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Laser Physics

Specific features of the BCS-BEC crossover and thermodynamics in the 2D resonant Fermi gas with p-wave pairing

M. Yu. Kagan, S. L. Ogarkov

Published Apr 1, 2008• 7 citations
Publisher

Abstract

The 2D resonant Fermi gas with p -wave pairing is considered n the BCS-BEC regime. For the 2D analog of the superfluid A1 phase, the Leggett equations [1] for superfluid gap Δ and chemical potential μ are analytically solved at T = 0 and the spectrum of the collective excitations (acoustic waves) is analyzed in the BCS regime (μ > 0), where the triplet Cooper pairs emerge; in the BEC regime (μ < 0), where the triplet local pairs (molecules) emerge; and in the transition region, where μ → 0. At low temperatures, the contribution of the superfluid Fermi quasiparticles of the resonant gas to heat capacity C v and the density of normal component ρ n is also calculated. At μ = 0, the fermionic contribution to ρ n and C v are represented as power functions of temperature (ρ n ∼ T 3 and C v ∼ T 2 ). However, similar power contributions to these quantities are related to phonons (bosonic acoustic oscillations). The possibility of the experimental observation of the nontrivial topological term with the charge Q = 1 in the BCS regime of the 2D A1 phase is briefly discussed.

DOI
10.1134/s1054660x08040282

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The 2D resonant Fermi gas with p -wave pairing is considered n the BCS-BEC regime. For the 2D analog of the superfluid A1 phase, the Leggett equations [1] for superfluid gap Δ and chemical potential μ are analytically solved at T = 0 and the spectrum of the collective excitations (acoustic waves) is analyzed in the BCS regime (μ > 0), where the triplet Cooper pairs emerge; in the BEC regime (μ < 0), where the triplet local pairs (molecules) emerge; and in the transition region, where μ → 0. At low temperatures, the contribution of the superfluid Fermi quasiparticles of the resonant gas to heat capacity C v and the density of normal component ρ n is also calculated. At μ = 0, the fermionic contribution to ρ n and C v are represented as power functions of temperature (ρ n ∼ T 3 and C v ∼ T 2 ). However, similar power contributions to these quantities are related to phonons (bosonic acoustic oscillations). The possibility of the experimental observation of the nontrivial topological term with the charge Q = 1 in the BCS regime of the 2D A1 phase is briefly discussed.
We consider 3D and 2D fully (100%) polarized resonance superfluid Fermi-gas with p-wave pairing in the regime of BCS-BEC crossover. For low temperatures T « T cp ( T cp is a p-wave critical temperature) we evaluate the contribution of the superfluid fermionic quasiparticles and bosonic collective waves (phonons) in the specific heat ( C v ) and the normal density (ρ n ) in the BCS-regime for the chemical potential μ > 0, in BEC-regime for μ < 0 and in the interesting intermediate regime for μ → 0. We discuss an experimental possibility to observe a chiral anomaly (which leads to mass-current non-conservation at T = 0) in 3D A1-phase in ballistic regime as well as a topological term with a charge Q = 1 in the 2D fully polarized axial phase in BCS-regime.
We solve the Leggett equations for BCS-BEC crossover of the resonance p-wave superfluid. We calculate sound velocity, specific heat and the normal density for the BCS domain (μ>0), the BEC domain (μ<0), and for the interesting interpolation point (μ=0) in the 100%-polarized A1 phase in 3D. We are especially interested in the quasiparticle contribution coming from the zeros of the superfluid gap in the A1 phase. We discuss the spectrum of orbital waves and the superfluid hydrodynamics at temperature T→0. In this context we elucidate the difficult problem of the chiral anomaly and mass-current nonconcervation appearing in the BCS domain. We present the different approaches taken to solve this problem. To clarify this problem experimentally we propose an experiment for measurement of the anomalous current in the superfluid A1 phase in the presence of aerogel for He3 and in the presence of Josephson tunneling structures for ultracold gases in magnetic traps.
