Functional-integral representation of atomic mixtures

TL;DR

This paper develops a functional integral approach to study a mixture of spin-1/2 fermionic atoms and molecules in an optical lattice, revealing phase transitions, superfluidity, and fluctuation effects.

Contribution

It introduces a novel functional integral framework for atomic mixtures, analyzing phase diagrams and fluctuation-induced interactions in a lattice system.

Findings

Identification of phase diagram with Mott insulators and superfluid phase

Gaussian fluctuations induce a repulsive dimer-dimer interaction

Analysis of spin imbalance effects on the system

Abstract

A mixture of spin-1/2 fermionic atoms and molecules of paired fermionic atoms is studied in an optical lattice. The molecules are formed by an attractive nearest-neighbor interaction. A functional integral is constructed for this many-body system and analyzed in terms of a mean-field approximation and Gaussian fluctuations. This provides a phase diagram with the two merging Mott insulators and an intermediate superfluid. The Gaussian fluctuations give rise to an induced repulsive dimer-dimer interaction mediated by the unpaired fermions. The effect of an unbalanced distribution of spin-up and spin-down fermions is also discussed.