Low energy Collective Modes of a Superfluid Trapped atomic Fermi Gas

We consider the low energy collective mode spectrum of a superfluid Fermi gas in a spherical trap in the collisionless regime. Using a self-consistent random-phase approximation, the effects of superfluidity on modes of dipole and quadrupole symmetries are systematically examined. The spectrum is calculated for varying pairing strength and temperature and we identify several spectral features such as the emergence of Goldstone modes that can be used to detect the onset of superfluidity. Our analysis is relevant for present experiments aimed at observing a superfluid phase transition in trapped Fermi gases.Comment: 2 color figures include

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.

Collective excitations in a fermion-fermion mixture with different Fermi surfaces

In this paper, collective excitations in a homogeneous fermion-fermion mixture with different Fermi surfaces are studied. In the Fermi liquid phase, the zero-sound velocity is found to be larger than the largest Fermi velocity. With attractive interactions, the superfluid phase appears below a critical temperature, and the phase mode is the low-energy collective excitation. The velocity of the phase mode is proportional to the geometric mean of the two Fermi velocities. The difference between the two velocities may serve as a tool to detect the superfluid phase.Comment: 4 pages. To be published in Phys. Rev.

Ideal Gases in Time-Dependent Traps

We investigate theoretically the properties of an ideal trapped gas in a time-dependent harmonic potential. Using a scaling formalism, we are able to present simple analytical results for two important classes of experiments: free expansion of the gas upon release of the trap; and the response of the gas to a harmonic modulation of the trapping potential is investigated. We present specific results relevant to current experiments on trapped Fermions.Comment: 5 pages, 3 eps figure

Laser probing of Cooper-paired trapped atoms

We consider a gas of trapped Cooper-paired fermionic atoms which are manipulated by laser light. The laser induces a transition from an internal state with large negative scattering length (superfluid) to one with weaker interactions (normal gas). We show that the process can be used to detect the presence of the superconducting order parameter. Also, we propose a direct way of measuring the size of the gap in the trap. The efficiency and feasibility of this probing method is investigated in detail in different physical situations.Comment: 9 pages, 8 figure

Hartree-Fock-Bogoliubov theory versus local-density approximation for superfluid trapped fermionic atoms

We investigate a gas of superfluid fermionic atoms trapped in two hyperfine states by a spherical harmonic potential. We propose a new regularization method to remove the ultraviolet divergence in the Hartree-Fock-Bogoliubov equations caused by the use of a zero-range atom-atom interaction. Compared with a method used in the literature, our method is simpler and has improved convergence properties. Then we compare Hartree-Fock-Bogoliubov calculations with the semiclassical local-density approximation. We observe that for systems containing a small number of atoms shell effects, which cannot be reproduced by the semiclassical calculation, are very important. For systems with a large number of atoms at zero temperature the two calculations are in quite good agreement, which, however, is deteriorated at non-zero temperature, especially near the critical temperature. In this case the different behavior can be explained within the Ginzburg-Landau theory.Comment: 12 pages, 8 figures, revtex; v2: references and clarifying remarks adde

Spin Excitations in a Fermi Gas of Atoms

We have experimentally investigated a spin excitation in a quantum degenerate Fermi gas of atoms. In the hydrodynamic regime the damping time of the collective excitation is used to probe the quantum behavior of the gas. At temperatures below the Fermi temperature we measure up to a factor of 2 reduction in the excitation damping time. In addition we observe a strong excitation energy dependence for this quantum statistical effect.Comment: 4 pages, 3 figure

Antiferromagnetic noise correlations in optical lattices

We analyze how noise correlations probed by time-of-flight (TOF) experiments reveal antiferromagnetic (AF) correlations of fermionic atoms in two-dimensional (2D) and three-dimensional (3D) optical lattices. Combining analytical and quantum Monte Carlo (QMC) calculations using experimentally realistic parameters, we show that AF correlations can be detected for temperatures above and below the critical temperature for AF ordering. It is demonstrated that spin-resolved noise correlations yield important information about the spin ordering. Finally, we show how to extract the spin correlation length and the related critical exponent of the AF transition from the noise.Comment: 4 pages, 4 figure