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.
We investigate interfacial Faraday instabilities in a quasi-two-dimensional, phase-separated binary Bose-Einstein condensate driven by periodic modulation of the interspecies scattering length. In the strongly immiscible regime, the interspecies interaction energy is concentrated near the internal interface, linking the modulation to interfacial tension and the capillary restoring force. We quantify the first-order tension response through its logarithmic sensitivity and account for nonlinear tension variations at finite modulation amplitudes. A sharp-interface capillary model and Floquet analysis yield discrete azimuthal-mode frequencies and primary instability tongues that shift toward higher driving frequencies with increasing mode order. Gross-Pitaevskii simulations reveal star-shaped interface patterns with threefold to eightfold rotational symmetry. The eightfold mode exhibits subharmonic oscillations and approximately exponential growth of its period-averaged amplitude over a small-deformation interval. These results provide a route to frequency-selective excitation of interfacial capillary modes through interspecies-interaction control.
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∝k3/2 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.
Abstract We develop the Quadruple-Parabola Approximation (QPA), an analytical, piecewise-quadratic trial-function model for the static, planar, zero-temperature interface of a phase-separated binary Bose--Einstein condensate (BEC) mixture with unequal healing lengths, $\xii_1\neq\xii_2$. The construction extends the Double- and Triple-Parabola Approximations (DPA, TPA) by assigning independent curvatures and matching positions to the two components whilepreserving exact linear solvability. The DPA, TPA, and QPA trial families are nested by construction, so that evaluating every trial profile in the exact Gross--Pitaevskii (GP) functional establishes the variational ordering $\si_{\rm DPA}\ge\si_{\rm TPA}\ge\si_{\rm QPA}\ge\si_{\rm GP}$ for arbitrary $\xii$; the QPA reproduces the TPAexactly in the symmetric limit $\xii=1$ and obeys an exact species-exchange covariance, $\si(K,\xii)=\xii\,\si(K,1/\xii)$, both verified numerically. Benchmarked against an independent GP boundary-value solver over
K∈{1.2,1.5,2,3,5} and $\xii\in\{0.5,0.7,1,1/0.7,2\}$, the QPA systematically lowers the variational interfacial tension relative to the TPA in every asymmetric case tested -- removing up to
∼30% of the TPA's residual tension error in the weakest-segregation, most-asymmetric regime, though typically only a few percent elsewhere -- while the DPA over-estimates the tension by
9--
42% against
6.0--
9.6% for the TPA and QPA. This energy improvement does not translate into a smaller pointwise profile error: with a properly
L-independent
L2 metric, the QPA profile error exceeds the TPA's in the majority of (species,
K, $\xii$) combinations tested, but the TPA is not universally superior -- in
8 of
40 such combinations, concentrated at
K≥2 and related in mirrored pairs by the species-exchange covariance, the QPA is marginally better instead. Within the parameter window, optimisation protocol, and admissible domain explored here, neither the TPA nor the QPA reaches sub-percent tension accuracy. The results clarify both the usefulness and the intrinsic limitations of piecewise-quadratic interfacial models for binary quantum fluids: alarger variational trial family can be a genuinely better energetic approximation without being a better pointwise one.
Nambu-Goldstone modes in immiscible two-component Bose-Einstein condensates are studied theoretically. In a uniform system, a flat domain wall is stabilized and then the translational invariance normal to the wall is spontaneously broken in addition to the breaking of two U(1) symmetries in the presence of two complex order parameters. We clarify the properties of the low-energy excitations and identify that there exist two Nambu-Goldstone modes: an in-phase phonon with a linear dispersion and a ripplon with a fractional dispersion. The signature of the characteristic dispersion can be verified in segregated condensates in a harmonic potential.