The effects of the dipole interaction on the equilibrium and nonequilibrium properties of $^{3}\mathit{B}$ are calculated using the quasiclassical theory. In zero field, the dipole interaction distorts the l=1 gap, generates an l=3 gap, and induces a new rotated planar phase next to the normal-state transition. The field dependence of the Leggett angle ${\ensuremath{\theta}}_{L}$ is calculated to order (\ensuremath{\gamma}H/\ensuremath{\Delta}${)}^{2}$, including the effect of nonquasiparticle corrections. Using the equilibrium properties as input, we calculate the zero-field NMR frequencies in the collisionless regime. A calculation of the field dependence of the longitudinal NMR frequency reveals the existence of a Fermi-liquid oscillation term due to the out-of-phase motion of the normal and superfluid components. Finally, we compare the collisionless and hydrodynamic theories of NMR.
The effects of the dipole interaction on the equilibrium and nonequilibrium properties of 3B are calculated using the quasiclassical theory. In zero field, the dipole interaction distorts the l=1 gap, generates an l=3 gap, and induces a new rotated planar phase next to the normal-state transition. The field dependence of the Leggett angle \ensuremathθL is calculated to order (\ensuremath{\gamma}H/\ensuremath{\Delta})2, including the effect of nonquasiparticle corrections. Using the equilibrium properties as input, we calculate the zero-field NMR frequencies in the collisionless regime. A calculation of the field dependence of the longitudinal NMR frequency reveals the existence of a Fermi-liquid oscillation term due to the out-of-phase motion of the normal and superfluid components. Finally, we compare the collisionless and hydrodynamic theories of NMR.
The field dependence of the magnetic susceptibility and collective mode frequencies of superfluid 3B are calculated perturbatively in (\ensuremath{\gamma}H/\ensuremath{\Delta}) using the quasiclassical theory. With the aid of this perturbation theory, we interpret the gap distortion, nonlinear susceptibility, and collective excitations of the order parameter in terms of additional correlations between Cooper pairs that are induced by a magnetic field. We also calculate the dispersion splittings of the real squashing modes in a magnetic field. In addition to the nonlinear Zeeman shifts of these modes, which occur in strong magnetic fields (\ensuremath{\gamma}H\ensuremath{\sim}0.10\ensuremath{\Delta}), there are low-field (\ensuremath{\gamma}H\ensuremath{\sim}q2vf2/\ensuremath{\Delta}) nonlinearities of the collective mode frequencies resulting from the field dependence of the quantization axis. Our results for all of these response properties of 3B depend upon a small number of material parameters; thus measurements of these properties can provide detailed information on the quasiparticle interactions.
In this thesis we study the effects of the dipole-dipole interaction on the physics of ultracold quantum gases, both bosonic and fermionic, within the theoretical framework provided by the mean-field regime. This kind of interaction takes place in ultracold atomic gases (for instance 52Cr or 164Dy) due to their atomic magnetic dipole moment, and in ultracold molecular gases due to the magnetic or electric dipole moment. \n \nIn the case of quantum gases of bosonic atoms, or Bose-Einstein condensates, the dipole-dipole interaction can be studied within mean-field approximation using the Gross-Pitaevskii equation, which now contains a new non-linear term due to the dipole-dipole interaction. We investigate, on the one hand dipolar condensates confined in harmonic traps, and on the other dipolar condensates confined in toroidal traps. In the harmonic geometry, our focus is on the study of the ground state and the quantized vortex state, where the density profile is characterized as well as some properties leading to the process of vortex formation, such as the critical frequency and the energy barrier that has to be overcome to bring the vortex from the surface to the centre of the gas. We finish the study of dipolar condensates in harmonic traps by dynamically simulating the precession frequency of an off-center vortex in a non-rotating condensate. \n \nIn the toroidal geometry the dipolar effects are strongly magnified when the polarization axis of the dipoles is perpendicular to the trap symmetry axis. In this case, the anisotropic structure of the density can be understood as the response of the system to the double-well effective potential along the ring. We have studied the dynamics of this system when the initial number of atoms in the left and right wells is imbalanced, predicting Josephson and self-trapping oscillations depending on the initial condition. This has led us to name this new system as Self-induced Josephson Junction. We have studied in detail the self-trapping regime and we have seen that the particle flux inversion is closely related to the crossing of vortices across the Josephson junctions. This result opens the door to establishing a more direct connection between the phase-slip regime, widely addressed in superfluid helium, and the self-trapping regime of condensates. \n \nIn the case of quantum gases of fermionic dipolar particles, we have studied how the radial quadrupole mode allows one to distinguish between hydrodynamic and collisionless regimes. We have analytically calculated the frequency of this mode in the mean-field approximation, generalizing the results from the Thomas-Fermi approximation for trapped ideal Fermi gases. On the one hand, we observe that the frequency in the hydrodynamic regime is smaller than in non-dipolar Fermi gases, while in the collisionless regime the frequency is larger or smaller than that corresponding to the non-interacting system depending on the geometry of the harmonic trap. On the other hand, we predict that reducing the trap deformation (aspect ratio) an observable jump in the frequency of the radial quadrupole mode would take place, which would correspond to the transition between the collisionless and hydrodynamic regimes, for instance when the gas undergoes the transition to the superfluid state.
