Superfluid equation of state of dilute composite bosons

TL;DR

This paper develops an exact theoretical framework for the BEC-BCS crossover focusing on the dilute regime, revealing that composite bosons behave similarly to elementary bosons up to a certain order in density.

Contribution

It introduces a precise theory treating dimers as made of two fermions and calculates the equation of state at zero temperature, highlighting the effects of composite nature.

Findings

Chemical potential expansion matches elementary boson results up to n^{3/2} order.

Composite nature effects appear only at the next order, n^2.

The theory provides an exact description of the BEC regime with explicit dimer treatment.

Abstract

We present an exact theory of the BEC-BCS crossover in the BEC regime, which treats explicitely dimers as made of two fermions. We apply our framework, at zero temperature, to the calculation of the equation of state. We find that, when expanding the chemical potential in powers of the density n up to the Lee-Huang-Yang order, proportional to n^3/2, the result is identical to the one of elementary bosons in terms of the dimer-dimer scattering length a_M, the composite nature of the dimers appearing only in the next order term proportional to n^2 .