Interface dynamics of a two-component Bose-Einstein condensate driven by an external force

Abstract

The dynamics of an interface in a two-component Bose-Einstein condensate driven by a spatially uniform time-dependent force is studied. Starting from the Gross-Pitaevskii Lagrangian, the dispersion relation for linear waves and instabilities at the interface is derived by means of a variational approach. A number of diverse dynamical effects for different types of the driving force is demonstrated, which includes the Rayleigh-Taylor instability for a constant force, the Richtmyer-Meshkov instability for a pulse force, dynamic stabilization of the Rayleigh-Taylor instability and onset of the parametric instability for an oscillating force. Gaussian Markovian and non-Markovian stochastic forces are also considered. It is found that the Markovian stochastic force does not produce any average effect on the dynamics of the interface, while the non-Markovian force leads to exponential perturbation growth.

Quantum swapping of immiscible Bose-Einstein condensates as an alternative to the Rayleigh-Taylor instability

“…Recent results on the linear and nonlinear stages of the quantum RTI may be found in Refs. [12,16]. Still, contrary to the classical case, the RTI is not the only way for the immiscible BEC components to exchange places.…”

“…To finish this subsection, we point out that the bulk oscillations are similar (though not identical) to the counterphase mode of the BEC interface perturbations identified in the linear theory of Ref. [16]. We remind that the counterphase mode involves oscillations of the interpenetration depth of the BEC components locally at the interface.…”

“…Close to the interface, where the TFA breaks down, the density profile can be approximated with the expression for a nontrapped system [16,23,24],…”

“…The characteristic penetration depth of BEC density profiles may be interpreted as the interface width; it is estimated as int =ξ 0 / √ γ [16,23], or, in dimensionless units…”

“…Recently there has been much interest in the quantum hydrodynamics and nonlinear responce of two-component BECs [1][2][3][4][5][6][7][8][9] and, in particular, in the development of quasihydrodynamic instabilities at the interface separating the immiscible components [10][11][12][13][14][15][16]. Among these phenomena, the quantum Rayleigh-Taylor instability (RTI) is, probably, one of the most representative and fascinating [12,16]. The RTI releases the excessive potential energy stored in the system and transforms it into kinetic energy of the flow, by means of interface waves that grow into mushroom-shaped bubbles.…”