This thesis presents theoretical work in s- and p-wave resonantly paired Fermi gases at zero temperature. In the BEC regime of the wide-resonance s-wave BCS-BEC crossover, the chemical potential, speed of sound, condensate depletion, and ground state energy are computed. The quantities are calculated in a low density approximation. The bosonic scattering length is computed diagrammatically to be approximately 0.60a with a the fermionic scattering length, confirming a well-known result. The perturbative approach breaks down in the intermediate BCS-BEC crossover regime which is not investigated. Quantum corrections are computed in the low density expansion, and the mass-imbalanced two-species Fermi gas is investigated. For identical fermions, it is discussed how p-wave Feshbach resonances naturally fall into two classes of "weak" and "strong", depending on the short-distance physics. It is shown how bound fermionic trimers appear in the strongly-resonant superfluid. The appearance of the trimer under the strengthening of the resonance is investigated, and the lifetime of p-wave diatomic molecules due to collisional relaxation into trimers is estimated.
We derive an expression for the superfluid density of a uniform two-component Fermi gas through the BCS-BEC crossover in terms of the thermodynamic potential in the presence of an imposed superfluid flow. Treating the pairing fluctuations in a Gaussian approximation following the approach of Nozi\`eres and Schmitt-Rink, we use this definition of ${\ensuremath{\rho}}_{s}$ to obtain an explicit result which is valid at finite temperatures and over the full BCS-BEC crossover. It is crucial that the BCS gap $\ensuremath{\Delta}$, the chemical potential $\ensuremath{\mu}$, and ${\ensuremath{\rho}}_{s}$ all include the effect of fluctuations at the same level in a self-consistent manner. We show that the normal fluid density ${\ensuremath{\rho}}_{n}\ensuremath{\equiv}n\ensuremath{-}{\ensuremath{\rho}}_{s}$ naturally separates into a sum of contributions from Fermi BCS quasiparticles $({\ensuremath{\rho}}_{n}^{F})$ and Bose collective modes $({\ensuremath{\rho}}_{n}^{B})$. The expression for ${\ensuremath{\rho}}_{n}^{F}$ is just Landau's formula for a BCS Fermi superfluid but now calculated over the BCS-BEC crossover. The expression for the Bose contribution ${\ensuremath{\rho}}_{n}^{B}$ is more complicated and only reduces to Landau's formula for a Bose superfluid in the extreme BEC limit, where all the fermions have formed stable Bose pairs and the Bogoliubov excitations of the associated molecular Bose condensate are undamped. In a companion paper, we present numerical calculations of ${\ensuremath{\rho}}_{s}$ using an expression equivalent to the one derived in this paper, over the BCS-BEC crossover, including unitarity, and at finite temperatures.
The low-energy modes of a superfluid atomic Fermi gas at zero temperature are investigated. The Bose-Einstein-condensate (BEC) side of the superfluid phase is studied in detail. The atoms are assumed to be in only one internal state, so that for a sufficiently diluted gas the pairing of fermions can be considered effective in the l=1 channel only. In agreement with previous works on p-wave superfluidity in Fermi systems, it is found that the px+ipyp_x+ip_ypx​+ipy​ phase represents the lowest energy state in both the Bardeen-Cooper-Schrieffer (BCS) and BEC sides. Our calculations show that at low energy three branches of collective modes can emerge, with different species of dispersion relations: a phonon-like mode, a single-particle-like mode and a gapped mode. A comparison with the Bogoliubov excitations of the corresponding spinor Bose condensate is made. They reproduce the dispersion relations of the excitation modes of the p-wave superfluid Fermi gas to a high accuracy.
We solve the Leggett equations for the BCS-BEC crossover in a three dimensional resonance p -wave superfluid with the symmetry of the A 1 phase. We calculate the sound velocity, the normal density, and the specific heat for the BCS domain (μ > 0), for the BEC domain (μ < 0), and close to the important point μ = 0 in the 100% polarized case. We find the indications of a quantum phase transition close to the point μ( T = 0) = 0. Deep in the BCS and BEC domains, the crossover ideas of Leggett, Nozieres, and Schmitt-Rink work quite well. We discuss the spectrum of orbital waves, the paradox of intrinsic angular momentum and the complicated problem of chiral anomaly in the BCS A 1 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 ωτ ≫ 1 occurs. We propose to use aerogel or nonmagnetic impurities to reach the hydrodynamic regime ωτ ≪ 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 3 He at low temperatures.