Signature of the Fulde-Ferrell-Larkin-Ovchinnikov Phase in the Collective Modes of a Trapped Ultracold Fermi Gas

We study theoretically the collective modes of a two-component Fermi gas with attractive interactions in a quasi-one-dimensional harmonic trap. We focus on an imbalanced gas in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Using a mean-field theory, we study the response of the ground state to time-dependent potentials. For potentials with short wavelengths, we find dramatic signatures in the large-scale response of the gas which are characteristic of the FFLO phase. This response provides an effective way to detect the FFLO state in experiments.

Figure 1

Response 28 of a homogeneous system in the FFLO phase to a spin-asymmetric periodic potential (1). The area of the circle is proportional to the amplitude of the response. The polarization $p\equiv \frac{k_{F\uparrow }-k_{F\downarrow }}{k_{F\uparrow }+k_{F\downarrow }}=0.15$, and the interactions strength is $\gamma =1.5$. Two gapless sound modes are seen to emerge around $k\simeq 0$ and $k\simeq k^{*}\equiv 2(k_{F_{\uparrow }}-k_{F\downarrow })$. The simulation was done on 270 lattice sites.

Figure 2

Configuration with fully paired phase towards the edge of the trap. (a) densities and the value of the superfluid gap $\Delta$. (b) response of the spin-dipole mode to excitations of different wavelengths (arbitrary units). Here $p=0.048$, $\gamma =0.93$ (measured in center), number of particles $N=290$, lattice spacing $a=3.3\times {10}^{-3}{N}^{1/2}{a}_{ho}$. The perturbing potential has a fixed amplitude, while the wavelength is varied.

Figure 3

Configuration with fully polarized phase towards the edge. Here $p=0.25$, $\gamma =1.5$, $a/(N^{1/2}{a}_{ho})=4.7\times {10}^{-3}$, $N=143$. Otherwise the same as Fig. 2.