Landau damping: Instability mechanism of superfluid Bose gases moving in optical lattices

We investigate Landau damping of Bogoliubov excitations in a dilute Bose gas moving in an optical lattice at finite temperatures. Using a one-dimensional tight-binding model, we explicitly obtain the Landau damping rate, the sign of which determines the stability of the condensate. We find that the sign changes at a certain condensate velocity, which is exactly the same as the critical velocity determined by the Landau criterion of superfluidity. This coincidence of the critical velocities reveals the microscopic mechanism of the Landau instability. This instability mechanism shows that a thermal cloud plays a crucial role in the breakdown of superfluids, since the thermal cloud is a vital source of Landau damping. We also examine the possibility of simultaneous disappearance of all damping processes.

Figure 1

Condensate fraction $n_0∕n$ in an optical lattice as a function of the condensate quasimomentum $k∕q_B$ at different temperatures $\eta =k_{B}T∕J$, where $q_B=\pi ∕d$ is the Bragg vector and $U∕J$ is fixed to 1.

Figure 2

Quasimomentum $\tilde{p}$ satisfying $E_p+E_{p+\tilde{p}}=E_{\tilde{p}}$ with $p⪡\tilde{p}$. Both $\tilde{p}$ and $k$ are normalized by the Bragg vector $q_B=\pi ∕d$, where $d$ is a lattice spacing. $\alpha =U{n}_0∕J$ is set to 1.

Figure 3

Damping possibility diagram. Damping processes are possible to exist only in the shaded area. Dashed line indicates the critical quasimomentum of the condensate given by Eq. (48).

Figure 4

Landau damping rate ${\gamma }_{k,-0.01q_B}$ in the 1D optical lattice with $U∕J=1$ as a function of a condensate quasimomentum $k<k_c$ at different temperatures $\eta =k_{B}T∕J$. $\gamma$ and $k$ are normalized to the hopping matrix element $J$ and the Bragg vector $q_B$, respectively.

Figure 5

Stability diagram of the BEC in the optical lattice with $\alpha =0.5$. The shaded area is where the excitation energy $E_{k,p}$ is negative, thus the system is energetically unstable. In this area, the Landau damping rate ${\gamma }_{k,p}$ is also negative [Eq. (47)] and the inverse process of the usual Landau damping is dominant. Both $k$ and $p$ are normalized by $q_B=\pi ∕d$, where $d$ is a lattice spacing.