Bose-Einstein condensation of heteronuclear bound states formed in a Fermi gas of two atomic species: microscopic approach

TL;DR

This paper develops a microscopic theoretical framework to describe Bose-Einstein condensation of heteronuclear molecules formed in a two-species Fermi gas, analyzing equilibrium conditions, energy spectra, and experimental relevance at low temperatures.

Contribution

It introduces a novel microscopic approach combining the Bogoliubov model and second quantization for heteronuclear molecules in a Fermi gas, valid at low temperatures.

Findings

Conditions for heteronuclear molecule condensate coexistence with Fermi gas components.

Ground state energy and excitation spectrum of the system.

Analytical and numerical analysis of the equilibrium equations.

Abstract

We study a many-body system of interacting fermionic atoms of two species that are in thermodynamic equilibrium with their condensed heteronuclear bound states (molecules). In order to describe such an equilibrium state, we use a microscopic approach that involves the Bogoliubov model for a weakly interacting Bose gas and approximate formulation of the second quantization method in the presence of bound states of particles elaborated earlier by the authors. This microscopic approach is valid at low temperatures, when the average kinetic energy of all the components in the system is small in comparison with the bound state energy. The coupled equations, which relate the chemical potentials of fermionic components and molecular condensate density, are obtained within the proposed theory. At zero temperature, these equations are analyzed both analytically and numerically, attracting the relevant experimental data. We find the conditions at which a condensate of heteronuclear molecules coexists in equilibrium with degenerate components of a Fermi gas. The ground state energy and single-particle excitation spectrum are found. The boundaries of the applicability of the developed microscopic approach are analyzed.