BCS-Bose-Einstein condensation (BEC) crossover is effected by increasing pairing strength between fermions from weak to strong in the particle-particle channel, and has attracted a lot of attention since the experimental realization of quantum degenerate atomic Fermi gases. Here we study the effect of the (often dropped) particle-hole channel on the zero T gap Δ(0), superfluid transition temperature Tc, the pseudogap at Tc, and the mean-field ratio 2Δ(0)/, from BCS through BEC regimes, using a pairing fluctuation theory which includes self-consistently the contributions of finite-momentum pairs and features a pseudogap in single particle excitation spectrum. Summing over the infinite particle-hole ladder diagrams, we find a complex dynamical structure for the particle-hole susceptibility χph, and conclude that neglecting the self-energy feedback causes a serious over-estimate of χph. While our result in the BCS limit agrees with Gor'kov et al., the particle-hole channel effect becomes more complex and pronounced in the crossover regime, where χph is reduced by both a smaller Fermi surface and a big (pseudo)gap. Deep in the BEC regime, the particle-hole channel contributions drop to zero. We predict a density dependence of the magnetic field at the Feshbach resonance, which can be used to quantify χph and test different theories.BCS-Bose-Einstein condensation (BEC) crossover is effected by increasing pairing strength between fermions from weak to strong in the particle-particle channel, and has attracted a lot of attention since the experimental realization of quantum degenerate atomic Fermi gases. Here we study the effect of the (often dropped) particle-hole channel on the zero T gap Δ(0), superfluid transition temperature Tc, the pseudogap at Tc, and the mean-field ratio 2Δ(0)/, from BCS through BEC regimes, using a pairing fluctuation theory which includes self-consistently the contributions of finite-momentum pairs and features a pseudogap in single particle excitation spectrum. Summing over the infinite particle-hole ladder diagrams, we find a complex dynamical structure for the particle-hole susceptibility χph, and conclude that neglecting the self-energy feedback causes a serious over-estimate of χph. While our result in the BCS limit agrees with Gor'kov et al., the particle-hole channel effect becomes more complex and pronounced in the crossover regime, where χph is reduced by both a smaller Fermi surface and a big (pseudo)gap. Deep in the BEC regime, the particle-hole channel contributions drop to zero. We predict a density dependence of the magnetic field at the Feshbach resonance, which can be used to quantify χph and test different theories.

arXiv:1109.2307Scientific ReportsMay 17, 201610 citations

Single particle excitations in the BCS-BEC crossover region

Yoji Ohashi

Bulletin of the American Physical SocietyMar 23, 20050 citations

BCS-BEC crossover in nuclear matter with the relativistic Hartree-Bogoliubov theory

T. Sun, Bao Yuan Sun, Jie Meng

Based on the relativistic Hartree-Bogoliubov theory, the influence of the pairing interaction strength on the dineutron correlations and the crossover from superfluidity of neutron Cooper pairs in the ${}^{1\phantom{\rule{-0.16em}{0ex}}}{S}_{0}$ channel to Bose-Einstein condensation of dineutron pairs is systematically investigated in the nuclear matter. The bare nucleon-nucleon interaction Bonn-B is taken in the particle-particle channel with an effective factor to simulate the medium effects and take into account the possible ambiguity of pairing force, and the effective interaction PK1 is used in the particle-hole channel. If the effective factor is larger than $1.10$ , a dineutron Bose-Einstein condensation (BEC) state appears in the low-density limit, and if it is smaller than $0.85$ , the neutron Cooper pairs are found totally in the weak coupling Bardeen-Cooper-Schrieffer (BCS) region. The reference values of several characteristic quantities which characterize the BCS-BEC crossover are obtained, respectively, from the dimensionless parameter $1/({k}_{\mathrm{Fn}}a)$ with $a$ the scattering length and ${k}_{\mathrm{Fn}}$ the neutron Fermi momentum, the zero-momentum transfer density correlation function $D(0)$ , and the effective chemical potential ${\ensuremath{\nu}}_{\mathrm{n}}$.Based on the relativistic Hartree-Bogoliubov theory, the influence of the pairing interaction strength on the dineutron correlations and the crossover from superfluidity of neutron Cooper pairs in the ${}^{1\phantom{\rule{-0.16em}{0ex}}}{S}_{0}$ channel to Bose-Einstein condensation of dineutron pairs is systematically investigated in the nuclear matter. The bare nucleon-nucleon interaction Bonn-B is taken in the particle-particle channel with an effective factor to simulate the medium effects and take into account the possible ambiguity of pairing force, and the effective interaction PK1 is used in the particle-hole channel. If the effective factor is larger than $1.10$, a dineutron Bose-Einstein condensation (BEC) state appears in the low-density limit, and if it is smaller than $0.85$, the neutron Cooper pairs are found totally in the weak coupling Bardeen-Cooper-Schrieffer (BCS) region. The reference values of several characteristic quantities which characterize the BCS-BEC crossover are obtained, respectively, from the dimensionless parameter $1/({k}_{\mathrm{Fn}}a)$ with $a$ the scattering length and ${k}_{\mathrm{Fn}}$ the neutron Fermi momentum, the zero-momentum transfer density correlation function $D(0)$, and the effective chemical potential ${\ensuremath{\nu}}_{\mathrm{n}}$.

