Unconventional Bose-Einstein Condensations Beyond the "No-node" Theorem

TL;DR

This paper reviews new types of Bose-Einstein condensates that break the traditional constraints of the 'no-node' theorem, exhibiting complex wavefunctions and spontaneous time-reversal symmetry breaking in ultra-cold bosonic systems.

Contribution

It introduces and discusses unconventional Bose-Einstein condensates beyond the 'no-node' theorem, including states with complex wavefunctions due to orbital and spin-orbit interactions.

Findings

Observation of Bose-Einstein condensation at non-zero momentum

Identification of orbital angular momentum ordering

Detection of spin textures like skyrmions

Abstract

Feynman's "no-node" theorem states that the conventional many-body ground-state wavefunctions of bosons in the coordinate representation is positive-definite. This implies that time-reversal symmetry cannot be spontaneously broken. In this article, we review our progress in studying a class of new states of unconventional Bose-Einstein condensations beyond this paradigm. These states can either be the long-lived metal-stable states of ultra-cold bosons in high orbital bands in optical lattices as a result of the "orbital-Hund's rule" interaction, or the ground states of spinful bosons with spin-orbit coupling linearly dependent on momentum. In both cases, Feynman's argument does not apply. The resultant many-body wavefunctions are complex-valued and thus break time-reversal symmetry spontaneously. Exotic phenomena in these states include the Bose-Einstein condensation at non-zero momentum, the ordering of orbital angular momentum moments, the half-quantum vortex, and the spin texture of skyrmions.