We have used torsional oscillators, containing disk-shaped slabs of superfluid (3)He-A, to probe the chiral orbital textures created by cooling into the superfluid state while continuously rotating. Comparing the observed flow-driven textural transitions with numerical simulations of possible textures shows that an oriented monodomain texture with l antiparallel to the angular velocity Ω(0) is left behind after stopping rotation. The bias toward a particular chirality, while in the vortex state, is due to the inequivalence of energies of vortices of opposite circulation. When spun-up from rest, the critical velocity for vortex nucleation depends on the sense of rotation relative to that of l. A different type of vorticity, apparently linked to the slab's rim by a domain wall, appears when the angular velocity, Ω, is parallel to l.
We have measured the critical velocity ${\ensuremath{\upsilon}}_{\mathrm{c}}$ at which ${}^{3}\mathrm{He}\ensuremath{-}\mathrm{A}$ in a rotating cylinder becomes unstable against the formation of quantized vortex lines with continuous (singularity-free) core structure. We find that ${\ensuremath{\upsilon}}_{\mathrm{c}}$ is distributed between a maximum and a minimum limit, which we ascribe to a dependence on the texture of the orbital angular momentun axis $\stackrel{^}{\mathbf{l}}(\mathbf{r})$ in the cylinder. Slow cooldown through
Tc in rotation yields $\stackrel{^}{\mathbf{l}}(\mathbf{r})$ textures for which the measured ${\ensuremath{\upsilon}}_{\mathrm{c}}$'s are in good agreement with the calculated instability of the expected $\stackrel{^}{\mathbf{l}}$ texture.
We study the orbital angular momentum (OAM)
Lz of two-dimensional chiral
(px+ipy)ν-wave superfluids (SFs) in the presence of an axisymmetric multiply quantized vortex (MQV) with vorticity
k on a disk at zero temperature, in the framework of Bogoliubov-de Gennes (BdG) theory. Focusing on spectral asymmetry (or spectral flow), we find that
Lz=(k+ν)N/2 for any integer
ν and
k in the Bose-Einstein Condensation (BEC) regime, where
N is the total number of fermions. While in the weak-pairing Bardeen-Cooper-Schrieffer (BCS) regime, only for chiral
p+ip-wave SF with
k=±1,
Lz=(k+ν)N/2 still holds. For chiral SFs with
ν≥2 or
∣k∣≥2 in the BCS regime, the OAM
Lz is remarkably reduced from its ``full" value in the BEC regime. However, the deviations differ in these two cases. For chiral SFs with
ν≥2,
Lz is sharply suppressed in this ideal setting with a specular wall, while the suppression caused by the
∣k∣≥2 vortex is moderate, which is core-size dependent. Furthermore, for
p+ip-wave SF with
k=−1, the total OAM
Lz is zero, but the distribution
Lz(r) is nontrivial compared with that of vortex-free
s-wave SF, in which the total OAM is zero as well. For chiral SFs with
ν≥2 and
∣k∣≥2, the effects of circulation due to vortex and chiral pairing can coexist, and hence depress the OAM simultaneously. These observations can be explained by spectral asymmetry and unpaired fermions in the ground state of the BdG Hamiltonian. We also investigate the spatial distribution of particle density, OAM, by solving the BdG equation.
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 have measured the resistive and reactive mutual friction coefficients in rotating superfluid ${}^{3}\mathrm{H}\mathrm{e}\ensuremath{-}A$ at
29.3bars pressure. The results agree with those predicted from the equation of orbital hydrodynamics for two quantum continuous vortices if the previously measured value of the orbital viscosity is used. Our results put an upper limit on the orbital inertia of less than $0.005\ensuremath{\Elzxh}$ per Cooper pair. We explain our observation of history-dependent textures by noting that the ease of formation of continuous vortices depends on the relative direction of
l and the rotation axis.
We experimentally study the emergence of high-energy equilibrium states in a chiral vortex gas of like-circulation vortices realized within a disk-shaped atomic Bose-Einstein condensate. In contrast to the familiar triangular Abrikosov lattice, the lowest-energy state of the superfluid in a rotating frame, we observe the formation of rotating vortex equilibria that are highly disordered and have significant energy per vortex. Experimental stirring protocols realize equilibrium states at both positive and negative absolute temperatures of the vortex gas. At sufficiently high energies the system exhibits a symmetry breaking transition, resulting in an off-axis equilibrium phase that no longer shares the symmetry of the container. By initializing vortices in a non-equilibrium distribution with sufficient energy, relaxation to equilibrium is observed within experimental timescales and an off-axis equilibrium state emerges at negative absolute temperature. The observed equilibria are in close agreement with mean field theory of the microcanonical ensemble of the vortex gas.