BCS-BEC (an acronym formed from Bardeen, Cooper, Schrieffer and Bose–Einstein condensation) crossover physics has customarily been addressed in the framework of the scattering length theory (SLT), which requires regularization/renormalization of equations involving infinities. This paper gives a frame by frame picture, as it were, of the crossover scenario without appealing to SLT. While we believe that the intuitive approach followed here will make the subject accessible to a wider readership, we also show that it sheds light on a feature that has not been under the purview of the customary approach: the role of the hole–hole scatterings vis-à-vis the electron–electron scatterings as one goes from the BCS to the BEC end. More importantly, we show that there are critical values of the concentration (n)and the interaction parameter (λ) at which the condensation of Cooper pairs takes place; this is a finding in contrast with the view that such pairs are automatically condensed.BCS-BEC (an acronym formed from Bardeen, Cooper, Schrieffer and Bose–Einstein condensation) crossover physics has customarily been addressed in the framework of the scattering length theory (SLT), which requires regularization/renormalization of equations involving infinities. This paper gives a frame by frame picture, as it were, of the crossover scenario without appealing to SLT. While we believe that the intuitive approach followed here will make the subject accessible to a wider readership, we also show that it sheds light on a feature that has not been under the purview of the customary approach: the role of the hole–hole scatterings vis-à-vis the electron–electron scatterings as one goes from the BCS to the BEC end. More importantly, we show that there are critical values of the concentration (n)and the interaction parameter (λ) at which the condensation of Cooper pairs takes place; this is a finding in contrast with the view that such pairs are automatically condensed.

International Journal of Modern Physics BJan 28, 20148 citations

Measurements of the interactions in a paired zero temperature lithium-6 gas throughout the BEC-BCS crossover

Kamar, Ramsey I.

Understanding the effects of interactions on the ground-state of a paired degenerate Fermi gas throughout the BEC-BCS crossover has been a long standing physical quest for which countless papers have been written. The crossover describes the smooth transition of the physics of a BEC of tightly bound dimers to that of a paired BCS superfluid. A Feshbach resonance is used to tune the interactions necessary to study the crossover. Right around resonance the interactions are expected to be parameterized by a single universal parameter beta [1--3]. This thesis describes a measurement of the axial size of paired, 6Li clouds in the BEC-BCS crossover and provides a comparison with theory. In the BEC regime, absolute measurements of the molecular scattering length are compared with the atomic scattering length and the ratio is compared with theory. Finally, a measurement of beta is made and compared with theory.Understanding the effects of interactions on the ground-state of a paired degenerate Fermi gas throughout the BEC-BCS crossover has been a long standing physical quest for which countless papers have been written. The crossover describes the smooth transition of the physics of a BEC of tightly bound dimers to that of a paired BCS superfluid. A Feshbach resonance is used to tune the interactions necessary to study the crossover. Right around resonance the interactions are expected to be parameterized by a single universal parameter beta [1--3]. This thesis describes a measurement of the axial size of paired, 6Li clouds in the BEC-BCS crossover and provides a comparison with theory. In the BEC regime, absolute measurements of the molecular scattering length are compared with the atomic scattering length and the ratio is compared with theory. Finally, a measurement of beta is made and compared with theory.

