arXiv:1410.6124

Capillary waves at the interface of two Bose-Einstein condensates. Long wavelengths asymptotic by trial function approach

Todor M. Mishonov

Published Oct 22, 2014• 0 citations

Abstract

The dispersion relation for capillary waves at the boundary of two different Bose condensates is investigated using a trial wave-function approach applied to the Gross-Pitaevskii (GP) equations. The surface tension is expressed by the parameters of the GP equations. In the long wave-length limit the usual dispersion relation is re-derived while for wavelengths comparable to the healing length we predict significant deviations from the $ω\propto k^{3/2}$ law which can be experimentally observed. We approximate the wave variables by a frozen order parameter, i.e. the wave function is frozen in the superfluid analogous to the magnetic field in highly conductive space plasmas.

DOI: 10.48550/arxiv.1410.6124

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arXiv:1410.6124

Capillary waves at the interface of two Bose-Einstein condensates. Long wavelengths asymptotic by trial function approach

Todor M. Mishonov

Published Oct 22, 2014• 0 citations

arXiv HTML PDF

Abstract

ω\propto k^{3/2}

law which can be experimentally observed. We approximate the wave variables by a frozen order parameter, i.e. the wave function is frozen in the superfluid analogous to the magnetic field in highly conductive space plasmas.

DOI: 10.48550/arxiv.1410.6124

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Capillary-wave dynamics and interface structure modulation in binary Bose-Einstein condensate mixtures

Joseph O. Indekeu, Nguyễn Văn Thụ, Chang-You Lin +1 more

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ω\propto k^{3/2}

K

(

>1

) of the phase segregation. The dispersion relation $\ensuremath{\omega}(k)\ensuremath{\propto}{k}^{3/2}$ is derived directly from the Bogoliubov--de Gennes equations in the limit that the wavelength $2\ensuremath{\pi}/k$ is much larger than the interface width. The proportionality constant in the dispersion relation provides the static interfacial tension. A correction term in $\ensuremath{\omega}(k)$ of order

{k}^{5/2}

is calculated analytically within the DPA model. The combined result is tested against numerical diagonalization of the exact Bogoliubov--de Gennes equations. Satisfactory agreement is obtained in the range of physically relevant wavelengths. The ripplon dispersion relation is relevant to state-of-the-art experiments using (quasi)uniform optical-box traps. Furthermore, within the DPA model explicit expressions are obtained for the structural deformation of the interface due to the passing of the capillary wave. It is found that the amplitude of the wave is enhanced by an amount that is quadratic in the ratio of the phase velocity $\ensuremath{\omega}/k$ to the sound velocity

c

. For generic mixtures consisting of condensates with unequal healing lengths, an additional modulation is predicted of the common value of the condensate densities at the interface.

K

. An exact solution to the Gross-Pitaevskii (GP) equations is obtained for the special case ${\ensuremath{\xi}}_{2}/{\ensuremath{\xi}}_{1}=1/2$ and

K=3/2

. Furthermore, applying a double-parabola approximation (DPA) to the energy density featured in GP theory allows us to define a DPA model, which is much simpler to handle than GP theory but nevertheless still captures the main physics. In particular, a compact analytic expression for the interfacial tension is derived that is useful for all ${\ensuremath{\xi}}_{1},\phantom{\rule{0.28em}{0ex}}{\ensuremath{\xi}}_{2}$, and

K

. An application to wetting phenomena is presented for condensates adsorbed at an optical wall. The wetting phase boundary obtained within the DPA model nearly coincides with the exact one in GP theory.

\xi_{0}

despite not being selected explicitly. We present a variational method to construct analytical solution for vortices of any quantum of circulation from the core to any finite extent. Using our analysis we predict hydrogen BEC to produce the thinnest vortex line.