Cusp catastrophe of symmetry breaking in two-component Bose–Einstein condensates

Abstract

Bifurcation analysis is applied to the spontaneous spatial symmetry breaking occurring in the ground state of two-component Bose-Einstein condensates. The cusp catastrophe describing the supercritical pitchfork bifurcation associated with the symmetry breaking is derived via the identification of the local curvature of the Gross-Pitaevskii energy functional. The bifurcation diagram and universal scaling laws for the eigenvalue and energy are obtained from the catastrophe function.

Caustics, catastrophes, and symmetries in curved beams

“…The caustic-symmetry correspondence is rigorously demonstrated within both complementary frames, the geometric as well as the ondulatory frame. The findings of this work could be useful in the application of the catastrophe theory to other areas beyond the optical beams since the fold and cusp catastrophes are a powerful tool in diverse areas of chemistry [25,26], physics [27][28][29], and cosmology [30,31], in addition to other sciences such as medicine [32,33].…”

Directional Bloch surface wave coupling enabled by magnetic spin-momentum locking of light

“…[23][24][25][26][27] So far, most investigations focused on using the rotating electric component of light as the source of SAM for originating the transverse spindirection coupling. [27][28][29] A recent study demonstrated that the magnetic component of light can play the same role of offering SAM in the SOI of light. 17 In that work, the light coupler has an electric dipole response, leading to a power conversion to the waves driven by the electric optical eld.…”