We investigate the fermionic quasiparticle branch of superfluid Fermi gases in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover and calculate the quasiparticle lifetime and energy shift due to its coupling with the collective mode. The only close-to-resonance process that low-energy quasiparticles can undergo at zero temperature is the emission of a bosonic excitation from the phononic branch. Close to the minimum of the branch we find that the quasiparticles remain undamped, allowing us to compute corrections to experimentally relevant quantities such as the energy gap, location of the minimum, effective mass, and Landau critical velocity.
In this Letter, we study the effect of quasiparticle interactions in a Bose-Fermi superfluid mixture. We consider the lifetime of a quasiparticle of the Bose superfluid due to its interaction with quasiparticles in the Fermi superfluid. We find that this damping rate, i.e., the inverse of the lifetime, has quite a different threshold behavior at the BCS and the BEC side of the Fermi superfluid. The damping rate is a constant near the threshold momentum in the BCS side, while it increases rapidly in the BEC side. This is because, in the BCS side, the decay process is restricted by the constraint that the fermion quasiparticle is located near the Fermi surface, while such a restriction does not exist in the BEC side where the damping process is dominated by bosonic quasiparticles of the Fermi superfluid. Our results are related to the collective mode experiment in the recently realized Bose-Fermi superfluid mixture.
The quasiparticle excitations and dynamical stability of an atomic Bose-Einstein condensate coupled to a quantum degenerate Fermi gas of atoms at zero temperature is studied. The Fermi gas is assumed to be either in the normal state or to have undergone a phase transition to a superfluid state by forming Cooper pairs. The quasiparticle excitations of the Bose-Einstein condensate exhibit a dynamical instability due to a resonant exchange of energy and momentum with quasiparticle excitations of the Fermi gas. The stability regime for the bosons depends on whether the Fermi gas is in the normal state or in the superfluid state. We show that the energy gap in the quasiparticle spectrum for the superfluid state stabilizes the low-energy excitations of the condensate. In the stable regime, we calculate the boson quasiparticle spectrum, which is modified by the fluctuations in the density of the Fermi gas.
We report results of quantum Monte Carlo calculations of the ground state of dilute Fermi gases with attractive short-range two-body interactions. The strength of the interaction is varied to study different pairing regimes which are characterized by the product of the
s-wave scattering length and the Fermi wave vector,
akF. We report results for the ground-state energy, the pairing gap $\ensuremath{\Delta}$, and the quasiparticle spectrum. In the weak-coupling regime, $1∕a{k}_{F}<\ensuremath{-}1$, we obtain Bardeen-Cooper-Schrieffer (BCS) superfluid and the energy gap $\ensuremath{\Delta}$ is much smaller than the Fermi gas energy
EFG. When
a>0, the interaction is strong enough to form bound molecules with energy
Emol. For $1∕a{k}_{F}\ensuremath{\gtrsim}0.5$, we find that weakly interacting composite bosons are formed in the superfluid gas with $\ensuremath{\Delta}$ and gas energy per particle approaching $\ensuremath{\mid}{E}_{\mathrm{mol}}\ensuremath{\mid}∕2$. In this region, we seem to have Bose-Einstein condensation (BEC) of molecules. The behavior of the energy and the gap in the BCS-to-BEC transition region, $\ensuremath{-}0.5<1∕a{k}_{F}<0.5$, is discussed.
We consider a 3D homogeneous superfluid at low temperature
T with 2 types of excitations, gapless phonons with a linear dispersion relation at low wavenumber, and gapped quasiparticles with a quadratic dispersion relation around extrema. We calculate the scattering amplitude of a phonon on a quasiparticle to leading order in
T for all subsonic quasiparticle velocities, with a
S-matrix formalism between exact asymptotic states dressed by virtual phonons. We then characterize the erratic motion of the quasiparticle in the superfluid due to its unceasing collisions with thermal phonons through mean force
F(k), longitudinal and transverse
k-dependent momentum diffusion coefficients, and spatial diffusion coefficient. At the minimum location
k0 of the dispersion relation, where the velocity vanishes,
F(k) varies linearly with velocity with an isotropic friction coefficient; if
k0=0, the momentum diffusion is also isotropic and
F(k0)=0; if
k0>0, it is not, and
F(k0) is nonzero but subleading with respect to friction by one order in
T. The velocity time correlation function, whose integral is the spatial diffusion coefficient, decays with the mean velocity damping rate if
k0=0; if
k0>0, it has a second exponential component, with an amplitude and a damping rate lower by a factor
∝T (it is the velocity direction thermalization rate). We also characterize force and momentum diffusion close to the stability domain sonic edge. Our general expressions are expected to be exact to leading order in
T. We illustrate them in the BCS approximation, for a fermionic quasiparticle (an unpaired fermion) in a superfluid of spin 1/2 fermions, realisable with cold atoms in flat bottom traps. We also refute the statement of Lerch, Bartosch and Kopietz (2008), that there would be no fermionic quasiparticle in such a superfluid.
Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.