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arXiv:1903.11457 · Condensed Matter Physics

On the finite-size effects in two segregated Bose-Einstein condensates restricted by a hard wall

Quyet, Thu, Tam, Phat

Published Mar 1, 2019• 3 citations

Abstract

The finite-size effects in two segregated Bose-Einstein condensates (BECs) restricted by a hard wall is studied by means of the Gross-Pitaevskii equations in the double-parabola approximation (DPA).Starting from the consistency between the boundary conditions (BCs) imposed on condensates in confined geometry and in the full space, we find all possible BCs together with the corresponding condensate profiles and interface tensions.We discover two finite-size effects: a) The ground state derived from the Neumann BC is stable whereas the ground states derived from the Robin and Dirichlet BCs are unstable.b) Thereby, there equally manifest two possible wetting phase transitions originating from two unstable states.However, the one associated with the Robin BC is more favourable because it corresponds to a smaller interface tension.

DOI: 10.5488/cmp.22.13001

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The finite-size effects in two segregated Bose-Einstein condensates (BECs) restricted by a hard wall is studied by means of the Gross-Pitaevskii equations in the double-parabola approximation (DPA).Starting from the consistency between the boundary conditions (BCs) imposed on condensates in confined geometry and in the full space, we find all possible BCs together with the corresponding condensate profiles and interface tensions.We discover two finite-size effects: a) The ground state derived from the Neumann BC is stable whereas the ground states derived from the Robin and Dirichlet BCs are unstable.b) Thereby, there equally manifest two possible wetting phase transitions originating from two unstable states.However, the one associated with the Robin BC is more favourable because it corresponds to a smaller interface tension.

The ripplon modes of two segregated Bose-Einstein condensates (BECs) confined by one and two hard walls are respectively studied by means of the hydrodynamic approach within the Gross-Pitaevskii (GP) theory. For the system at rest we find that due to the spatial restriction the dispersion relations are of the form

\omega \sim {k^2}

in low momentum limit for both cases, while for the system in motion parallel to the interface the dispersion relations for both cases are

\omega \sim k

at low momentum limit and, furthermore, the system becomes unstable.

The interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths ${\ensuremath{\xi}}_{1}$ and ${\ensuremath{\xi}}_{2}$ and by the interspecies repulsive interaction

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.

In this study, we determine the interface position of a binary Bose-Einstein condensate mixture in the prewetting phase, confined by a hard wall, at absolute zero temperature. An approximate analytical result is obtained by employing the double-parabola approximation (DPA) to the quartic potential energy density within the Gross-Pitaevskii (GP) theory. The interface position depends on the control parameter and the chemical potential ratio. Our analytical result shows good agreement with numerical results, which indicates that the DPA is a reliable method. This study provides insights for experiments focused on observing the wetting transition of gases in the Bose-Einstein condensate phase.

In previous work within Gross-Pitaevskii (GP) theory for ultracold gases, wetting phase transitions were predicted for a phase-segregated two-component Bose-Einstein condensate (BEC) adsorbed at an optical wall. The wetting phase diagram was found to depend on intrinsic atomic parameters, being the masses and the scattering lengths, and on the extrinsic wall boundary condition. Here we study wetting transitions in GP theory without an optical wall in a setting with three phase-segregated BEC components instead of two. The boundary condition is removed by replacing the wall with the third component and treating the three phases on an equal footing. This leads to an unequivocal wetting phase diagram that depends only on intrinsic atomic parameters. It features first-order and critical wetting transitions, and prewetting phenomena. The phase boundaries are computed by numerical solution of the GP equations. In addition, useful analytic results are obtained by extending the established double-parabola approximation to three components.