Superfluid phase transition in trapped atomic Fermi gas

Superfluid phase transition in an atomic Fermi gas confined to a harmonic trap is studied. The critical transition temperature and the temperature dependence and spatial shape of the order parameter are determined. The spectrum and wave functions of single-particle and collective excitations are obtained for a gas in the superfluid phase. The excitation eigenfrequencies exhibit a pronounced temperature dependence, allowing, e.g., identification of the superfluid phase.     

Formation of a vortex lattice in a rotating BCS Fermi gas

We investigate theoretically the formation of a vortex lattice in a superfluid two-spin component Fermi gas in a rotating harmonic trap, in a BCS-type regime of condensed non-bosonic pairs. Our analytical solution of the superfluid hydrodynamic equations, both for the 2D BCS equation of state and for the 3D unitary quantum gas, predicts that the vortex free gas is subject to a dynamic instability for fast enough rotation. With a numerical solution of the full time dependent BCS equations in a 2D model, we confirm the existence of this dynamic instability and we show that it leads to the formation of a regular pattern of quantum vortices in the gas.     

Kohn-Sham theory of an atomic Fermi gas

We point out that, when repulsive interactions between two fermions are not integrable, as the case may be for atomic fermions, the original Kohn-Sham density functional must be revised.     

Conversion of an atomic Fermi gas to a long-lived molecular Bose gas

We have converted an ultracold Fermi gas of 6Li atoms into an ultracold gas of 6Li2 molecules by adiabatic passage through a Feshbach resonance. Approximately 1.5 x 10(5) molecules in the least-bound, v=38, vibrational level of the X1Sigma(+)(g) singlet state are produced with an efficiency of 50%. The molecules remain confined in an optical trap for times of up to 1 s before we dissociate them by a reverse adiabatic sweep.     

Crossover temperature of Bose-Einstein condensation in an atomic Fermi gas

We show that in an atomic Fermi gas near a Feshbach resonance the crossover between a Bose-Einstein condensate of diatomic molecules and a Bose-Einstein condensate of Cooper pairs occurs at positive detuning, i.e., when the molecular energy level lies in the two-atom continuum. We determine the crossover temperature as a function of the applied magnetic field and find excellent agreement with the experiment of C. A. Regal et al. [Phys. Rev. Lett. 92, 040403 (2004)]] who has recently observed this crossover temperature.     

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.     

Structure of a quantized vortex near the BCS-BEC crossover in an atomic Fermi gas

In order to clarify the structure of a singly quantized vortex in a superfluid fermion gas near the Feshbach resonance, we numerically solve the generalized Bogoliubov-de Gennes equation in the boson-fermion model. The superfluid gap, which contains contributions from both condensed fermion pairs and condensed bosons, is self-consistently determined, and the quasiparticle excitation levels bound in the vortex core are explicitly shown. We find that the boson condensate contributes to enhance the matter density depletion and the discreteness of localized quasiparticle spectrum inside the core. It is predicted that the matter density depletion and the discrete core levels are detectable in the vicinity of the BCS-Bose-Einstein condensation crossover point.     

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.     

Quantum phase transition in an atomic bose gas with a feshbach resonance

We show that in an atomic Bose gas near a Feshbach resonance a quantum phase transition occurs between a phase with only a molecular Bose-Einstein condensate and a phase with both an atomic and a molecular Bose-Einstein condensate. We show that the transition is characterized by an Ising order parameter. We also determine the phase diagram of the gas as a function of magnetic field and temperature: the quantum critical point extends into a line of finite temperature Ising transitions.     

Mott-insulator transition in a two-dimensional atomic Bose gas

Cold atoms in periodic potentials are versatile quantum systems for implementing simple models prevalent in condensed matter theory. Here we realize the 2D Bose-Hubbard model by loading a Bose-Einstein condensate into an optical lattice, and study the resulting Mott insulator. The measured momentum distributions agree quantitatively with theory (no adjustable parameters). In these systems, the Mott insulator forms in a spatially discrete shell structure which we probe by focusing on correlations in atom shot noise. These correlations show a marked dependence on the lattice depth, consistent with the changing size of the insulating shell expected from simple arguments.     

Pauli blocking of collisions in a quantum degenerate atomic Fermi gas.

We have produced an interacting quantum degenerate Fermi gas of atoms composed of two spin states of magnetically trapped 40K. The relative Fermi energies are adjusted by controlling the population in each spin state. Thermodynamic measurements reveal a resulting imbalance in the mean energy per particle between the two species, which is a factor of 1.4 at our lowest temperature. This imbalance of energy comes from a suppression of collisions between atoms in the gas due to the Pauli exclusion principle. Through measurements of the thermal relaxation rate we have directly observed this Pauli blocking as a factor of 2 reduction in the effective collision cross section in the quantum degenerate regime.     

