Collective modes in asymmetric ultracold Fermi systems

Abstract

We derive the low energy effective action for the collective modes in systems of fermions interacting via a short-range s-wave attraction, featuring unequal chemical potentials for the two fermionic species (asymmetric systems). As a consequence of the attractive interaction, fermions form a condensate that spontaneously breaks the U(1) symmetry associated with total number conservation. Therefore at sufficiently small temperatures and asymmetries, the system is a superfluid. We reproduce previous results for the stability conditions of the system as a function of the four-fermion coupling and asymmetry. We obtain these results analyzing the coefficients of the low energy effective Lagrangian of the modes describing fluctuations in the magnitude (Higgs mode) and in the phase (Goldstone mode) of the difermion condensate. We find that for certain values of parameters, the mass of the Higgs mode decreases with increasing mismatch between the chemical potentials of the two populations, if we keep the scattering length and the gap parameter constant. Furthermore, we find that the energy cost for creating a position dependent fluctuation of the condensate is constant in the gapped region and increases in the gapless region. These two features may lead to experimentally detectable effects. As an example, we argue that if the superfluid is put in rotation, the square of the radius of the outer core of a vortex should sharply increase on increasing the asymmetry, when we pass through the relevant region in the gapless superfluid phase. Finally, by gauging the global U(1) symmetry, we relate the coefficients of the effective Lagrangian of the Goldstone mode with the screening masses of the gauge field.Comment: 41 pages, 6 figures. Expanded introduction, improved figures, conclusions unchanged. Version to match the published versio

Crystalline color superconductors

“…Pinning down the correct ground state of neutral quark matter in β equilibrium is not simple because another difficulty emerges. This problem, already present in simple two-level systems, see for example Gubankova et al (2010), has a rather general character (Alford and Wang, 2005), and is due to an instability connected to the Meissner mass. For sufficiently large chemical potential differences, the system becomes magnetically unstable, meaning that the Meissner mass becomes imaginary.…”

“…Quite generally, the imaginary value of the Meissner mass can be understood as a tendency of the system toward an inhomogeneous phase (Gubankova et al, 2010;Hong, 2005;Iida and Fukushima, 2006). This can be easily seen in a toy model system for the case of a U (1) symmetry, in which one can show that the coefficient of the gradient term of the low-energy fluctuations around the ground state of the effective action is proportional to the Meissner mass squared (Gubankova et al, 2010).…”

“…Before discussing the case of two-flavor quark matter, we show how gapless superconductivity may arise considering the simpler case of a nonrelativistic twolevel fermionic gas, thus avoiding the formal complications due to flavor and color degrees of freedom. For definiteness, we review the system discussed by Gubankova et al (2010) consisting of two unbalanced populations of fermionic species ψ 1 and ψ 2 , with opposite spin, at vanishing temperature, having the hamiltonian density…”

“…Considering homogeneous phases, a metastable superconducting phase exists for δµ ≥ δµ 1 , but still the system cannot develop fermionic massless modes, because at δµ = ∆ 0 various instabilities appear (Gubankova et al, 2010(Gubankova et al, , 2006Mannarelli et al, 2006a;Pao et al, 2006;Sheehy and Radzihovsky, 2006;Wu and Yip, 2003). To explain what happens, let us consider the low-energy spectrum of the system, which can be described considering the fluctuations of ∆(x) around the mean field solution ∆ 0 .…”

Phonon contribution to the shear viscosity of a superfluid Fermi gas in the unitarity limit

“…Actually, in this perspective, the low energy spectrum contains also the degree of freedom associated to the oscillation of the absolute value of the difermion condensate, see e.g. [30][31][32]. But considering only gaussian fluctuation, the radial degree of freedom can be integrated out and only results in a modification of the phonon dispersion law.…”