Abstract A Fermi gas described within the Bardeen–Cooper–Schrieffer (BCS) theory can be converted into a Bose–Einstein condensate (BEC) of composite molecules (dimers) by adiabatically tuning the interaction. The sequence of states that emerge in the process of such a conversion is referred to as the BCS–BEC crossover. We here review the theoretical and experimental results obtained for the BCS–BEC crossover in three- and quasi-two-dimensional quantum gases in the limiting geometry of traps and on optical lattices. We discuss nontrivial phenomena in the hydrodynamics of superfluid quantum gases and fluids, including the collective excitation spectrum in the BCS–BEC crossover, the hydrodynamics of rotating Bose condensates containing a large number of quantized vortices, and the intriguing problem of the chiral anomaly in the hydrodynamics of superfluid Fermi systems with an anisotropic p-wave pairing. We also analyze spin-imbalanced quantum gases and the potential to realize the triplet p-wave pairing via the Kohn–Luttinger mechanism in those gases. Recent results on two-dimensional Fermi-gas preparation and the observation of fluctuation phenomena related to the Berezinskii–Kosterlitz–Thouless transition in those gases are also reviewed. We briefly discuss the recent experimental discovery of the BCS–BEC crossover and anomalous superconductivity in bilayer graphene and the role of graphene, other Dirac semimetals (for example, bismuth), and 2D optical lattices as potential reference systems that exhibit all of the effects reviewed here.Abstract A Fermi gas described within the Bardeen–Cooper–Schrieffer (BCS) theory can be converted into a Bose–Einstein condensate (BEC) of composite molecules (dimers) by adiabatically tuning the interaction. The sequence of states that emerge in the process of such a conversion is referred to as the BCS–BEC crossover. We here review the theoretical and experimental results obtained for the BCS–BEC crossover in three- and quasi-two-dimensional quantum gases in the limiting geometry of traps and on optical lattices. We discuss nontrivial phenomena in the hydrodynamics of superfluid quantum gases and fluids, including the collective excitation spectrum in the BCS–BEC crossover, the hydrodynamics of rotating Bose condensates containing a large number of quantized vortices, and the intriguing problem of the chiral anomaly in the hydrodynamics of superfluid Fermi systems with an anisotropic p-wave pairing. We also analyze spin-imbalanced quantum gases and the potential to realize the triplet p-wave pairing via the Kohn–Luttinger mechanism in those gases. Recent results on two-dimensional Fermi-gas preparation and the observation of fluctuation phenomena related to the Berezinskii–Kosterlitz–Thouless transition in those gases are also reviewed. We briefly discuss the recent experimental discovery of the BCS–BEC crossover and anomalous superconductivity in bilayer graphene and the role of graphene, other Dirac semimetals (for example, bismuth), and 2D optical lattices as potential reference systems that exhibit all of the effects reviewed here.

Physics-UspekhiNov 4, 201837 citations

Quantum Phase Transition in the BCS-to-BEC Evolution of p-wave Fermi Gases

S. S. Botelho, C. A. R. Sá de Melo

arXiv:cond-mat/0504263Journal of Low Temperature PhysicsSep 1, 200586 citations

Kosterlitz-Thouless transition and vortex-antivortex lattice melting in two-dimensional Fermi gases with p - or d -wave pairing

Gaoqing Cao, Lianyi He, Xu-Guang Huang

We present a theoretical study of the finite-temperature Kosterlitz-Thouless (KT) and vortex-antivortex lattice (VAL) melting transitions in two-dimensional Fermi gases with $p$ - or $d$ -wave pairing. For both pairings, when the interaction is tuned from weak to strong attractions, we observe a quantum phase transition from the Bardeen-Cooper-Schrieffer (BCS) superfluidity to the Bose-Einstein condensation (BEC) of difermions. The KT and VAL transition temperatures increase during this BCS-BEC transition and approach constant values in the deep BEC region. The BCS-BEC transition is characterized by the nonanalyticities of the chemical potential, the superfluid order parameter, and the sound velocities as functions of the interaction strength at both zero and finite temperatures; however, the temperature effect tends to weaken the nonanalyticities compared to the zero-temperature case. The effect of mismatched Fermi surfaces on the $d$ -wave pairing is also studied.We present a theoretical study of the finite-temperature Kosterlitz-Thouless (KT) and vortex-antivortex lattice (VAL) melting transitions in two-dimensional Fermi gases with $p$- or $d$-wave pairing. For both pairings, when the interaction is tuned from weak to strong attractions, we observe a quantum phase transition from the Bardeen-Cooper-Schrieffer (BCS) superfluidity to the Bose-Einstein condensation (BEC) of difermions. The KT and VAL transition temperatures increase during this BCS-BEC transition and approach constant values in the deep BEC region. The BCS-BEC transition is characterized by the nonanalyticities of the chemical potential, the superfluid order parameter, and the sound velocities as functions of the interaction strength at both zero and finite temperatures; however, the temperature effect tends to weaken the nonanalyticities compared to the zero-temperature case. The effect of mismatched Fermi surfaces on the $d$-wave pairing is also studied.

