Bose-Fermi Pair Correlations in Attractively Interacting Bose-Fermi Atomic Mixtures

TL;DR

This paper investigates the static properties and pair correlations in attractively interacting Bose-Fermi mixtures at zero temperature, revealing enhanced attraction effects for small mass ratios and complex dispersion behaviors influenced by particle ratios.

Contribution

It provides a detailed analysis of Bose-Fermi pair correlations and medium effects in atomic mixtures, highlighting the impact of mass and number ratios on energy, pressure, and quasiparticle dispersions.

Findings

Attractive energy contributions are greatly enhanced for small mass ratios.

Bose-Fermi pairs exhibit a standard quasiparticle dispersion for mass ratios ≥ 1.

For small mass ratios, Bose-Fermi pairs with finite momentum experience strong attraction.

Abstract

We study static properties of attractively interacting Bose-Fermi mixtures of uniform atomic gases at zero temperature. Using Green's function formalism we calculate boson-fermion scattering amplitude and fermion self-energy in the medium to lowest order of the hole line expansion. We study ground state energy and pressure as functions of the scattering length for a few values of the boson-fermion mass ratio $m_b/m_f$ and the number ratio $N_b/N_f$. We find that the attractive contribution to energy is greatly enhanced for small values of the mass ratio. We study the role of the Bose-Fermi pair correlations in the mixture by calculating the pole of the boson-fermion scattering amplitude in the medium. The pole shows a standard quasiparticle dispersion for a Bose-Fermi pair, for $m_b/m_f\geq 1$. For small values of the mass ratio, on the other hand, a Bose-Fermi pair with a finite center-of-mass momentum experiences a strong attraction, implying large medium effects. In addition, we also study the fermion dispersion relation. We find two dispersion branches with the possibility of the avoided crossings. This strongly depends on the number rario $N_b/N_f$.