Composite bosons in the 2D BCS-BEC crossover from Gaussian fluctuations

Abstract

We study Gaussian fluctuations of the zero-temperature attractive Fermi gas in the 2D BCS-BEC crossover showing that they are crucial to get a reliable equation of state in the BEC regime of composite bosons, bound states of fermionic pairs. A low-momentum expansion up to the fourth order of the quadratic action of the fluctuating pairing field gives an ultraviolent divergent contribution of the Gaussian fluctuations to the grand potential. Performing dimensional regularization we evaluate the effective coupling constant in the beyond-mean-field grand potential. Remarkably, in the BEC regime our grand potential gives exactly the Popov's equation of state of 2D interacting bosons, and allows us to identify the scattering length $a_B$ of the interaction between composite bosons as $a_B=a_F/(2^{1/2}{e}^{1/4})=\mathrm{0.551...}{a}_F$, with $a_F$ is the scattering length of fermions. Remarkably, the value from our analytical relationship between the two scattering lengths is in full agreement with that obtained by recent Monte Carlo calculations.

arXiv comment5 pages, no figures, submitted for publication; typos corrected; to be published in Phys. Rev. A as a Rapid Communication

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• Fermi-to-Bose crossover in a trapped quasi-2D gas of fermionic atoms
• Superfluid density and critical velocity near the fermionic Berezinskii-Kosterlitz-Thouless transition
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• Josephson effect as signature of electron-hole superfluidity in bilayers of van der Waals heterostructures
• Quantum fluctuations and vortex-antivortex unbinding in the 2D BCS-BEC crossover
• Fulde-Ferrell superfluids in spinless ultracold Fermi gases
• Goldstone and Higgs Hydrodynamics in the BCS-BEC Crossover
• Scattering length of composite bosons in the 3D BCS-BEC crossover
• First and second sound in two-dimensional bosonic and fermionic superfluids
• Orbital Limit and Gaussian Fluctuation Effects in Flat Band Superconductors with PseudoMagnetic Fields