Dipole polarizability of a trapped superfluid Fermi gas

The polarization produced by the relative displacement of the potentials trapping two spin species of a dilute Fermi gas with N=N is calculated at unitarity by assuming phase separation between the superfluid and a polarized phase at zero temperature. Because of the energy cost associated with pair breaking, the dipole polarizability is strongly quenched and exhibits important deviations from the ideal gas behavior even for nonlinear displacements of the order of the size of the atomic cloud. The behavior in the presence of different trapping frequencies (monopole polarization) for the two spin species is also discussed. Our results suggest new experimental perspectives to explore the quantum phases of interacting Fermi gases.     

Dark lump excitations in superfluid Fermi gases

We study the linear and nonlinear properties of two-dimensional matter-wave pulses in disk-shaped superfluid Fermi gases.A Kadomtsev-Petviashvili I(KPI) solitary wave has been realized for superfluid Fermi gases in the limited cases of Bardeen-Cooper-Schrieffer(BCS) regime,Bose-Einstein condensate(BEC) regime,and unitarity regime.Onelump solution as well as one-line soliton solutions for the KPI equation are obtained,and two-line soliton solutions with the same amplitude are also studied in the limited cases.The dependence of the lump propagating velocity and the sound speed of two-dimensional superfluid Fermi gases on the interaction parameter are investigated for the limited cases of BEC and unitarity.     

Atom interferometric detection of the pairing order parameter in a Fermi gas

We propose two interferometric schemes to experimentally detect in real space the onset of pair condensation in a two-spin-component Fermi gas. Two atomic wave packets are coherently extracted from the gas at different positions and are mixed by a matter-wave beam splitter: we show that the spatial long-range order of the atomic pairs in the gas reflects in the atom counting statistics in the beam splitter output channels. The same long-range order is also shown to create a matter-wave grating in the overlapping region of the two extracted wave packets, grating that can be revealed by a light-scattering experiment.     

BCS-BEC crossover at finite temperature for superfluid trapped Fermi atoms

We consider the BCS-BEC (Bose-Einstein-condensate) crossover for a system of trapped Fermi atoms at finite temperature, both below and above the superfluid critical temperature, by including fluctuations beyond mean field. We determine the superfluid critical temperature and the pair-breaking temperature as functions of the attractive interaction between Fermi atoms, from the weak- to the strong-coupling limit (where bosonic molecules form as bound-fermion pairs). Density profiles in the trap are also obtained for all temperatures and couplings.     

Josephson oscillation of a superfluid Fermi gas

Using the complete numerical solution of a time-dependent three-dimensional mean-field model we study the Josephson oscillation of a superfluid Fermi gas (SFG) at zero temperature formed in a combined axially-symmetric harmonic plus one-dimensional periodic optical-lattice (OL) potentials after displacing the harmonic trap along the axial OL axis. We study the dependence of Josephson frequency on the strength of the OL potential. The Josephson frequency decreases with increasing strength as found in the experiment of Cataliotti et al. [Science 293, 843 (2001)] for a Bose-Einstein condensate and of the experiment of Pezzè et al. [Phys. Rev. Lett. 93, 120401 (2004)] for an ideal Fermi gas. We demonstrate a breakdown of Josephson oscillation in the SFG for a large displacement of the harmonic trap. These features of Josephson oscillation of a SFG can be tested experimentally.     

Thermodynamics of a trapped unitary Fermi gas

We present the first model-independent comparison of recent measurements of the entropy and of the critical temperature of a unitary Fermi gas, performed by Luo et al., with the most complete results currently available from finite temperature Monte Carlo calculations. The measurement of the critical temperature in a cold fermionic atomic cloud is consistent with a value T(c) = 0.23(2)epsilon(F) in the bulk, as predicted by the present authors in their Monte Carlo calculations.     

