Cavity-induced emergent topological spin textures in a Bose Einstein condensate

• Published in: arXiv.org 2018-07
• Main Authors: Ostermann, Stefan, Hon-Wai Lau, Ritsch, Helmut, Mivehvar, Farokh
• Format: Article
• Language: English
• Subjects: Coherent scattering; Condensates; Density; Dynamical systems; Electromagnetic fields; Magnons; Nonlinear dynamics; Optical resonators; Photons; Quantum phenomena; Spin-orbit interactions
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1807.03316

The coupled nonlinear dynamics of ultracold quantum matter and electromagnetic field modes in an optical resonator exhibits a wealth of intriguing collective phenomena. Here we study a \(\Lambda\)-type, three-component Bose-Einstein condensate coupled to four dynamical running-wave modes of a ring cavity, where only two of the modes are externally pumped. However, the unpumped modes play a crucial role in the dynamics of the system due to coherent back-scattering of photons. On a mean- field level we identify three fundamentally different steady-state phases with distinct characteristics in the density and spatial spin textures: a combined density and spin wave, a continuous spin spiral with a homogeneous density, and a spin spiral with a modulated density. The spin-spiral states, which are topological, are intimately related to cavity-induced spin-orbit coupling emerging beyond a critical pump power. The topologically trivial density-wave--spin-wave state has the characteristics of a supersolid with two broken continuous symmetries. The transitions between different phases are either simultaneously topological and first order, or second order. The proposed setup allows the simulation of intriguing many-body quantum phenomena by solely tuning the pump amplitudes and frequencies, with the cavity output fields serving as a built-in nondestructive observation tool.