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Physica Scripta

Modulational Instability of Two Colliding Bose–Einstein Condensates

Padma Kant Shukla, Lennart STENFLO, Renato Fedele

Published Jan 1, 2001• 11 citations
Publisher

Abstract

It is found that two colliding Bose–Einstein condensate wave packets are modulationally unstable. An explicit expression for the growth rate of a purely growing modulational instability is presented.
DOI
10.1238/physica.regular.064a00553

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We investigate nonlinear dynamics induced by the modulation instability of a two-component mixture in an atomic Bose-Einstein condensate. The nonlinear dynamics is examined using numerical simulations of the time-dependent coupled Gross-Pitaevskii equations. The unstable modulation grows from initially miscible condensates into various types of vector solitary waves, depending on the combinations of the sign of the coupling constants (intracomponent and intercomponent). We discuss the detailed features of the modulation instability, dynamics of solitary wave formation, and an analogy with the collapsing dynamics in a single-component condensate with attractive interactions.
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Modulational instability of a uniform two-dimensional binary Bose-Einstein condensate (BEC) in the presence of quantum fluctuations is studied. The analysis is based on the coupled Gross-Pitaevskii equations. It is shown that quantum fluctuations can induce instability when the BEC density is below a threshold. The dependence of the growth rate of modulations on the BEC parameters is found. It is observed that an asymmetry of the interaction parameters and/or initial densities of the components typically decreases the growth rate. Further development of the instability results in the BEC breaking up into a set of quantum droplets. These droplets merge dynamically with each other, so the total number of droplets decreases rapidly. The rate of this decrease is evaluated numerically for different initial parameters.