Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Dalat University Journal of Science

THE INTERFACE POSITION OF A BOSE-EINSTEIN CONDENSATE MIXTURE RESTRICTED BY A HARD WALL IN THE DOUBLE-PARABOLA APPROXIMATION

Duy Thanh Pham, Thanh Hai Dang

Published Jul 1, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.37569/dalatuniversity.15.3s.1475(2025)

Related papers

THE THERMODYNAMIC CONTACT ANGLE IN THE PREWETTING PHASE OF A BINARY BOSE-EINSTEIN CONDENSATE MIXTURE

Pham Duy Thanh, Nguyễn Văn Thụ

To investigate the prewetting state of a Bose-Einstein condensate (BEC) mixture adsorbed on an optical hard wall at zero temperature, we consider a system in which condensate 1 coexists with condensate 2 with the chemical potential held fixed. Using the double parabola approximation (DPA) and solving the coupled Gross-Pitaevskii equations, we derive an analytical expression for the thermodynamic contact angle based on Youngs equation. Although the resulting formula is not algebraically simple, it reveals that complete wetting can occur before the bulk coexistence point is reached, indicating the presence of a continuous (second-order) prewetting transition. Our findings are in agreement with theoretical predictions in the literature and emphasize that the wetting film thickness grows smoothly without a discontinuous jump. This work provides useful guidance for the design of experiments aimed at observing wetting phenomena in Bose-Einstein condensates.

Journal of Science Natural Science•Sep 30, 2025•0 citations

Static interfacial properties of Bose-Einstein-condensate mixtures

Joseph O. Indekeu, Chang-You Lin, Nguyễn Văn Thụ +2 more

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.

arXiv:1502.00419•Physical Review A•Mar 13, 2015•50 citations

Interface potential and line tension for Bose-Einstein condensate mixtures near a hard wall

Bert Van Schaeybroeck, Patrick Navez, Joseph O. Indekeu

Within Gross-Pitaevskii (GP) theory we derive the interface potential $V(\ensuremath{\ell})$ which describes the interaction between the interface separating two demixed Bose-condensed gases and an optical hard wall at a distance $\ensuremath{\ell}$. Previous work revealed that this interaction gives rise to extraordinary wetting and prewetting phenomena. Calculations that explore nonequilibrium properties by using $\ensuremath{\ell}$ as a constraint provide a thorough explanation for this behavior. We find that at bulk two-phase coexistence, $V(\ensuremath{\ell})$ for both complete wetting and partial wetting is monotonic with exponential decay. Remarkably, at the first-order wetting phase transition, $V(\ensuremath{\ell})$ is independent of $\ensuremath{\ell}$. This anomaly explains the infinite continuous degeneracy of the grand potential reported earlier. As a physical application, using $V(\ensuremath{\ell})$ we study the three-phase contact line where the interface meets the wall under a contact angle $\ensuremath{\theta}$. Employing an interface displacement model we calculate the structure of this inhomogeneity and its line tension $\ensuremath{\tau}$. Contrary to what happens at a usual first-order wetting transition in systems with short-range forces, $\ensuremath{\tau}$ does not approach a nonzero positive constant for $\ensuremath{\theta}\ensuremath{\rightarrow}0$, but instead approaches zero (from below) in the manner $\ensuremath{\tau}\ensuremath{\propto}\ensuremath{-}\ensuremath{\theta}$ as would be expected for a critical wetting transition. This hybrid character of $\ensuremath{\tau}$ is a consequence of the absence of a barrier in $V(\ensuremath{\ell})$ at wetting. For a typical $V(\ensuremath{\ell})=\mathcal{S}\phantom{\rule{0.16em}{0ex}}exp(\ensuremath{-}\ensuremath{\ell}/\ensuremath{\xi})$, with $\mathcal{S}$ the spreading coefficient and $\ensuremath{\xi}$ a decay length, we conjecture that $\ensuremath{\tau}=\ensuremath{-}2\phantom{\rule{0.16em}{0ex}}(1\ensuremath{-}ln2)\phantom{\rule{0.16em}{0ex}}\ensuremath{\gamma}\phantom{\rule{0.16em}{0ex}}\ensuremath{\xi}\phantom{\rule{0.16em}{0ex}}sin\ensuremath{\theta}$ is exact within GP theory, with $\ensuremath{\gamma}$ the interfacial tension and $0\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}\ensuremath{\pi}$.

arXiv:2201.04871•Physical Review A•May 23, 2022•5 citations

Adsorbed Index for Critical Wetting Phase Transition in Ternary Bose-Einstein Condensates

Nguyen Van Thu, Phạm Thế Song, Hoang Van Quyet

We identify the adsorbed index as an experimentally accessible order parameter for the wetting phase transition in dilute ternary Bose–Einstein condensates (BECs). By tracking the nucleation and growth of a surfactant film of the third component at the interface between two immiscible condensates, we show that the adsorbed index exhibits a logarithmic divergence with the chemical-potential ratio in the prewetting phase. Numerical Gross–Pitaevskii calculations are consistent with analytical predictions from the double-parabola approximation, confirming the reliability of the approach. Unlike the conventional surfactant layer thickness, which becomes ill-defined near the nucleation point, the adsorbed index remains well defined throughout the entire prewetting-wetting regime and is directly proportional to the number of condensed atoms in the surfactant component, a quantity that is readily measurable in ultracold-atom experiments and tunable via Feshbach resonances. Our results offer a realistic opportunity to observe wetting transitions in multicomponent quantum gases.

