Shina Tan

BCS–BEC crossover: From high temperature superconductors to ultracold superfluids

Abstract We review the BCS to Bose–Einstein condensation (BEC) crossover scenario which is based on the well known crossover generalization of the BCS ground state wavefunction Ψ 0 . While this ground state has been summarized extensively in the literature, this Review is devoted to less widely discussed issues: understanding the effects of finite temperature, primarily below T c , in a manner consistent with Ψ 0 . Our emphasis is on the intersection of two important problems: high T c superconductivity and superfluidity in ultracold fermionic atomic gases. We address the “pseudogap state” in the copper oxide superconductors from the vantage point of a BCS–BEC crossover scenario, although there is no consensus on the applicability of this scheme to high T c . We argue that it also provides a useful basis for studying atomic gases near the unitary scattering regime; they are most likely in the counterpart pseudogap phase. That is, superconductivity takes place out of a non-Fermi liquid state where preformed, metastable fermion pairs are present at the onset of their Bose condensation. As a microscopic basis for this work, we summarize a variety of T-matrix approaches, and assess their theoretical consistency. A close connection with conventional superconducting fluctuation theories is emphasized and exploited.

Energetics of a strongly correlated Fermi gas

Abstract The energy of the two-component Fermi gas with the s-wave contact interaction is a simple linear functional of its momentum distribution: E internal = ℏ 2 Ω C / 4 π am + ∑ k σ ( ℏ 2 k 2 / 2 m ) ( n k σ - C / k 4 ) where the external potential energy is not included, a is the scattering length, Ω is the volume, n k σ is the average number of fermions with wave vector k and spin σ , and C ≡ lim k → ∞ k 4 n k ↑ = lim k → ∞ k 4 n k ↓ . This result is a universal identity . Its proof is facilitated by a novel mathematical idea, which might be of utility in dealing with ultraviolet divergences in quantum field theories. Other properties of this Fermi system, including pair correlations and the dimer–fermion scattering length, are also studied.

Large momentum part of a strongly correlated Fermi gas

It is well known that the momentum distribution of the two-component Fermi gas with large scattering length has a tail proportional to

Generalized virial theorem and pressure relation for a strongly correlated Fermi gas

1/k^4

Universal Fermi Gases in Mixed Dimensions

at large

Universal Fermi Gas with Two-and Three-Body Resonances

k

Relaxation of a High-Energy Quasiparticle in a One-Dimensional Bose Gas

. We show that the magnitude of this tail is equal to the adiabatic derivative of the energy with respect to the reciprocal of the scattering length, multiplied by a simple constant. This result holds at any temperature (as long as the effective interaction radius is negligible) and any large scattering length; it also applies to few-body cases. We then show some more connections between the

Confinement-induced Efimov resonances in Fermi-Fermi mixtures

1/k^4

Higher-order local and non-local correlations for 1D strongly interacting Bose gas

tail and various physical quantities, in particular the rate of change of energy in a DYNAMIC sweep of the inverse scattering length.

Manipulation of p-Wave Scattering of Cold Atoms in Low Dimensions Using the Magnetic Field Vector

Abstract For a two-component Fermi gas in the unitarity limit (i.e., with infinite scattering length), there is a well-known virial theorem, first shown by J.E. Thomas et al. A few people rederived this result, and extended it to few-body systems, but their results are all restricted to the unitarity limit. Here I show that there is a generalized virial theorem for FINITE scattering lengths. I also generalize an exact result concerning the pressure to the case of imbalanced populations.