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arXiv:0910.1440 · Physical Review A

Rayleigh-Taylor instability and mushroom-pattern formation in a two-component Bose-Einstein condensate

Kazuki Sasaki, Naoya Suzuki, Daisuke Akamatsu, Hiroki Saito

Published Dec 4, 2009• 118 citations
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Abstract

The Rayleigh-Taylor instability at the interface in an immiscible two-component Bose-Einstein condensate is investigated using the mean field and Bogoliubov theories. Rayleigh-Taylor fingers are found to grow from the interface and mushroom patterns are formed. Quantized vortex rings and vortex lines are then generated around the mushrooms. The Rayleigh-Taylor instability and mushroom-pattern formation can be observed in a trapped system.

DOI
10.1103/physreva.80.063611

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The Rayleigh-Taylor instability at the interface in an immiscible two-component Bose-Einstein condensate is investigated using the mean field and Bogoliubov theories. Rayleigh-Taylor fingers are found to grow from the interface and mushroom patterns are formed. Quantized vortex rings and vortex lines are then generated around the mushrooms. The Rayleigh-Taylor instability and mushroom-pattern formation can be observed in a trapped system.
Instabilities, where small fluctuations seed the formation of large-scale structures, govern dynamics in a variety of fluid systems. The Rayleigh-Taylor instability (RTI), present from tabletop to astronomical scales, is an iconic example characterized by mushroom-shaped incursions appearing when immiscible fluids are forced together. Despite its ubiquity, RTI experiments are challenging; here, we report the observation of the RTI in an immiscible binary superfluid consisting of a two-component Bose-Einstein condensate. We force these components together to initiate the instability, and observe the growth of mushroom-like structures. The interface can also be stabilized, allowing us to spectroscopically measure the "ripplon" interface modes. Last, we use matter-wave interferometry to transform the superfluid velocity field at the interface into a vortex chain. These results-in agreement with our theory-demonstrate the close connection between the RTI in classical and quantum fluids.
Three-component Bose-Einstein condensates (BECs) offer a rich platform for exploring inquisitive quantum phenomena. We investigate the Rayleigh-Taylor instability at the two interfaces in a phase-separated three-component BEC in the mean-field framework. The instability in the system can be instigated in various ways owing to the versatility of the three-component system and the subsequent dynamics for certain cases has been studied in detail. We also study the impact of immiscibility of the intermediate component on the onset of instability in the system. The rotational symmetry of the system breaks when the atom-atom interaction is tuned in such a way that the interface between the components becomes unstable giving rise to nonlinear patterns of mushroom shapes which grow exponentially with time. We identify these nonlinear patterns as the solutions of the angular Mathieu equation, representing the normal modes.
The Rayleigh-Taylor instability is a gravitational instability in two fluids where the heavier fluid is set over the lighter fluid. The instability occurs both in classical fluids and quantum fluids. We numerically study the Rayleigh-Taylor instability using coupled Gross-Pitaevskii equations for two-component Bose-Einstein condensates. We carry out numerical simulations that the heavier component is set in a torus initially which is surrounded by the lighter component. When the torus falls, the Rayleigh-Taylor instability develops and a sagging pattern appears. This instability is investigated for the two cases with and without a vortex ring inside the torus. We find that a vortex ring suppresses the instability when the radius of the torus is small.
Dynamical instabilities at the interface between two Bose-Einstein condensates that are moving relative to each other are investigated using mean-field and Bogoliubov analyses. Kelvin-Helmholtz instability is dominant when the interface thickness is much smaller than the wavelength of the unstable interface mode, whereas the counter-superflow instability becomes dominant in the opposite case. These instabilities emerge not only in an immiscible system but also in a miscible system where an interface is produced by external potential. Dynamics caused by these instabilities are numerically demonstrated in rotating trapped condensates.