The functional renormalization group is used for the BCS-BEC crossover in gases of ultracold fermionic atoms. In a simple truncation, we see how universality and an effective theory with composite bosonic diatom states emerge. We obtain a unified picture of the whole phase diagram. The flow reflects different effective physics at different scales. In the BEC limit as well as near the critical temperature, it describes an interacting bosonic theory.

arXiv:cond-mat/0701198Physical Review AAug 1, 200787 citations

arXiv:1512.04067 · Journal of Superconductivity and Novel Magnetism

Reliable Equation of State for Composite Bosons in the 2D BCS-BEC Crossover

Luca Salasnich

Published Dec 19, 2015• 1 citation

arXiv HTML PDF

DOI: 10.1007/s10948-015-3290-4

Related papers

Equation of state of ultracold fermions in the 2D BEC-BCS crossover

Igor Boettcher, Luca Bayha, Dhruv Kedar +7 more

Bulletin of the American Physical SocietyMar 17, 20161 citation

Crossover from BCS to composite-boson (local-pair) superconductivity in quasi-2D systems

Eduard V. Gorbar, В. М. Локтев, Sergei G. Sharapov

arXiv:cond-mat/9503004Physica C SuperconductivityFeb 1, 199622 citations

The crossover from BEC to BCS in the interacting 2D Fermi gas

Shasta Ramachandran, Scott Jensen, Y. Alhassid

Bulletin of the American Physical SocietyMar 17, 20210 citations

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

Luca Salasnich, Flavio Toigo

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 ${a}_{B}$ of the interaction between composite bosons as ${a}_{B}={a}_{F}/({2}^{1/2}{e}^{1/4})=0.551...{a}_{F}$ , 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.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 ${a}_{B}$ of the interaction between composite bosons as ${a}_{B}={a}_{F}/({2}^{1/2}{e}^{1/4})=0.551...{a}_{F}$, 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:1410.3995Physical Review AJan 26, 201528 citations

Scattering length of composite bosons in the three-dimensional BCS-BEC crossover

Luca Salasnich, Giacomo Bighin

We study the zero-temperature grand potential of a three-dimensional superfluid made of ultracold fermionic alkali-metal atoms in the BCS-BEC crossover. In particular, we analyze the zero-point energy of both fermionic single-particle excitations and bosonic collective excitations. The bosonic elementary excitations, which are crucial to obtain a reliable equation of state in the Bose-Einstein condensate regime, are obtained with a low-momentum expansion up to the forth order of the quadratic (Gaussian) action of the fluctuating pairing field. By performing a cutoff regularization and renormalization of Gaussian fluctuations, we find that the scattering length ${a}_{B}$ of composite bosons, bound states of fermionic pairs, is given by ${a}_{B}=(2/3)\phantom{\rule{4pt}{0ex}}{a}_{F}$ , where ${a}_{F}$ is the scattering length of fermions.We study the zero-temperature grand potential of a three-dimensional superfluid made of ultracold fermionic alkali-metal atoms in the BCS-BEC crossover. In particular, we analyze the zero-point energy of both fermionic single-particle excitations and bosonic collective excitations. The bosonic elementary excitations, which are crucial to obtain a reliable equation of state in the Bose-Einstein condensate regime, are obtained with a low-momentum expansion up to the forth order of the quadratic (Gaussian) action of the fluctuating pairing field. By performing a cutoff regularization and renormalization of Gaussian fluctuations, we find that the scattering length ${a}_{B}$ of composite bosons, bound states of fermionic pairs, is given by ${a}_{B}=(2/3)\phantom{\rule{4pt}{0ex}}{a}_{F}$, where ${a}_{F}$ is the scattering length of fermions.

arXiv:1502.06452Physical Review AMar 9, 20153 citations

Flow equations for the BCS-BEC crossover

Sebastian Diehl, Holger Gies A, Jan Martin Pawlowski +1 more

arXiv:cond-mat/0701198Physical Review AAug 1, 200787 citations

{a}_{B}

of the interaction between composite bosons as

{a}_{B}={a}_{F}/({2}^{1/2}{e}^{1/4})=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.

{a}_{B}

of composite bosons, bound states of fermionic pairs, is given by

{a}_{B}=(2/3)\phantom{\rule{4pt}{0ex}}{a}_{F}

, where

{a}_{F}

is the scattering length of fermions.