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arXiv:0805.2512 · Physical Review A

Interface tension of Bose-Einstein condensates

Bert Van Schaeybroeck

Published Aug 20, 2008• 91 citations
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Abstract

Motivated by recent observations of phase-segregated binary Bose-Einstein condensates, we propose a method to calculate the excess energy due to the interface tension of a trapped configuration. By this method one should be able to numerically reproduce the experimental data by means of a simple Thomas-Fermi approximation, combined with interface excess terms and the Laplace equation. Using the Gross-Pitaevskii theory, we find expressions for the interface excesses which are accurate in a very broad range of the interspecies and intraspecies interaction parameters. We also present finite-temperature corrections to the interface tension which, aside from the regime of weak segregation, turn out to be small.

DOI
10.1103/physreva.78.023624

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Comment on "Interface tension of Bose-Einstein condensates" by Bert Van Schaeybroeck, Phys. Rev. A 78, 023624-9 (2008)

Todor M. Mishonov

The purpose of the comment is to point out that the leading term of the Ginzburg-Landau nonanalytical correction to the interface tension of Bose-Einstein condensates with strong segregation and the surface tension of extreme type-I superconductors are described by a common coefficient derived from the universal equation for the phase boundary. The agreement between the numerical value of the coefficients gives a hint that this can be an exact result which deserves to be checked. The outcome will be of interest for physicists working in both fields.

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arXiv:1804.11156•Apr 30, 2018•0 citations
Motivated by recent observations of phase-segregated binary Bose-Einstein condensates, we propose a method to calculate the excess energy due to the interface tension of a trapped configuration. By this method one should be able to numerically reproduce the experimental data by means of a simple Thomas-Fermi approximation, combined with interface excess terms and the Laplace equation. Using the Gross-Pitaevskii theory, we find expressions for the interface excesses which are accurate in a very broad range of the interspecies and intraspecies interaction parameters. We also present finite-temperature corrections to the interface tension which, aside from the regime of weak segregation, turn out to be small.
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 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.
We investigate the effects of quantum fluctuations (QFs) and finite-range interatomic interactions on the ground state and wall tension of a Bose-Einstein condensate (BEC) at zero temperature by means of modified Gross-Pitaevskii equations. The QFs are shown to stiffen the condensate near the hard wall, narrowing the density profile and raising the wall tension above its mean-field value by an amount proportional to square-root of the gas parameter. Finite-range corrections always reduces the wall tension relative to the QFs correction value regardless of the effective range. We find the ordering γ0<γII<γIγ_0 < γ_{\rm II} < γ_{\rm I}γ0​<γII​<γI​ in the dilute regime and identify a crossover condition under which the two beyond-mean-field contributions mutually cancel. These results provide an experimentally accessible way for probing beyond-LHY physics through precision measurements of the wall tension in ultracold Bose gases.
The dynamics of quantum fluctuations of weakly coupled Bose–Einstein condensates (BECs) can be described by an effective Bose–Josephson Hamiltonian. By requiring that the mean-field approximation on this effective Hamiltonian reproduces the low energy dynamics of the Gross–Pitaevskii equation, we obtain parameters for the effective Hamiltonian. This approach is particularly suitable when the BECs are in the Thomas–Fermi regime. Considering the problem of the splitting of a trapped BEC into two BEC fragments, our results for the dynamics of the depletion, collapses and revivals of the phase coherence are in good agreement with a recent numerical microscopic calculation from Streltsov et al (2007 Phys. Rev. Lett. 99 030402). In addition, the excitation energy of the lowest symmetric mode, which is the first relevant mode for the symmetric splitting process, is reproduced with reasonable accuracy all the way from the mean-field Josephson regime to the Fock regime.
The purpose of the comment is to point out that the leading term of the Ginzburg-Landau nonanalytical correction to the interface tension of Bose-Einstein condensates with strong segregation and the surface tension of extreme type-I superconductors are described by a common coefficient derived from the universal equation for the phase boundary. The agreement between the numerical value of the coefficients gives a hint that this can be an exact result which deserves to be checked. The outcome will be of interest for physicists working in both fields.
We study harmonically trapped two-species Bose-Einstein condensates within the Gross-Pitaevskii formalism. By invoking the Thomas-Fermi approximation, we derive an analytical solution for the miscible ground state in a particular region of the system's parameter space. This solution furnishes a simple formula for determining the relative strength of the interspecies interaction from a measurement of the density distribution of only one of the two species. Accompanying numerical simulations confirm its accuracy for sufficiently large numbers of condensed particles. The introduced formula provides a condensate-based scheme that complements the typical experimental methods of evaluating interspecies scattering lengths from collisional measurements on thermal samples.