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arXiv:0811.4284 · Physical Review A

Scattering resonances in a degenerate Fermi gas

Katharine J. Challis, Nicolai Gayle Nygaard, Klaus Mølmer

Published May 6, 2009• 1 citation
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Abstract

We consider elastic single-particle scattering from a one-dimensional trapped two-component superfluid Fermi gas when the incoming projectile particle is identical to one of the confined species. Our theoretical treatment is based on the Hartree-Fock ground state of the trapped gas and a configuration-interaction description of the excitations. We determine the scattering phase shifts for the system and predict Fano-type scattering resonances that are a direct consequence of interatomic pairing. We describe the main characteristics of the scattering resonances and make a comparison with the results of BCS mean-field theory.

DOI
10.1103/physreva.79.052701

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We consider elastic single-particle scattering from a one-dimensional trapped two-component superfluid Fermi gas when the incoming projectile particle is identical to one of the confined species. Our theoretical treatment is based on the Hartree-Fock ground state of the trapped gas and a configuration-interaction description of the excitations. We determine the scattering phase shifts for the system and predict Fano-type scattering resonances that are a direct consequence of interatomic pairing. We describe the main characteristics of the scattering resonances and make a comparison with the results of BCS mean-field theory.
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.
The main topic of these lectures is the physics of quantum degenerate atomic Fermi gases both under uniform confinement and in harmonic traps. To begin with, a general introduction on ideal Fermi gases is proposed. This "academic" limit is relevant in experiments where ultracold fermionic atoms are all polarized in a single spin state: the low atom momenta together with the fermionic nature of the atoms forbid atomic s-wave scattering and the atoms can be considered as free. Interactions are then introduced for the case of a gas with two spin components. Interactions can be tuned via Feshbach resonances and control the microscopic features of the superfluid phase, ranging from the BCS limit (formation of Cooper pairs) to the BEC limit (Bose-Einstein condensation of dimers). Various theoretical approaches for the description of the BCS-BEC crossover and their predictions in comparison with the experimental results are discussed.
We present a unique theoretical description of the physics of the spherically trapped NNN-atom degenerate Fermi gas at zero temperature based on an ordinary Schr\"odinger equation with a microscopic, two-body interaction potential. With a careful choice of coordinates and a variational wave function, the many-body Schr\"odinger equation can be accurately described by a linear, one-dimensional effective Schr\"odinger equation in a single collective coordinate, the rms radius of the gas. Comparisons of the energy, rms radius, and peak density of the ground-state energy are made to those predicted by Hartree-Fock (HF) theory. Also the lowest radial excitation frequency (the breathing mode frequency) agrees with a sum rule calculation, but deviates from a HF prediction.
We investigate the ground state properties of normal and superfluid phases of a mixture of Fermi atoms at zero temperature in a quasi-one-dimensional harmonic trap. Assuming pairing occurs in the Hartree-Fock single-particle states (obtained using atomic orbitals approach) we calculate the spectrum of elementary excitations of the system. We find that for strong enough attraction between different kinds of fermions the state consisting of Cooper pairs becomes energetically favorable. For even stronger attraction a discontinuity located at the Fermi surface appears in the spectrum of elementary excitations. At the same time the chemical potential changes its sign and the system goes from the gas of Cooper pairs to the condensed phase of molecular dimers realizing the BCS to Bose-Einstein condensate crossover in one-dimensional space.
We investigate the collective oscillations in the BCS-BEC crossover region of a trapped Fermi superfluid at T=0. We explicitly include the effect of a Feshbach resonance, which leads to a tunable pairing interaction adjusted by the threshold energy of the resonance, as well as the associated mol ecules. In a previous paper,we obtained solutions of the Bogoliubov-de Gennes coupled equations, describing a trapped Fermi superfluid ga s. Using these Bogoliubov quasi-particle excitations, we calculate the density correlation function in the Hartree-Fock-Bogoliubov generalized random phase approximation (HFB-GRPA). Previous discussions of collective modes were based on solving the T=0 equation of motion for the superfluid in a trap, ignoring the effect of single-particle excitations. We determine the frequencies of the quadrupole and the monopole modes. In the crossover region, the frequencies of these two modes are shown to be stro ngly depressed by the threshold energy of the two-particle continuum, originating from Andreev single-particle bound states (or in-gap states) localized at the edge of the trap. This effect becomes less important as one enters the BEC regime, due to the absence of these low energy fermion bound states. This suppression of collective mode frequencies by the two-particle continuum may be a useful experimental signature of the single-particle energy gap in the crossover region of trapped Fermi superfluids.
We solve the two-particle s-wave scattering problem for ultracold atom gases confined in arbitrary quasi-one-dimensional (1D) trapping potentials, allowing for two different atom species. As a consequence, the centre-of-mass and relative degrees of freedom do not factorize. We derive bound-state solutions and obtain the general scattering solution, which exhibits several resonances in the 1D scattering length induced by the confinement. We apply our formalism to two experimentally relevant cases: (i) interspecies scattering in a two-species mixture, and (ii) the two-body problem for a single species in a non-parabolic trap.