Thermodynamics and structural transition of binary atomic Bose-Fermi mixtures in box or harmonic potentials: A path-integral study

TL;DR

This study uses a path-integral approach to analyze the thermodynamics and structural phase transitions in binary Bose-Fermi mixtures under different trapping potentials, providing phase diagrams and density profiles.

Contribution

It introduces a path-integral formalism to evaluate thermodynamic properties and phase transitions in Bose-Fermi mixtures, including phase diagrams and trap structures at finite temperatures.

Findings

Identification of phase separation via effective potential loops

Phase diagrams for Li-Li mixtures at various temperatures

Finite-temperature density profiles in harmonic traps

Abstract

Experimental realizations of a variety of atomic binary Bose-Fermi mixtures have brought opportunities for studying composite quantum systems with different spin-statistics. The binary atomic mixtures can exhibit a structural transition from a mixture into phase separation as the boson-fermion interaction increases. By using a path-integral formalism to evaluate the grand partition function and thermodynamic grand potential, we obtain the effective potential of binary Bose-Fermi mixtures. Thermodynamic quantities in a broad range of temperatures and interactions are also derived. The structural transition can be identified as a loop of the effective potential curve, and the volume fraction of phase separation can be determined by the lever rule. For $^6$Li-$^7$Li and $^6$Li-$^{41}$K mixtures, we present the phase diagrams of the mixtures in a box potential at zero and finite temperatures. Due to the flexible densities of atomic gases, the construction of phase separation is more complicated when compared to conventional liquid or solid mixtures where the individual densities are fixed. For harmonically trapped mixtures, we use the local density approximation to map out the finite-temperature density profiles and present typical trap structures, including the mixture, partially separated phases, and fully separated phases.