Landau damping in a mixture of Bose and Fermi superfluids

We study Landau damping in a Bose-Fermi superfluid mixture at finite temperatures. We find that at low temperatures, the Landau damping rate will be exponentially suppressed on both the BCS side and the BEC side of the Fermi superfluid. The momentum dependence of the damping rate is obtained, and it is quite different from the BCS side to the BEC side since the dominated low-energy excitations are different on the two sides. The relation between our result and the collective mode experiment in the recently realized Bose-Fermi superfluid mixture is also discussed.

Figure 1

Schematic of dispersions of the bosonic Goldstone mode in Bose superfluid $\left(E_{\mathbf{k}}^b\right)$, the fermionic pair-breaking mode in Fermi superfluid $\left(E_{\mathbf{k}}^f\right)$, and the bosonic Goldstone mode in Fermi superfluid $\left(E_{\mathbf{k}}^m\right)$. (a) is on the BCS side and (b) is on the BEC side.

Figure 2

Damping rates $\gamma$ in units of ${\gamma }_0({\gamma }_0\equiv E_F/\hslash )$ with $1/\left(k_F{a}_f\right)=-0.5$ on the BCS side. (a) Damping rates as a function of momentum; (b) damping rates as a function of temperature.

Figure 3

Damping rates $\gamma$ in units of ${\gamma }_0({\gamma }_0\equiv E_F/\hslash )$ with $1/\left(k_F{a}_f\right)=0.5$ on the BEC side. (a) Damping rates as a function of momentum; (b) damping rates as a function of temperature.