Phase diagram and deformed phase separation for a trapped Fermi gas with population imbalance and BCS pairing interaction

We study the phase separated state of an ultracold atomic Fermi gas confined in a three-dimensional quantum harmonic trap with a BCS pairing interaction. Examining various finite-temperature phase diagrams, we investigate the interplay between the filling of the quantum trap energy levels and the pairing energy. We find that a low (high) filling leads to a large (small) critical population imbalance for the superfluid/normal transition, together with a fully (partially) polarized normal part. We also show that the decrease of the density leads to a changeover of the shape of the superfluid core from an equipotential form to a deformed one. Moreover, we clarify the intrinsic mechanisms that lead to the deformation, providing a unified scenario for phase separation and deformation in a trapped Fermi gas, allowing for a possible interpretation of the apparently controversial experimental findings.     

Structure of the superfluid ground state of an atomic Fermi gas near the Feshbach resonance

The ground state of an atomic Fermi gas near the Feshbach resonance for a negative scattering length is investigated using the variational method. The structure of the superfluid state is formed by two coherently coupled subsystems, viz., the quasimolecular subsystem in a closed channel and the subsystem of atomic pairs in an open channel. The derived system of equations makes it possible to describe the properties of the ground state for arbitrary values of the parameters (in particular, to find the gap in the single-particle Fermi excitation spectrum and the speed of sound characterizing the branch of collective Bose excitations).     

Evolution from BCS to BEC superfluidity in p-wave Fermi gases

We consider the evolution of superfluid properties of a three-dimensional p-wave Fermi gas from a weak coupling Bardeen-Cooper-Schrieffer (BCS) to strong coupling Bose-Einstein condensation (BEC) limit as a function of scattering volume. At zero temperature, we show that a quantum phase transition occurs for p-wave systems, unlike the s-wave case where the BCS to BEC evolution is just a crossover. Near the critical temperature, we derive a time-dependent Ginzburg-Landau (GL) theory and show that the GL coherence length is generally anisotropic due to the p-wave nature of the order parameter, and becomes isotropic only in the BEC limit.     

Spin interaction with an ideal Fermi gas

We consider the equilibrium dynamics of a system consisting of a spin interacting with an ideal Fermi gas on the lattice , 3. We present two examples: when this system is unitarily equivalent to an ideal Fermi gas or to a spin in an ideal Fermi gas without interaction between them.     

Collective mode evidence of high-spin bosonization in a trapped one-dimensional atomic Fermi gas with tunable spin

We calculate the frequency of collective modes of a one-dimensional repulsively interacting Fermi gas with high-spin symmetry confined in harmonic traps at zero temperature. This is a system realizable with fermionic alkaline-earth-metal atoms such as ¹⁷³Yb, which displays an exact SU(κ$\kappa$) spin symmetry with κ?2$\kappa ?2$ and behaves like a spinless interacting Bose gas in the limit of infinite spin components κ→∞$\kappa \to \infty$, namely high-spin bosonization. We solve the homogeneous equation of state of the high-spin Fermi system by using Bethe ansatz technique and obtain the density distribution in harmonic traps based on local density approximation. The frequency of collective modes is calculated by exactly solving the zero-temperature hydrodynamic equation. In the limit of large number of spin-components, we show that the mode frequency of the system approaches that of a one-dimensional spinless interacting Bose gas, as a result of high-spin bosonization. Our prediction of collective modes is in excellent agreement with a very recent measurement for a Fermi gas of ¹⁷³Yb atoms with tunable spin confined in a two-dimensional tight optical lattice.     

Far-from-equilibrium dynamics of an ultracold Fermi gas

Nonequilibrium dynamics of an $\mathcal{N}$ -fold spin-degenerate ultracold Fermi gas is described in terms of beyond-mean-field Kadanoff?CBaym equations for correlation functions. Using a nonperturbative expansion in powers of $1/\mathcal{N}$ , the equations are derived from the two-particle irreducible effective action in Schwinger?CKeldysh formulation. The definition of the nonperturbative approximation on the level of the effective action ensures vital conservation laws as, e.g., for the total energy and particle number. As an example, the long-time evolution of a homogeneous, twofold spin-degenerate Fermi gas is studied in one spatial dimension after an initial preparation far from thermal equilibrium. Analysis of the fluctuation-dissipation relation shows that, at low energies, the gas does not thermalize.     

On the possibility of a superfluid transition in a Fermi gas of neutral particles at ultralow temperatures

The possibility of triplet Cooper pairing in a Fermi gas of neutral particles in magnetic traps at ultralow temperatures is predicted. Estimates are presented for the superfluid transition temperature. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 4, 273–276 (25 August 1996)