Anomalous Phonon Dispersion of an Ultracold $$^6\mathrm{{Li}}$$ 6 Li – $$^{40}\mathrm{{K}}$$ 40 K Mixture in a Square Optical Lattice

Abstract

A necessary condition for the damping of the long-wavelength excitations of the superfluid phase (referred to as superfluid phonons) due to the three-particle process is to have an anomalous phonon dispersion. The existence of anomalous phonon dispersion has been confirmed in superfluid \(^4\mathrm {He}\). There are no experimental data suggesting that this phenomenon exists in superfluid Fermi gases. To the best of our knowledge, the existence of anomalous dispersion has been theoretically predicted only in atomic spin balanced Fermi gas close to the unitarity limit. The numerical results reported here suggest that the anomalous long-wavelength dispersion can be realized in mass and spin imbalanced atomic Fermi gases away from the unitary limit. In particular, the numerical solution of the Bethe–Salpeter equation in a weak-coupling regime shows that the long-wavelength part of the collective-mode dispersion of the superfluid Fulde–Ferrell phase of a mixture of population-imbalanced Lithium-6 and Potassium-40 atoms in a square lattice at some values of polarization, interacting strength and temperature initially bends upward before bending over.