The long-wavelength, low-frequency "collisionless" collective oscillations of a superfluid Fermi liquid are studied throughout the region 0<T<Tc with the help of a field-theoretic formalism developed in a previous paper. It is found that any collective mode (other than the density fluctuation) that is possible in the normal phase persists below Tc as an oscillation of the normal component, but disappears at some finite temperature which in general depends on the Landau interaction parameters F0,F1,Z0, etc. The behavior of the density-fluctuation mode depends critically on F0, if the latter is negative, there is a well-defined collective oscillation only for $T\ensuremath{\ll}{T}_{c}$, while if it is small and positive, the oscillation is well defined for $T\ensuremath{\ll}{T}_{c}$ and $T\ensuremath{-}{T}_{c}\ensuremath{\ll}{T}_{c}$ but not in the intermediate region. If F0 is large and positive, the density-fluctuation collective mode exists throughout the whole region 0<T<Tc and its velocity is approximately temperature-independent.
Abstract The low-temperature properties of a wide range of many-fermion systems spanning metals, quantum gases and liquids to nuclear matter are well understood within the framework of Landau’s theory of Fermi liquids. The low-energy physics of these systems is governed by interacting fermionic quasiparticles with momenta and energies near a Fermi surface in momentum space. Nonequilibrium properties are described by a kinetic equation for the distribution function for quasiparticles proposed by Landau. Quasiparticle interactions with other quasiparticles, phonons, or impurities lead to internal forces acting on a distribution of nonequilibrium quasiparticles, as well as collision processes that ultimately limit the transport of mass, heat, charge, and magnetization, as well as limiting the coherence times of quasiparticles. For Fermi liquids that are close to a second-order phase transition, e.g., Fermi liquids that undergo a superfluid transition, incipient Cooper pairs—long-lived fluctuations of the ordered phase—provide a new channel for scattering quasiparticles, as well as corrections to internal forces acting on the distribution of nonequilibrium quasiparticles. We develop the theory of quasiparticle transport for Fermi liquids in the vicinity of a BCS-type superfluid transition starting from Keldysh’s field theory for nonequilibrium, strongly interacting fermions. The leading corrections to Fermi-liquid theory for nonequilibrium quasiparticle transport near a Cooper instability arise from the virtual emission and absorption of incipient Cooper pairs. Our theory is applicable to quasiparticle transport in superconductors, nuclear matter, and the low-temperature phases of liquid 3He. As an implementation of the theory we calculate the pairing-fluctuation corrections to the attenuation of zero sound in liquid 3He near the superfluid transition and demonstrate quantitative agreement with experimental results.
The microscopic theory of a superfluid Fermi liquid at finite temperature is developed for the case of a pure system with S-wave pairing, and applied to the calculation of the static properties. As a function of $\ensuremath{\theta}\ensuremath{\equiv}\frac{T}{{T}_{c}}$ these properties are determined entirely by the Landau parameters F0, F1, Z0, etc., characterizing quasiparticle interactions in the normal phase. In particular the spin susceptibility $\ensuremath{\chi}$ and the density of the normal component ${\ensuremath{\rho}}_{n}$ are given by $\frac{\ensuremath{\chi}(\ensuremath{\theta})}{\ensuremath{\chi}(1)}=(1+\frac{1}{4}{Z}_{0})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{4}{Z}_{0}f(\ensuremath{\theta})]},$ $\frac{{\ensuremath{\rho}}_{n}}{\ensuremath{\rho}}=(1+\frac{1}{3}{F}_{1})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{3}{F}_{1}f(\ensuremath{\theta})]},$ where the universal function $f(\ensuremath{\theta})\ensuremath{\equiv}\ensuremath{-}{[\ensuremath{\nu}(0)]}^{\ensuremath{-}1}{\ensuremath{\Sigma}}_{\mathrm{p}}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is the "effective density of states near the Fermi surface" relative to its value $\ensuremath{\nu}(0)$ in the normal phase. Thus the often-quoted expression ${\ensuremath{\rho}}_{n}=\frac{1}{3}{\ensuremath{\Sigma}}_{\mathrm{p}}{\mathrm{p}}^{2}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is valid for an interacting system only in the limit $T\ensuremath{\rightarrow}0$. In the latter part of the paper a simple phenomenological theory of "Fermi-liquid" effects on $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ is developed for arbitrary conditions (including the presence of impurities and pairing with $l\ensuremath{\ne}0$); it is found that under most circumstances explicit expressions for $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ may be obtained which involve only the Landau parameters and a suitably generalized effective density of states. The theory should apply to the possible superfluid phase of He3 and to most superconductors. It is suggested that the Knight shift in nontransition-metal superconductors should display some "Fermi-liquid" effects. The weak-field dc penetration depth $\ensuremath{\lambda}(T)$ is shown to be insensitive to such effects both in the Pippard limit and near Tc; however, in a London superconductor at lower temperatures the correction to $\ensuremath{\lambda}(T)$ should be observable and yield a direct estimate of F1.
Abstract Motivated by the first experimental realization by the Ecole Normale Supérieure (ENS) group of a mixture of a Bose–Einstein condensate with a Fermi superfluid continuously changing from a Bardeen–Cooper–Schrieffer (BCS) superfluid to a Bose–Einstein condensate (BEC) (Ferrier-Barbut et al 2014 Science 345 1035 ), we analytically study the dipole modes of the superfluid Bose–Fermi mixture in the BCS-BEC crossover. The analytical approach can explicitly reveal relationships between the frequencies of the dipole modes and the microscopic properties of the novel system. We start from coupled hydrodynamic equations, where the equation of state for the Fermi superfluid in the crossover is an analytical fitting formula based on experimental data, and by using a scaling approach we analytically study eigenfrequencies of the dipole modes for the coupled system in the ENS experimental parameters. Without the boson–fermion interaction in the equilibrium density profiles, our theoretical results can be reduced to the mean-field model and is consistent with the experimental data. However, by further taking into account the boson–fermion interaction numerically and analytically, we find that the results disagree with the experiment, especially in the parameter regime where the boson interaction is smaller than the boson–fermion interaction.