Rayleigh-Taylor instability in a two-component Bose-Einstein condensate with rotational symmetry

The interfacial instability and subsequent dynamics in a phase-separated two-component Bose-Einstein condensate with rotational symmetry are studied. When the interatomic interaction or the trap frequency is changed, the Rayleigh-Taylor instability breaks the rotational symmetry of the interface, which is subsequently deformed into nonlinear patterns including mushroom shapes.

Figure 1

(a)–(d) Dynamics of the column-density profiles $D_1=\int {\left|{\psi }_1\right|}^{2}dz$ (upper panels) and $D_2=\int {\left|{\psi }_2\right|}^{2}dz$ (lower panels) in an axisymmetric trap with $({\omega }_{\perp },{\omega }_z)=2\pi \times (25,1250)$ Hz. The scattering length $a_{11}$ is linearly increased from $80a_B$ to $240a_B$ between $t=0$ and $t=40$ ms, and after that $a_{11}$ is fixed to $240a_B$. The numbers of atoms are $N_1=N_2={10}^5$. The unit of the column density is ${10}^{12}$ ${\mathrm{cm}}^{-2}$. (e) Cross-sectional phase profile ${\phi }_j=\arg \left[{\psi }_j(z=0)\right]$ of the lower half region of (c). The circles in (e) indicate examples of quantized vortices created under the caps of the mushrooms. The field of view is $65.4\times 65.4$ $\mu \mathrm{m}$ in (a)–(d) and $65.4\times 32.7$ $\mu \mathrm{m}$ in (e).

Figure 2

Dynamics of the column-density profiles $D_1$ and $D_2$ for $N_1=1.8\times {10}^5$ and $N_2=2\times {10}^4$. Other parameters are the same as those in Fig. 1.

Figure 3

(a)–(c) Dynamics of the cross-sectional density profiles $d_1={\left|{\psi }_1(z=0)\right|}^2$ and $d_2={\left|{\psi }_2(z=0)\right|}^2$ of components one and two and (d), (e) the isodensity surfaces of component two in a spherically symmetric trap with frequency ${\omega }_1(t=0)={\omega }_2=2\pi \times 33.3$ Hz. The trap frequency ${\omega }_1$ is increased such that ${\omega }_1^2$ is linearly increased from ${({\omega }_1/{\omega }_2)}^2=1$ to 3 between $t=0$ and $t=30$ ms, and after that ${({\omega }_1/{\omega }_2)}^2$ is fixed to 3. The scattering length of component one is $a_{11}=200a_B$, and the numbers of atoms are $N_1=N_2=5.2\times {10}^6$. The unit of the density is $3.0\times {10}^{14}$ ${\mathrm{cm}}^{-3}$. The field of view of each panel is $56.6\times 56.6$ $\mu \mathrm{m}$.

Figure 4

Imaginary part of the Bogoliubov excitation frequency Im$\Omega$ as a function of ${({\omega }_1/{\omega }_2)}^2$. The parameters are the same as those in Fig. 3. The modes for $l\le 10$ are plotted, where $l$ is defined in Eq. (3). The vertical line indicates ${({\omega }_1/{\omega }_2)}^2=3$, corresponding to the parameter in Fig. 3.