This fact has been demonstrated in several different types of experiments [1].
This paper provides a brief description of recent experiments measuring the fluid circulation in 3He. In the B phase, the circulation around a 16 m diameter wire is found to be quantized in units of h/2m. Possible future experiments are also described. It is widely believed that quantized circulation is a fundamental property of any superfluid system [1]. The fluid circulation must be quantized in units of h/nm, where m is the mass of the individual atoms in the fluid and n is an integer that depends on the microscopic process responsible for the macroscopic quantum state. For the case of 4He, the interacting atoms experience a Bose condensation into the superfluid state and n = 1. This fact has been demonstrated in several different types of experiments [1].
This doctoral thesis consists of experimental studies on rotating superfluid helium-3 at millikelvin temperatures. Superfluid 3He provides an example of ordered systems where quantum phenomena are visible on a macroscopic scale. The order parameter is described by a 3x3 complex matrix leading to different superfluid phases with different properties. The A and B phases support topologically different kinds of defects, most notably vortex lines. Vortex lines are most easily created and studied in uniform rotation. Because of quantum nature, the circulation around the vortices is quantized in units of κ0 = h/2m3.\n\nIn superfluid 3He nuclear magnetic resonance (NMR) provides a means to distinguish between different types of vortices and count them one by one. During the course of this work the sensitivity of the NMR spectrometer was improved by an order of magnitude, which enabled the direct measurement of the circulation of a vortex in the A phase that carries two circulation quanta (2κ0). Up to now the circulation of the known quantized vortex types in other quantum fluids, which include superfluid 4He, superconductors, and Bose-Einstein -condensates, has been singly quantized.\n\nOther NMR experiments reported in the thesis are: (1) The first qualitative measurements of vortex annihilation in the A and B phases of 3He. These measurements tell the lowest rotation velocity that stabilizes an array of vortex lines with a given number of vortices, and how it depends on the type of the defect. (2) Studies of vortex arrays with both singly and doubly quantized A phase vortex lines coexisting in the experimental container. 3He-A provides a unique system in which this kind of arrangement can be done. (3) In order to improve the vortex detection sensitivity in the B phase even further, the response of different nonlinear spin precession modes to superfluid-normal fluid counterflow was studied. A new mode, where the orbital angular momentum is oriented transverse to the external magnetic field, was found.
We report the first observation of quantized circulation in superfluid 3B. The apparatus consists of a straight vibrating wire immersed in liquid 3He, which is cooled by a rotating nuclear demagnetization cryostat. The experiment is carried out at about 250 \ensuremath{\mu}K. The superfluid at this temperature is in the ballistic quasiparticle regime. Circulation around the wire is found to be stable only when it takes on the values -h/2m3, 0, and +h/2m3, where h is Planck's constant and m3 is the mass of the 3He atom. This experiment confirms that superfluid 3B is a Cooper-paired superfluid with a macroscopic quantum wave function.
The authors present evidence of stable nonzero circulation in superfluid [sup 3]He-A around a 16[mu]m diameter wire. The measurements are made on a rotating cryostat at T [approx] 0.15[Tc]. Circulation affects the splitting of the wire's normal modes, which changes the beat frequency in the emf across the wire as it vibrates in a magnetic field. The different beat frequencies at 14 and at 21 bar suggest that circulation is present at 21 bar. Furthermore, at 21 bar the beat frequency is a linear function of rotation velocity, as is expected if circulation is trapped around the wire. At 14 bar no effect of rotation is observed. The authors propose that at 21 bar the ground state texture has nonzero circulation of order h/2m[sub 3].
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.
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.
We present a brief overview of crucial historical stages in creation of superfluidity theory and of the current state of the microscopic theory of superfluid 4He. We pay special attention to the role of Bose-Einstein condensates (BECs) in understanding of physical mechanisms of superfluidity and identification of quantum mechanical structure of 4He superfluid component below λ-point, in particular—the possibility that at least two types of condensates may appear and coexist simultaneously in superfluid 4He. In this context we discuss the properties of the binary mixtures of BECs and types of excitations, which may appear due to intercomponent interaction in such binary mixtures of condensates. We also discuss current status of investigations of persistent currents in toroidal optical traps and present an outlook of our recent findings on this subject.