(a, d) Spatial distribution of eigen wavefunctions along the $ z $ direction in an isotropic harmonic trap, with $\mathit \Omega=0.5E_r$ and $\varGamma_z=5E_r$. For the numerical calculations here, we take a cylindrical coordinate, discretizing $ z\in[-30, 30] $ into $ 480 $ segments, and the radial coordinate $ \rho\in[0, 4] $ into $ 8 $ segments. We plot the radial-integrated spatial distribution of the $ 800 $ eigenstates with the smallest real components, colored according to ${\rm Re}(E)$ (see color bar). Specifically, $\tilde{\psi}_1(z)=2\pi \int \rho {\rm d}\rho \psi_1(\rho,z)$. (b, e) Propagation of the condensate wavefunction in the bulk. (c, f) Growth rate as a function of the shift velocity at $ t=0.6 $. The peak shift velocity $ v_m\approx 16.04 $ in (c) and $ v_m\approx 13.33 $ in (f). The trapping potential is $ \omega=\omega_0=100 $ Hz in (a, b, c), and $ \omega=2\omega_0=200 $ Hz in (d, e, f). The unit of time is $ 10 $ ms, so the longest evolution time in (b, e) is $ 6 $ ms.

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(a, d) Spatial distribution of eigen wavefunctions along the $z$ direction in an isotropic harmonic trap, with $\mathit \Omega=0.5E_r$ and $\varGamma_z=5E_r$ . For the numerical calculations here, we take a cylindrical coordinate, discretizing $z\in[-30, 30]$ into $480$ segments, and the radial coordinate $\rho\in[0, 4]$ into $8$ segments. We plot the radial-integrated spatial distribution of the $800$ eigenstates with the smallest real components, colored according to ${\rm Re}(E)$ (see color bar). Specifically, $\tilde{\psi}_1(z)=2\pi \int \rho {\rm d}\rho \psi_1(\rho,z)$ . (b, e) Propagation of the condensate wavefunction in the bulk. (c, f) Growth rate as a function of the shift velocity at $t=0.6$ . The peak shift velocity $v_m\approx 16.04$ in (c) and $v_m\approx 13.33$ in (f). The trapping potential is $\omega=\omega_0=100$ Hz in (a, b, c), and $\omega=2\omega_0=200$ Hz in (d, e, f). The unit of time is $10$ ms, so the longest evolution time in (b, e) is $6$ ms.