arXiv:1708.00124Physical Review ADec 22, 20175 citations

The BEC — BCS Crossover in Ultracold Fermi Gases

R. Combescot

WORLD SCIENTIFIC eBooksMar 1, 20130 citations

BCS-BEC crossover in strongly interacting Fermi gases

Giancarlo Calvanese Strinati

Bulletin of the American Physical SocietyMar 22, 20050 citations

Quantum Monte Carlo studies of superfluid Fermi gases

Siyuan Chang, Vijay R. Pandharipande, Joseph Carlson +1 more

We report results of quantum Monte Carlo calculations of the ground state of dilute Fermi gases with attractive short-range two-body interactions. The strength of the interaction is varied to study different pairing regimes which are characterized by the product of the $s$ -wave scattering length and the Fermi wave vector, $a{k}_{F}$ . We report results for the ground-state energy, the pairing gap $\ensuremath{\Delta}$, and the quasiparticle spectrum. In the weak-coupling regime, $1∕a{k}_{F}<\ensuremath{-}1$, we obtain Bardeen-Cooper-Schrieffer (BCS) superfluid and the energy gap $\ensuremath{\Delta}$ is much smaller than the Fermi gas energy ${E}_{\mathrm{FG}}$ . When $a>0$ , the interaction is strong enough to form bound molecules with energy ${E}_{\mathrm{mol}}$ . For $1∕a{k}_{F}\ensuremath{\gtrsim}0.5$, we find that weakly interacting composite bosons are formed in the superfluid gas with $\ensuremath{\Delta}$ and gas energy per particle approaching $\ensuremath{\mid}{E}_{\mathrm{mol}}\ensuremath{\mid}∕2$. In this region, we seem to have Bose-Einstein condensation (BEC) of molecules. The behavior of the energy and the gap in the BCS-to-BEC transition region, $\ensuremath{-}0.5<1∕a{k}_{F}<0.5$, is discussed.We report results of quantum Monte Carlo calculations of the ground state of dilute Fermi gases with attractive short-range two-body interactions. The strength of the interaction is varied to study different pairing regimes which are characterized by the product of the $s$-wave scattering length and the Fermi wave vector, $a{k}_{F}$. We report results for the ground-state energy, the pairing gap $\ensuremath{\Delta}$, and the quasiparticle spectrum. In the weak-coupling regime, $1∕a{k}_{F}<\ensuremath{-}1$, we obtain Bardeen-Cooper-Schrieffer (BCS) superfluid and the energy gap $\ensuremath{\Delta}$ is much smaller than the Fermi gas energy ${E}_{\mathrm{FG}}$. When $a>0$, the interaction is strong enough to form bound molecules with energy ${E}_{\mathrm{mol}}$. For $1∕a{k}_{F}\ensuremath{\gtrsim}0.5$, we find that weakly interacting composite bosons are formed in the superfluid gas with $\ensuremath{\Delta}$ and gas energy per particle approaching $\ensuremath{\mid}{E}_{\mathrm{mol}}\ensuremath{\mid}∕2$. In this region, we seem to have Bose-Einstein condensation (BEC) of molecules. The behavior of the energy and the gap in the BCS-to-BEC transition region, $\ensuremath{-}0.5<1∕a{k}_{F}<0.5$, is discussed.

arXiv:physics/0404115Physical Review AOct 5, 2004221 citations

We present a theoretical study of the finite-temperature Kosterlitz-Thouless (KT) and vortex-antivortex lattice (VAL) melting transitions in two-dimensional Fermi gases with

p

- or

d

-wave pairing. For both pairings, when the interaction is tuned from weak to strong attractions, we observe a quantum phase transition from the Bardeen-Cooper-Schrieffer (BCS) superfluidity to the Bose-Einstein condensation (BEC) of difermions. The KT and VAL transition temperatures increase during this BCS-BEC transition and approach constant values in the deep BEC region. The BCS-BEC transition is characterized by the nonanalyticities of the chemical potential, the superfluid order parameter, and the sound velocities as functions of the interaction strength at both zero and finite temperatures; however, the temperature effect tends to weaken the nonanalyticities compared to the zero-temperature case. The effect of mismatched Fermi surfaces on the

d

-wave pairing is also studied.

s

-wave scattering length and the Fermi wave vector,

a{k}_{F}

. We report results for the ground-state energy, the pairing gap $\ensuremath{\Delta}$, and the quasiparticle spectrum. In the weak-coupling regime, $1∕a{k}_{F}<\ensuremath{-}1$, we obtain Bardeen-Cooper-Schrieffer (BCS) superfluid and the energy gap $\ensuremath{\Delta}$ is much smaller than the Fermi gas energy

{E}_{\mathrm{FG}}

. When

a>0

, the interaction is strong enough to form bound molecules with energy

{E}_{\mathrm{mol}}

. For $1∕a{k}_{F}\ensuremath{\gtrsim}0.5$, we find that weakly interacting composite bosons are formed in the superfluid gas with $\ensuremath{\Delta}$ and gas energy per particle approaching $\ensuremath{\mid}{E}_{\mathrm{mol}}\ensuremath{\mid}∕2$. In this region, we seem to have Bose-Einstein condensation (BEC) of molecules. The behavior of the energy and the gap in the BCS-to-BEC transition region, $\ensuremath{-}0.5<1∕a{k}_{F}<0.5$, is discussed.