VNU Journal of Science Mathematics - Physics•May 1, 2026•0 citations

Location of Interface Bose-Einstein Condensate Mixtures in Semi-infinite Space under Neumann Boundary Condition

Hoàng Văn Quyết

The location of interface plays a pivotal role in studying on wetting phase transition of Bose-Einstein condensates (BECs) mixture. Beside parameters of system, the position of the interface depends on the applied boundary condition. Using double-parabola approximation (DPA), we consider the dependence of position of interface on parameters in semi-infinite space under Neumann boundary condition.

VNU Journal of Science Mathematics - Physics•Jun 24, 2022•0 citations

Three-component Bose-Einstein condensates and wetting without walls

Joseph O. Indekeu, Nguyễn Văn Thụ, Jonas Berx

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.

arXiv:2309.13708•Physical Review A•Apr 24, 2025•2 citations
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.
To investigate the prewetting state of a Bose-Einstein condensate (BEC) mixture adsorbed on an optical hard wall at zero temperature, we consider a system in which condensate 1 coexists with condensate 2 with the chemical potential held fixed. Using the double parabola approximation (DPA) and solving the coupled Gross-Pitaevskii equations, we derive an analytical expression for the thermodynamic contact angle based on Youngs equation. Although the resulting formula is not algebraically simple, it reveals that complete wetting can occur before the bulk coexistence point is reached, indicating the presence of a continuous (second-order) prewetting transition. Our findings are in agreement with theoretical predictions in the literature and emphasize that the wetting film thickness grows smoothly without a discontinuous jump. This work provides useful guidance for the design of experiments aimed at observing wetting phenomena in Bose-Einstein condensates.
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 KKK. 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=3/2K=3/2K=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 KKK. 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.
Within Gross-Pitaevskii (GP) theory we derive the interface potential $V(\ensuremath{\ell})$ which describes the interaction between the interface separating two demixed Bose-condensed gases and an optical hard wall at a distance $\ensuremath{\ell}$. Previous work revealed that this interaction gives rise to extraordinary wetting and prewetting phenomena. Calculations that explore nonequilibrium properties by using $\ensuremath{\ell}$ as a constraint provide a thorough explanation for this behavior. We find that at bulk two-phase coexistence, $V(\ensuremath{\ell})$ for both complete wetting and partial wetting is monotonic with exponential decay. Remarkably, at the first-order wetting phase transition, $V(\ensuremath{\ell})$ is independent of $\ensuremath{\ell}$. This anomaly explains the infinite continuous degeneracy of the grand potential reported earlier. As a physical application, using $V(\ensuremath{\ell})$ we study the three-phase contact line where the interface meets the wall under a contact angle $\ensuremath{\theta}$. Employing an interface displacement model we calculate the structure of this inhomogeneity and its line tension $\ensuremath{\tau}$. Contrary to what happens at a usual first-order wetting transition in systems with short-range forces, $\ensuremath{\tau}$ does not approach a nonzero positive constant for $\ensuremath{\theta}\ensuremath{\rightarrow}0$, but instead approaches zero (from below) in the manner $\ensuremath{\tau}\ensuremath{\propto}\ensuremath{-}\ensuremath{\theta}$ as would be expected for a critical wetting transition. This hybrid character of $\ensuremath{\tau}$ is a consequence of the absence of a barrier in $V(\ensuremath{\ell})$ at wetting. For a typical $V(\ensuremath{\ell})=\mathcal{S}\phantom{\rule{0.16em}{0ex}}exp(\ensuremath{-}\ensuremath{\ell}/\ensuremath{\xi})$, with S\mathcal{S}S the spreading coefficient and $\ensuremath{\xi}$ a decay length, we conjecture that $\ensuremath{\tau}=\ensuremath{-}2\phantom{\rule{0.16em}{0ex}}(1\ensuremath{-}ln2)\phantom{\rule{0.16em}{0ex}}\ensuremath{\gamma}\phantom{\rule{0.16em}{0ex}}\ensuremath{\xi}\phantom{\rule{0.16em}{0ex}}sin\ensuremath{\theta}$ is exact within GP theory, with $\ensuremath{\gamma}$ the interfacial tension and $0\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}\ensuremath{\pi}$.
We identify the adsorbed index as an experimentally accessible order parameter for the wetting phase transition in dilute ternary Bose–Einstein condensates (BECs). By tracking the nucleation and growth of a surfactant film of the third component at the interface between two immiscible condensates, we show that the adsorbed index exhibits a logarithmic divergence with the chemical-potential ratio in the prewetting phase. Numerical Gross–Pitaevskii calculations are consistent with analytical predictions from the double-parabola approximation, confirming the reliability of the approach. Unlike the conventional surfactant layer thickness, which becomes ill-defined near the nucleation point, the adsorbed index remains well defined throughout the entire prewetting-wetting regime and is directly proportional to the number of condensed atoms in the surfactant component, a quantity that is readily measurable in ultracold-atom experiments and tunable via Feshbach resonances. Our results offer a realistic opportunity to observe wetting transitions in multicomponent quantum gases.
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.