Frequency and damping of the Scissors Mode of a Fermi gas

We calculate the frequency and damping of the scissors mode in a classical gas as a function of temperature and coupling strength. Our results show good agreement with the main features observed in recent measurements of the scissors mode in an ultracold gas of $^6$Li atoms. The comparison between theory and experiment involves no fitting parameters and thus allows an identification of non-classical effects at and near the unitarity limit.Comment: 4 pages, 2 figure

Effects of the trapping potential on a superfluid atomic Fermi Gas

We examine a dilute two-component atomic Fermi gas trapped in a harmonic potential in the superfluid phase. For experimentally realistic parameters, the trapping potential is shown to have crucial influence on various properties of the gas. Using an effective hamiltonian, analytical results for the critical temperature, the temperature dependence of the superfluid gap, and the energy of the lowest collective modes are derived. These results are shown to agree well with numerical calculations. We furthermore discuss in more detail a previous proposed method to experimentally observe the superfluid transition by looking at the collective mode spectrum. Our results are aimed at the present experimental effort to observe a superfluid phase transition in a trapped atomic Fermi gas.Comment: 2. revised version. Minor mistakes in equation references corrected. To appear in Phys. Rev.

Cooper pairing and single particle properties of trapped Fermi gases

We calculate the elementary excitations and pairing of a trapped atomic Fermi gas in the superfluid phase. The level spectra and pairing gaps undergo several transitions as the strength of the interactions between and the number of atoms are varied. For weak interactions, the Cooper pairs are formed between particles residing in the same harmonic oscillator shell. In this regime, the nature of the paired state is shown to depend critically on the position of the chemical potential relative to the harmonic oscillator shells and on the size of the mean field. For stronger interactions, we find a region where pairing occur between time-reversed harmonic oscillator states in different shells also.Comment: Slightly revised version: Mistakes in equation references in figures corrected. Accepted for Phys. Rev.

Shear viscosity and damping for a Fermi gas in the unitarity limit

The shear viscosity of a two-component Fermi gas in the normal phase is calculated as a function of temperature in the unitarity limit, taking into account strong-coupling effects that give rise to a pseudogap in the spectral density for single-particle excitations. The results indicate that recent measurements of the damping of collective modes in trapped atomic clouds can be understood in terms of hydrodynamics, with a decay rate given by the viscosity integrated over an effective volume of the cloud.Comment: 7 pages, 3 figures. Discussion significantly extended. Appendix added. To appear in PR

Viscous relaxation and collective oscillations in a trapped Fermi gas near the unitarity limit

The viscous relaxation time of a trapped two-component gas of fermions in its normal phase is calculated as a function of temperature and scattering length, with the collision probability being determined by an energy-dependent s-wave cross section. The result is used for calculating the temperature dependence of the frequency and damping of collective modes studied in recent experiments, starting from the kinetic equation for the fermion distribution function with mean-field effects included in the streaming terms.Comment: 10 pages, 9 figures; proof version, corrected typo in Eq. (23); accepted for publication in PR

Viscosity and Thermal Relaxation for a resonantly interacting Fermi gas

The viscous and thermal relaxation rates of an interacting fermion gas are calculated as functions of temperature and scattering length, using a many-body scattering matrix which incorporates medium effects due to Fermi blocking of intermediate states. These effects are demonstrated to be large close to the transition temperature $T_c$ to the superfluid state. For a homogeneous gas in the unitarity limit, the relaxation rates are increased by nearly an order of magnitude compared to their value obtained in the absence of medium effects due to the Cooper instability at $T_c$. For trapped gases the corresponding ratio is found to be about three due to the averaging over the inhomogeneous density distribution. The effect of superfluidity below $T_c$ is considered to leading order in the ratio between the energy gap and the transition temperature.Comment: 7 pages, 3 figure

Pairing of fermions in atomic traps and nuclei

Pairing gaps for fermionic atoms in harmonic oscillator traps are calculated for a wide range of interaction strengths and particle number, and compared to pairing in nuclei. Especially systems, where the pairing gap exceeds the level spacing but is smaller than the shell splitting $\hbar\omega$, are studied which applies to most trapped Fermi atomic systems as well as to finite nuclei. When solving the gap equation for a large trap with such multi-level pairing, one finds that the matrix elements between nearby harmonic oscillator levels and the quasi-particle energies lead to a double logarithm of the gap, and a pronounced shell structure at magic numbers. It is argued that neutron and proton pairing in nuclei belongs to the class of multi-level pairing, that their shell structure follows naturally and that the gaps scale as $\sim A^{-1/3}$ - all in qualitative agreement with odd-even staggering of nuclear binding energies. Pairing in large systems are related to that in the bulk limit. For large nuclei the neutron and proton superfluid gaps approach the asymptotic value in infinite nuclear matter: $\Delta\simeq 1.1$ MeV.Comment: 11 pages, 5 figure

Far-Field Plasmonic Resonance Enhanced Nano-Particle Image Velocimetry within a Micro Channel

In this paper, a novel far-field plasmonic resonance enhanced nanoparticle-seeded Particle Image Velocimetry (nPIV) has been demonstrated to measure the velocity profile in a micro channel. Chemically synthesized silver nanoparticles have been used to seed the flow in the micro channel. By using Discrete Dipole Approximation (DDA), plasmonic resonance enhanced light scattering has been calculated for spherical silver nanoparticles with diameters ranging from 15nm to 200nm. Optimum scattering wavelength is specified for the nanoparticles in two media: water and air. The diffraction-limited plasmonic resonance enhanced images of silver nanoparticles at different diameters have been recorded and analyzed. By using standard PIV techniques, the velocity profile within the micro channel has been determined from the images.Comment: submitted to Review of Scientific Instrument

Vortex Tubes in Turbulence Velocity Fields at Reynolds Numbers 300-1300

The most elementary structures of turbulence, i.e., vortex tubes, are studied using velocity data obtained in a laboratory experiment for boundary layers with microscale Reynolds numbers 295-1258. We conduct conditional averaging for enhancements of a small-scale velocity increment and obtain the typical velocity profile for vortex tubes. Their radii are of the order of the Kolmogorov length. Their circulation velocities are of the order of the root-mean-square velocity fluctuation. We also obtain the distribution of the interval between successive enhancements of the velocity increment as the measure of the spatial distribution of vortex tubes. They tend to cluster together below about the integral length and more significantly below about the Taylor microscale. These properties are independent of the Reynolds number and are hence expected to be universal.Comment: 8 pages, to appear in Physical Review

Low energy monopole Modes of a Trapped atomic Fermi Gas

We consider the low energy collective monopole modes of a trapped weakly interacting atomic Fermi gas in the collisionless regime. The spectrum is calculated for varying coupling strength and chemical potential. Using an effective Hamiltonian, we derive analytical results that agree well with numerical calculations in various regimes. The onset of superfluidity is shown to lead to effects such as the vanishing of the energy required to create a Cooper molecule at a critical coupling strength and to the emergence of pair vibration excitations. Our analysis suggests ways to experimentally detect the presence of the superfluid phase in trapped atomic Fermi gases.Comment: 5 pages & 1 figure. Accepted for Phys. Rev. Let