Magnetic Richtmyer-Meshkov instability in a two-component Bose-Einstein condensate

The magnetically induced Richtmyer-Meshkov (RM) instability in a two-component Bose-Einstein condensate (BEC) is investigated. We construct and study analytical models describing the development of the instability at both the linear and nonlinear stages. The models indicate interesting features of the instability: surface tension implies departure from the linear growth of modes and separation of droplets, which are qualitatively different from the traditional RM case of classical gases, and the trapping potential affects the later stages of the instability. We perform numerical simulations of the instability in a trapped BEC using the Gross-Pitaevskii equation and compare the simulation results to the model predictions.

Figure 1

Detachment of droplets in the RM instability.

Figure 2

Density of the lower component, showing the capillary waves on the interface at the point of maximum amplitude.

Figure 3

Cloud density of one component for times 6.4 and 12.7 ms after shock size $U=0.75\times {10}^{-3}\hspace{0.5em}{\text{ms}}^{-1}$.

Figure 4

Cloud density of one component for times 5.7, 8.0, and 12.7 ms after shock size $U=1.05\times {10}^{-3}\hspace{0.5em}{\text{ms}}^{-1}$.

Figure 5

Phase of portion of a cloud, 5.7 ms after shock of size $U=1.05\times {10}^{-3}\hspace{0.5em}{\text{ms}}^{-1}$ (a), showing density of a single finger (b), and phase of a single finger (c). A vortex pair is visible under the cap shown in (c); many of these pairs can be seen under the caps in (a).

Figure 6

Cloud density of one component at time 12.7 ms after shock size $U=2.1\times {10}^{-3}\hspace{0.5em}{\text{ms}}^{-1}$.

Figure 7

Plot of relative fringe growth versus shock magnitude, U. Analytic prediction (solid line), and numerical simulation for total finger growth (solid diamonds) and growth until first leveling off (open squares); see text.

Figure 8

Width of cloud in $x$ direction (parallel to the interface) as a function of time for perturbed (solid line) and unperturbed (dotted line) clouds.

Figure 9

Relative growth of fringe as function of time for pulse $U=0.75\times {10}^{-3}\hspace{0.5em}{\text{ms}}^{-1}$ (solid circles) and width of the cloud, $\langle x^2\rangle$ (solid line, arbitrary scale in $y$).