Superfluid equation of state of cold fermionic gases in the Bose-Einstein regime

Abstract

We present an exact many-body theory of ultracold fermionic gases for the Bose-Einstein condensation (BEC) regime of the BEC-BCS crossover. This is a purely fermionic approach which treats explicitely and systematically the dimers formed in the BEC regime as made of two fermions. We consider specifically the zero temperature case and calculate the first terms of the expansion of the chemical potential in powers of the density $n$. We derive first the mean-field contribution, which has the expected standard expression when it is written in terms of the dimer-dimer scattering length $a_M$. We go next in the expansion to the Lee-Huang-Yang order, proportional to $n^{3/2}$. We find the far less obvious result that it retains also the same expression in terms of $a_M$ as for elementary bosons. The composite nature of the dimers appears only in the next term proportional to $n^2$.

25 pages, 11 figures

References in corpus (6)

• Theory of ultracold Fermi gases
• Weakly bound dimers of fermionic atoms
• Precision Measurements of Collective Oscillations in the BEC-BCS Crossover
• Equation of state and collective frequencies of a trapped Fermi gas along the BEC-unitarity crossover
• Bound states of three and four resonantly interacting particles
• Superfluid equation of state of dilute composite bosons

Cited by in corpus (8)

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• Coboson many-body formalism for cold atom dimers with attraction between different fermion species only
• Equation of state of a polarized Fermi gas in the Bose-Einstein Condensate limit
• Atom-dimer scattering length for fermions with different masses: analytical study of limiting cases
• Atom-dimer scattering amplitude for fermionic mixtures with different masses: s-wave and p-wave contributions
• Mechanical stability of resonant Bose-Fermi mixtures
• Correlation Energy for Elementary Bosons: Physics of the Singularity