Composite bosons in the two-dimensional BCS-BEC crossover from Gaussian fluctuations

Year: 2015

Authors: Salasnich L., Toigo F.

Autors Affiliation: Dipartimento di Fisica e Astronomia “Galileo Galilei” and CNISM, Universit`a di Padova, Via Marzolo 8, 35131 Padova, Italy

Abstract: We study Gaussian fluctuations of the zero-temperature attractive Fermi gas in the two-dimensional (2D) BCS-BEC crossover showing that they are crucial to get a reliable equation of state in the Bose-Einstein condensation (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 aB of the interaction between composite bosons as aB=aF/(21/2e1/4)=0.551…aF, with aF 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.


Volume: 91      Pages from: 011604(R)-1  to: 011604(R)-5

KeyWords: quantum field theory; two-dìmensional systems; bose gases
DOI: 10.1103/PhysRevA.91.011604

Citations: 27
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