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

Abstract

The localized low-energy interfacial excitations, or Nambu-Goldstone modes, of phase-segregated binary mixtures of Bose-Einstein condensates are investigated analytically by means of a double-parabola approximation (DPA) to the Lagrangian density in Gross-Pitaevskii theory for a system in a uniform potential. Within this model analytic expressions are obtained for the excitations underlying capillary waves or "ripplons" for arbitrary strength $K(>1)$ of the phase segregation. The dispersion relation $\omega \propto k^{3/2}$ is derived directly from the Bogoliubov-de Gennes equations in limit that the wavelength $2\pi /k$ is much larger than the healing length $\xi$. The proportionality constant in the dispersion relation provides the static interfacial tension. A correction term in $\omega (k)$ of order $k^{5/2}$ is calculated analytically, entailing a finite-wavelength correction factor $(1+\frac{\sqrt{K-1}k\xi }{4\sqrt{2}(\sqrt{2}+\sqrt{K-1})})$. This prediction may be tested experimentally using (quasi-)uniform optical-box traps. 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 $\omega /k$ to the sound velocity $c$. For generic asymmetric mixtures consisting of condensates with unequal healing lengths an additional modulation is predicted of the common value of the condensate densities at the interface.

submitted to Physical Review A

References in corpus (7)

• Emergence of a Turbulent Cascade in a Quantum Gas
• Interface Tension of Bose-Einstein Condensates
• Static interfacial properties of Bose-Einstein condensate mixtures
• Nambu-Goldstone bosons with fractional-power dispersion relations
• Nambu-Goldstone Modes Propagating along Topological Defects: Kelvin and Ripple Modes from Small to Large Systems
• Observation of Weak Collapse in a Bose-Einstein Condensate
• Critical wetting, first-order wetting and prewetting phase transitions in binary mixtures of Bose-Einstein condensates

Cited by in corpus (7)

• Parametrically excited star-shaped patterns at the interface of binary Bose-Einstein condensates
• Instabilities of vortex-ring-bright soliton in trapped binary 3D Bose-Einstein condensates
• Interface properties in three-component Bose-Einstein condensates
• Rayleigh-Taylor instability in a phase-separated three-component Bose-Einstein condensate
• Hydrodynamic signatures and spectral properties of the quantum vortex
• Three-component Bose-Einstein condensates and wetting without walls
• Interface potential and line tension for Bose-Einstein condensate mixtures near a hard wall