Quantum Kelvin-Helmholtz instability in phase-separated two-component Bose-Einstein condensates

We theoretically study the Kelvin-Helmholtz instability in phase-separated two-component Bose-Einstein condensates using the Gross-Pitaevskii and Bogoliubov-de Gennes models. A flat interface between the two condensates is shown to deform into sawtooth or Stokes-type waves, leading to the formation of singly quantized vortices on the peaks and troughs of the waves. This scenario of interface instability in quantum fluids is quite different from that in classical fluids.

Figure 1

(Color online) Nonlinear dynamics of the dynamic KHI in phase-separated two-component BECs without dissipation for the relative velocity $V_{\text{r}}=V_1-V_2=0.98c>V_{\text{D}}$. (Upper panels) The height and color show the vorticity ${\omega }_{\text{eff}}$ and the density difference $n_1-n_2$ between the two condensates, respectively. (Lower panels) Two-dimensional plots of $n_1-n_2$. (Right panels) The phases ${\Theta }_j\left(j=1,2\right)$ of the condensates for (f). The circular arrows show the rotational direction of the superflow around each vortex.

Figure 2

(Color online) (a) Profiles of the wave functions of the two condensates $\left({\psi }_j\right)$ and the excitation $\left(\delta {\psi }_j\equiv u_j-v_j^{\ast }\right)$ in a shear-flow state. The real functions $\delta {\psi }_j$ for the lowest excitation with $k=0.29/\xi$ for $V_{\text{r}}=0.79c$ are localized around the interface layer. (b) Dispersion relation ${\omega }_0=\omega -V_{\text{eff}}k$ of the lowest modes. The broken and solid curves show $\text{Im}\left[{\omega }_0\left(k\right)\right]$ for $V_{\text{r}}/c=0.98$ and $\text{Re}\left[{\omega }_0\left(k\right)\right]$ for $V_{\text{r}}/c=0$, 0.59, 0.79, 0.84, and 0.98, respectively. (c) Phase diagram of the quantum KHI for $V_1=0$ and $V_2<0$. The curves are the boundaries of the DI and LI regions obtained by the BdG model (solid curves) and the hydrodynamic model (broken curves).

Figure 3

(Color online) Dynamics of the density difference $n_1-n_2$ in the quantum KHI with dissipation $\gamma =0.03$ for $V_{\text{L}}<V_{\text{r}}=0.79c<V_{\text{D}}$ (top) and $V_{\text{r}}=0.98c>V_{\text{D}}$ (bottom). The field of view is $32\xi \times 64\xi$.

Figure 4

(Color online) Dynamics of the density difference $n_1-n_2$ in the quantum KHI without dissipation in a trapped system. The total number of atoms is $3.1\times {10}^6$ with an equal population in each component. The trap potential is $U_j\left(\mathbf{r}\right)=\frac{m}{2}\left({\omega }_{\perp }^2{r}^2+{\omega }_z{z}^2\right)$ with $r^2=x^2+y^2$, ${\omega }_{\perp }=2\pi \times 80\text{Hz}$, and ${\omega }_z=2\pi \times 4\text{kHz}$, and the simulation is performed in quasitwo dimensions. The field of view is $72\times 72\mu {\text{m}}^2$.