Density profiles and collective excitations of a trapped two-component Fermi vapour

We discuss the ground state and the small-amplitude excitations of a degenerate vapour of fermionic atoms placed in two hyperfine states inside a spherical harmonic trap. An equations-of-motion approach is set up to discuss the hydrodynamic dissipation processes from the interactions between the two components of the fluid beyond mean-field theory and to emphasize analogies with spin dynamics and spin diffusion in a homogeneous Fermi liquid. The conditions for the establishment of a collisional regime via scattering against cold-atom impurities are analyzed. The equilibrium density profiles are then calculated for a two-component vapour of ⁴⁰K atoms: they are little modified by the interactions for presently relevant values of the system parameters, but spatial separation of the two components will spontaneously arise as the number of atoms in the trap is increased. The eigenmodes of collective oscillation in both the total particle number density and the concentration density are evaluated analytically in the special case of a symmetric two-component vapour in the collisional regime. The dispersion relation of the surface modes for the total particle density reduces in this case to that of a one-component Fermi vapour, whereas the frequencies of all other modes are shifted by the interactions.     

Vortex arrays in a rotating superfluid Fermi gas

The behavior of a dilute two-component neutral superfluid Fermi gas subjected to rotation is investigated within the context of a weak-coupling BCS theory. The microscopic properties at finite temperature are obtained by iterating the Bogoliubov-de Gennes equations to self-consistency. In the model, alkali atoms are strongly confined in quasi-two-dimensional traps produced by a deep one-dimensional optical lattice. The lattice depth significantly enhances the critical transition temperature and the critical rotation frequency at which the superfluidity ceases. As the rotation frequency increases, the triangular vortex arrays become increasingly irregular, indicating a quantum melting transition.     

Dynamic structure factor of a superfluid Fermi gas

We describe the excitation spectrum of a two-component neutral Fermi gas with attractive interactions in the superfluid phase at finite temperature by deriving a suitable Random-Phase approximation in the collisionless regime with the technique of functional derivatives. The obtained spectrum for the homogeneous gas at small wavevectors contains the Bogoliubov-Anderson phonon and is essentially different from the spectrum predicted by the static Bogoliubov theory, which instead shows an unphysically large response. We adapt the results for the homogeneous system to obtain the dynamic structure factor of a harmonically confined superfluid and we identify in the spectrum a unique feature of the superfluid phase. Received 28 March 2001     

Insulating behavior of a trapped ideal Fermi gas

We investigate theoretically and experimentally the center-of-mass motion of an ideal Fermi gas in a combined periodic and harmonic potential. We find a crossover from a conducting to an insulating regime as the Fermi energy moves from the first Bloch band into the band gap of the lattice. The conducting regime is characterized by an oscillation of the cloud about the potential minimum, while in the insulating case the center of mass remains on one side of the potential.     

Density excitations of a harmonically trapped ideal gas

The dynamic structure factor S(q, ω) of a harmonically trapped Bose gas has been calculated well above the Bose-Einstein condensation temperature by treating the gas cloud as a canonical ensemble of non-interacting classical particles. The static structure factor is found to vanish s8 q ² in the long-wavelength limit. We also incorporate a relaxation mechanism phenomenologically by including a stochastic friction force to study S(q, ω). A significant temperature dependence of the density fluctuation spectra is found. The Debye-Waller factor has been calculated for the trapped thermal cloud as a function of q and the number N of atoms. A substantial difference is found for small- and large-N clouds.     

Light induced space-time patterns in a superfluid Fermi gas

Patterns resulted from modulation instability are ubiquitous and have been extensively studied in optics and Bose-Einstein condensates. However, these patterns have not been realized in ultracold Fermi gases, although there has been considerable theoretical interest in this field. Here we report an experimental observation of space-time patterns in a superfluid Fermi gas excited by red-detuned laser light. Longitudinal spatially fluctuated laser beams induce the spontaneous formation of two different kinds of patterns. For strongly interacting Fermi gas, the induced patterns accompanied by phonon excitations demonstrate a striking“X”-type dispersion relation between frequency and wavevector. Then, the propagation of such patterns in the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer crossover is investigated, which is related to the speed of sound and agrees well with theoretical calculations. The observed patterns in noninteracting Fermi gases are stationary without phonon excitations and show a much longer lifetime.     

