skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Derivation of Hydrodynamics for the Gapless Mode in the BEC-BCS Crossover from the Exact One-Loop Effective Action

Abstract

We derive generalized two-superfluid continuity equations for the BEC-BCS crossover in the presence of a Feshbach resonance at T=0. In addition, we calculate the velocity of sound throughout both BCS and Bose-Einstein condensation (BEC) regimes.

Authors:
; ;  [1];  [2]
  1. Department of Physics, National Dong Hwa University, Hua-Lien, Taiwan 974 (China)
  2. (United Kingdom)
Publication Date:
OSTI Identifier:
20861590
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevLett.98.020603; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACTION INTEGRAL; BOSE-EINSTEIN CONDENSATION; CONTINUITY EQUATIONS; HYDRODYNAMICS; RESONANCE; SOUND WAVES; SUPERFLUIDITY; VELOCITY

Citation Formats

Lee, D.-S., Lin, C.-Y., Rivers, Ray J., and Blackett Laboratory, Imperial College, London SW7 2BZ. Derivation of Hydrodynamics for the Gapless Mode in the BEC-BCS Crossover from the Exact One-Loop Effective Action. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.020603.
Lee, D.-S., Lin, C.-Y., Rivers, Ray J., & Blackett Laboratory, Imperial College, London SW7 2BZ. Derivation of Hydrodynamics for the Gapless Mode in the BEC-BCS Crossover from the Exact One-Loop Effective Action. United States. doi:10.1103/PHYSREVLETT.98.020603.
Lee, D.-S., Lin, C.-Y., Rivers, Ray J., and Blackett Laboratory, Imperial College, London SW7 2BZ. Fri . "Derivation of Hydrodynamics for the Gapless Mode in the BEC-BCS Crossover from the Exact One-Loop Effective Action". United States. doi:10.1103/PHYSREVLETT.98.020603.
@article{osti_20861590,
title = {Derivation of Hydrodynamics for the Gapless Mode in the BEC-BCS Crossover from the Exact One-Loop Effective Action},
author = {Lee, D.-S. and Lin, C.-Y. and Rivers, Ray J. and Blackett Laboratory, Imperial College, London SW7 2BZ},
abstractNote = {We derive generalized two-superfluid continuity equations for the BEC-BCS crossover in the presence of a Feshbach resonance at T=0. In addition, we calculate the velocity of sound throughout both BCS and Bose-Einstein condensation (BEC) regimes.},
doi = {10.1103/PHYSREVLETT.98.020603},
journal = {Physical Review Letters},
number = 2,
volume = 98,
place = {United States},
year = {Fri Jan 12 00:00:00 EST 2007},
month = {Fri Jan 12 00:00:00 EST 2007}
}
  • The effective action describing the gapless Nambu-Goldstone, or Anderson-Bogoliubov, mode of a zero-temperature dilute Fermi gas at unitarity is derived up to next-to-leading order in derivatives from the microscopic theory. Apart from a next-to-leading order term that is suppressed in the BCS limit, the effective action obtained in the strong-coupling unitary limit is proportional to that obtained in the weak-coupling BCS limit.
  • The BCS-to-BEC crossover, as well as the nature of Cooper pairs, in superconducting and Fermi superfluid media is studied from the exact ground state wave function of the reduced BCS Hamiltonian. As the strength of the interaction increases, the ground state continuously evolves from a mixed system of quasifree fermions and pair resonances (BCS), to pair resonances and quasibound molecules (pseudogap), and finally to a system of quasibound molecules (BEC). A single unified scenario arises where the Cooper-pair wave function has a unique functional form. Several exact analytic expressions such as the binding energy and condensate fraction are derived. Wemore » compare our results with recent experiments in ultracold atomic Fermi gases.« less
  • We solve the Leggett equations for the BCS-BEC crossover in a three dimensional resonance p-wave superfluid with the symmetry of the A1 phase. We calculate the sound velocity, the normal density, and the specific heat for the BCS domain ({mu} > 0), for the BEC domain ({mu} < 0), and close to the important point {mu} = 0 in the 100% polarized case. We find the indications of a quantum phase transition close to the point {mu}(T = 0) = 0. Deep in the BCS and BEC domains, the crossover ideas of Leggett, Nozieres, and Schmitt-Rink work quite well. Wemore » discuss the spectrum of orbital waves, the paradox of intrinsic angular momentum and the complicated problem of chiral anomaly in the BCS A1 phase at T = 0. We present two different approaches to the chiral anomaly, based on supersymmetric hydrodynamics and on the formal analogy with the Dirac equation in quantum electrodynamics. We evaluate the damping of nodal fermions due to different decay processes in the superclean case at T = 0 and find that a ballistic regime {omega}{tau} >> 1 occurs. We propose to use aerogel or nonmagnetic impurities to reach the hydrodynamic regime {omega}{tau} << 1 at T = 0. We discuss the concept of the spectral flow and exact cancelations between time derivatives of anomalous and quasiparticle currents in the equation for the total linear momentum conservation. We propose to derive and solve the kinetic equation for the nodal quasiparticles in both the hydrodynamic and ballistic regimes to demonstrate this cancelation explicitly. We briefly discuss the role of the other residual interactions different from damping and invite experimentalists to measure the spectrum and damping of orbital waves in the A phase of {sup 3}He at low temperatures.« less
  • We perform a detailed study of the effective Lagrangian for the Goldstone mode of a superfluid Fermi gas at zero temperature in the whole BCS-BEC crossover. By using a derivative expansion of the response functions, we derive the most general form of this Lagrangian at the next to leading order in the momentum expansion in terms of four coefficient functions. This involves the elimination of all the higher order time derivatives by careful use of the leading order field equations. In the infinite scattering length limit where conformal invariance is realized, we show that the effective Lagrangian must contain anmore » unnoticed invariant combination of higher spatial gradients of the Goldstone mode, while explicit couplings to spatial gradients of the trapping potential are absent. Across the whole crossover, we determine all the coefficient functions at the one-loop level, taking into account the dependence of the gap parameter on the chemical potential in the mean-field approximation. These results are analytically expressed in terms of elliptic integrals of the first and second kind. We discuss the form of these coefficients in the extreme BCS and BEC regimes and around the unitary limit, and compare with recent work by other authors.« less
  • Cited by 4