Jan 1, 20060 citations

An exactly solvable model of the BCS-BEC crossover

Jean-Noël Fuchs, RECATI A, W. Zwerger

Jan 1, 20040 citations

BEC-BCS crossover in the ϵ expansion

Jiunn-Wei Chen, Eiji Nakano

The $ϵ$ expansion (expansion around four spatial dimensions) developed by Nishida and Son for a cold Fermi gas with infinite scattering length is extended to finite scattering length to study the Bose-Einstein condensate (BEC) to BCS crossover. A resummation of higher-order logarithms and a suitable extension of fermion coupling in $d$ dimensions are developed in order to apply the theory in the BCS regime. The ratio between the chemical potential and the Fermi energy, $\ensuremath{\mu}∕{\ensuremath{\epsilon}}_{F}$, is computed to next-to-leading order in the $ϵ$ expansion as a function of $\ensuremath{\eta}=1∕(a{k}_{F})$, where $a$ is the scattering length and ${k}_{F}$ is the Fermi momentum in a noninteracting system. Near the unitarity limit $\ensuremath{\mid}\ensuremath{\eta}\ensuremath{\mid}\ensuremath{\rightarrow}0$, we found $\ensuremath{\mu}∕{\ensuremath{\epsilon}}_{F}=0.475\ensuremath{-}0.707\ensuremath{\eta}\ensuremath{-}0.5{\ensuremath{\eta}}^{2}$. Near the BEC limit $\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{\infty}$, $\ensuremath{\mu}∕{\ensuremath{\epsilon}}_{F}=0.062∕\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{2}$, while near the BCS limit $\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$, $\ensuremath{\mu}∕{\ensuremath{\epsilon}}_{F}=1+0.707∕\ensuremath{\eta}$. Overall good agreement with quantum Monte Carlo results is found.The $ϵ$ expansion (expansion around four spatial dimensions) developed by Nishida and Son for a cold Fermi gas with infinite scattering length is extended to finite scattering length to study the Bose-Einstein condensate (BEC) to BCS crossover. A resummation of higher-order logarithms and a suitable extension of fermion coupling in $d$ dimensions are developed in order to apply the theory in the BCS regime. The ratio between the chemical potential and the Fermi energy, $\ensuremath{\mu}∕{\ensuremath{\epsilon}}_{F}$, is computed to next-to-leading order in the $ϵ$ expansion as a function of $\ensuremath{\eta}=1∕(a{k}_{F})$, where $a$ is the scattering length and ${k}_{F}$ is the Fermi momentum in a noninteracting system. Near the unitarity limit $\ensuremath{\mid}\ensuremath{\eta}\ensuremath{\mid}\ensuremath{\rightarrow}0$, we found $\ensuremath{\mu}∕{\ensuremath{\epsilon}}_{F}=0.475\ensuremath{-}0.707\ensuremath{\eta}\ensuremath{-}0.5{\ensuremath{\eta}}^{2}$. Near the BEC limit $\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{\infty}$, $\ensuremath{\mu}∕{\ensuremath{\epsilon}}_{F}=0.062∕\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{2}$, while near the BCS limit $\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$, $\ensuremath{\mu}∕{\ensuremath{\epsilon}}_{F}=1+0.707∕\ensuremath{\eta}$. Overall good agreement with quantum Monte Carlo results is found.

arXiv:cond-mat/0610011Physical Review AApr 23, 200728 citations

BCS–BEC crossover in cold atomic and in nuclear systems

Yoji Ohashi, Hiroyuki Tajima, Pieter van Wyk

Progress in Particle and Nuclear PhysicsNov 14, 201983 citations

The

ϵ

expansion (expansion around four spatial dimensions) developed by Nishida and Son for a cold Fermi gas with infinite scattering length is extended to finite scattering length to study the Bose-Einstein condensate (BEC) to BCS crossover. A resummation of higher-order logarithms and a suitable extension of fermion coupling in

d

dimensions are developed in order to apply the theory in the BCS regime. The ratio between the chemical potential and the Fermi energy, $\ensuremath{\mu}∕{\ensuremath{\epsilon}}_{F}$, is computed to next-to-leading order in the

ϵ

expansion as a function of $\ensuremath{\eta}=1∕(a{k}_{F})$, where

a

is the scattering length and

{k}_{F}

is the Fermi momentum in a noninteracting system. Near the unitarity limit $\ensuremath{\mid}\ensuremath{\eta}\ensuremath{\mid}\ensuremath{\rightarrow}0$, we found $\ensuremath{\mu}∕{\ensuremath{\epsilon}}_{F}=0.475\ensuremath{-}0.707\ensuremath{\eta}\ensuremath{-}0.5{\ensuremath{\eta}}^{2}$. Near the BEC limit $\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{\infty}$, $\ensuremath{\mu}∕{\ensuremath{\epsilon}}_{F}=0.062∕\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{2}$, while near the BCS limit $\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$, $\ensuremath{\mu}∕{\ensuremath{\epsilon}}_{F}=1+0.707∕\ensuremath{\eta}$. Overall good agreement with quantum Monte Carlo results is found.