Umklapp collisions and center-of-mass oscillations of a trapped Fermi gas

Starting from the Boltzmann equation, we study the center-of-mass oscillation of a harmonically trapped normal Fermi gas in the presence of a one-dimensional periodic potential. We show that for values of the Fermi energy above the first Bloch band the center of mass motion is overdamped in the collisional regime due to umklapp processes. This should be contrasted with the behavior of a superfluid where one instead expects the occurrence of persistent Josephson-like oscillations.     

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.     

Tunneling dynamics of superfluid Fermi gas in a triple-well potential

The tunneling dynamics of superfluid Fermi gas in a triple-well potential in the unitarity regime is investigated in the present paper. The fixed points of the (0, 0) mode and the (∏, ∏) mode are given. We find that the interaction parameter U and the coupling strength k could have an extreme effect on the quantum tunneling dynamics. We also find that, in the zero mode, only Josophson oscillation appears. However, for the ∏ mode, the trapping phenomena take place. An irregular oscillation of the particle number in each well could appear by adjusting the scanning period T* . It is noted that if the scanning period is less than a critical point T , the particle number will come back to the fixed point with small oscillation, while if T T* the particle number cannot come back to the fixed point, but with irregular oscillations. The dependence of the critical point T* on the system parameter of coupling strength k is numerically given.     

Dynamics of dark solitons in a trapped superfluid fermi gas

We study soliton oscillations in a trapped superfluid Fermi gas across the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. We derive an exact equation for the oscillation period in terms of observable quantities, which we confirm by solving the time-dependent Bogoliubov-de Gennes equations. Hence we reveal the appearance and dynamics of solitons across the crossover, and show that the period dramatically increases as the soliton becomes shallower on the BCS side of the resonance. Finally, we propose an experimental protocol to test our predictions.     

Exact solution for a trapped Fermi gas with population imbalance and BCS pairing

The problem of a two-component Fermi gas in a harmonic trap, with an imbalanced population and a pairing interaction of zero total momentum, is mapped onto the exactly solvable reduced BCS model. For a one-dimensional trap, the complete ground state diagram is determined with various topological features in ground state energy spectra. In addition to the conventional two-shell density profile of a paired core and polarized outer wings, a three-shell structure as well as a double-peak superfluid distribution are unveiled.     

Tomographic rf spectroscopy of a trapped Fermi gas at unitarity

We present spatially resolved radio-frequency spectroscopy of a trapped Fermi gas with resonant interactions and observe a spectral gap at low temperatures. The spatial distribution of the spectral response of the trapped gas is obtained using in situ phase-contrast imaging and 3D image reconstruction. At the lowest temperature, the homogeneous rf spectrum shows an asymmetric excitation line shape with a peak at 0.48(4)epsilonF with respect to the free atomic line, where epsilonF is the local Fermi energy.     

Pair correlations of an expanding superfluid Fermi gas

The pair correlation function of an expanding gas is investigated with an emphasis on the BEC-BCS crossover of a superfluid Fermi gas at zero temperature. At unitarity quantum Monte Carlo simulations reveal the occurrence of a sizable bunching effect due to interactions in the spin up-down channel which, at short distances, is larger than that exhibited by thermal bosons in the Hanbury-Brown-Twiss effect. We propose a local equilibrium ansatz for the pair correlation function which we predict will remain isotropic during the expansion even if the trapping potential is anisotropic, in contrast with the behavior of the density. The isotropy of the pair correlation function is an experimentally accessible signature, which makes a clear distinction with respect to the case of noninteracting gases and can be understood as a consequence of the violation of scaling.