arXiv:1206.3407Physical Review CJul 3, 201223 citations

Particle-hole fluctuations in BCS-BEC crossover

Stefan Floerchinger, Michael M. Scherer, Sebastian Diehl +1 more

The effect of particle-hole fluctuations for the BCS-BEC crossover is investigated by use of functional renormalization. We compute the Gorkov effect and the critical temperature for the whole range in the scattering length $a$ . On the BCS side for small negative $a$ we recover the Gorkov approximation, while on the BEC side of small positive $a$ the particle-hole fluctuations play no important role, and we find a system of interacting bosons. In the unitarity limit of infinite scattering length our quantitative estimate yields ${T}_{c}/{T}_{F}=0.264$ . We also investigate the crossover from broad to narrow Feshbach resonances---for the latter we obtain ${T}_{c}/{T}_{F}=0.204$ for ${a}^{\ensuremath{-}1}=0$. A key ingredient for our treatment is the computation of the momentum dependent four-fermion vertex and its bosonization in terms of an effective bound-state exchange.The effect of particle-hole fluctuations for the BCS-BEC crossover is investigated by use of functional renormalization. We compute the Gorkov effect and the critical temperature for the whole range in the scattering length $a$. On the BCS side for small negative $a$ we recover the Gorkov approximation, while on the BEC side of small positive $a$ the particle-hole fluctuations play no important role, and we find a system of interacting bosons. In the unitarity limit of infinite scattering length our quantitative estimate yields ${T}_{c}/{T}_{F}=0.264$. We also investigate the crossover from broad to narrow Feshbach resonances---for the latter we obtain ${T}_{c}/{T}_{F}=0.204$ for ${a}^{\ensuremath{-}1}=0$. A key ingredient for our treatment is the computation of the momentum dependent four-fermion vertex and its bosonization in terms of an effective bound-state exchange.

arXiv:0808.0150Physical Review BNov 26, 200869 citations

Universality and novel phases in the BCS-BEC crossover

W. Zwerger

Bulletin of the American Physical SocietyJun 8, 20070 citations

{}^{1\phantom{\rule{-0.16em}{0ex}}}{S}_{0}

channel to Bose-Einstein condensation of dineutron pairs is systematically investigated in the nuclear matter. The bare nucleon-nucleon interaction Bonn-B is taken in the particle-particle channel with an effective factor to simulate the medium effects and take into account the possible ambiguity of pairing force, and the effective interaction PK1 is used in the particle-hole channel. If the effective factor is larger than

1.10

, a dineutron Bose-Einstein condensation (BEC) state appears in the low-density limit, and if it is smaller than

0.85

, the neutron Cooper pairs are found totally in the weak coupling Bardeen-Cooper-Schrieffer (BCS) region. The reference values of several characteristic quantities which characterize the BCS-BEC crossover are obtained, respectively, from the dimensionless parameter

1/({k}_{\mathrm{Fn}}a)

with

a

the scattering length and

{k}_{\mathrm{Fn}}

the neutron Fermi momentum, the zero-momentum transfer density correlation function

D(0)

, and the effective chemical potential ${\ensuremath{\nu}}_{\mathrm{n}}$.

a

. On the BCS side for small negative

a

we recover the Gorkov approximation, while on the BEC side of small positive

a

the particle-hole fluctuations play no important role, and we find a system of interacting bosons. In the unitarity limit of infinite scattering length our quantitative estimate yields

{T}_{c}/{T}_{F}=0.264

. We also investigate the crossover from broad to narrow Feshbach resonances---for the latter we obtain

{T}_{c}/{T}_{F}=0.204

for ${a}^{\ensuremath{-}1}=0$. A key ingredient for our treatment is the computation of the momentum dependent four-fermion vertex and its bosonization in terms of an effective bound-state exchange.