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Journal of Experimental and Theoretical Physics Letters

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

Yu. Kagan, Leonid A. Maksimov

Published Jul 1, 2005• 0 citations
Publisher

Abstract

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).

DOI
10.1134/1.2056629

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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).
Within the framework of the variational approach the ground state is studied in a gas of Fermi atoms near the Feshbach resonance at negative scattering length. The structure of the originating superfluid state is formed by two coherently bound subsystems. One subsystem is that of quasi molecules in the closed channel and the other is a system of pairs of atoms in the open channel. The set of equations derived allows us to describe the properties of the ground state at an arbitrary magnitude of the parameters. In particular, it allows one to find a gap in the spectrum of single-particle Fermi excitations and sound velocity characterizing a branch of collective Bose excitations.
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A system of equal mixture of 6Li^6Li6Li atomic Fermi gas of two hyperfine states loaded into a cubic three-dimensional optical lattice is studied assuming a negative scattering length (BCS side of the Feshbach resonance). When the interaction is attractive, fermionic atoms can pair and form a superfluid. The dispersion of the phonon-like mode and the speed of sound in the long-wavelength limit are obtained by solving the Bethe-Salpeter equations for the collective modes of the attractive Hubbard Hamiltonian.
The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the sss-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
A Feshbach resonance in the s-wave scattering length occurs if the energy of the two atoms in the incoming open channel is close to the energy of a bound state in a coupled closed channel. Starting from the microscopic Hamiltonian that describes this situation, we derive the effective atom–molecule theory for a Bose gas near a Feshbach resonance. In order to take into account all two-body processes, we have to dress the bare couplings of the atom–molecule model with ladder diagrams. This results in a quantum field theory that exactly reproduces the scattering amplitude of the atoms and the bound-state energy of the molecules. Since these properties are incorporated at the quantum level, the theory can be applied both above and below the critical temperature of the gas. Moreover, making use of the true interatomic potentials ensures that no divergences are encountered at any stage of the calculation. We also present the mean-field theory for the Bose–Einstein condensed phase of the gas.