Quasiparticle scattering rate in a strongly polarized Fermi mixture

Abstract

We analyze the scattering rate of an impurity atom in a Fermi sea as a function of momentum and temperature in the BCS-BEC crossover. The cross section is calculated using a microscopic multichannel theory for the Feshbach resonance scattering, including finite range and medium effects. We show that pair correlations significantly increase the cross section for strong interactions close to the unitarity regime. They give rise to a molecule pole of the cross section at negative energy on the BEC side of the resonance, which smoothly evolves into a resonance at positive scattering energy with a nonzero imaginary part on the BCS side. The resonance is the analog of superfluid pairing for the corresponding population balanced system. Using Fermi liquid theory, we show that the low temperature scattering rate of the impurity atom is significantly increased due to these pair correlations for low momenta. We demonstrate that finite range and mass imbalance effects are significant for the experimentally relevant Li -°K mixture, and we finally discuss how the scattering rate can be measured using radio-frequency spectroscopy and Bose-Fermi mixtures.

Decoherence of Impurities in a Fermi Sea of Ultracold Atoms

“…The calculated decoherence rate is larger when medium effects are included in the T matrix. This is due to pair correlations, which can increase the collisional cross section significantly [39]. We see that the inclusion of these medium effects on the scattering matrix improves the agreement with the experimental data.…”

“…This gives strong evidence that the observed decoherence is, indeed, due to quasiparticle collisions. The significant asymmetry of the decoherence rate around 1=k F a ¼ 0 arises from the narrow nature of the FR [39]. The calculated decoherence rate is larger when medium effects are included in the T matrix.…”

“…3, we plot the calculated decoherence rate γ s =2 as a function of the interaction parameter. The lower solid line is obtained by using the vacuum scattering matrix T vac [39] in (1), whereas the upper solid line is obtained by using a T matrix which includes medium effects using the ladder approximation. The dashed lines include the effects of decay into the molecular state.…”

“…We have defined dp The dominant medium effects can be shown to enter in the scattering matrix T via ladder diagrams, whereas the quasiparticles can be assumed to have the ideal gas energy dispersion E K=Li p ¼ p 2 =2m K=Li [37,38]. The details of the calculation of γ p 1 are described in [39]. In addition, we account for the reduced quasiparticles' residue Z by multiplying the collision rate by Z calculated from the ladder approximation [8].…”

Variational Approach for Impurity Dynamics at Finite Temperature

“…However, our approximation will match the exact result when T T F since it contains the leading order contributions to the virial expansion. In general, thermal effects lead to an exponential decay of the amplitude |S(t)| at long times [14,45,46], while the phase of S(t) is determined by the dominant quasiparticle peaks in the energy spectrum, which are less sensitive to temperature. These features are all well-described within the variational approach [40].…”