Raman fingerprints on the Bloch sphere of a spinor Bose-Einstein condensate

TL;DR

This paper provides a geometric interpretation of Raman processes on the Bloch sphere for spinor Bose-Einstein condensates, demonstrating control over spin textures and topological states through experimental and theoretical analysis.

Contribution

It introduces a geometric model of Raman processes on the Bloch sphere for spinor BECs and demonstrates experimental control over spin textures using this framework.

Findings

Experimental validation with $^{87}$Rb BECs

Control of spin density and phase profiles

Creation of exotic topological spin textures

Abstract

We explore the geometric interpretation of a diabatic, two-photon Raman process as a rotation on the Bloch sphere for a pseudo-spin-1/2 system. The spin state of a spin-1/2 quantum system can be described by a point on the surface of the Bloch sphere, and its evolution during a Raman pulse is a trajectory on the sphere determined by properties of the optical beams: the pulse area, the relative intensities and phases, and the relative frequencies. We experimentally demonstrate key features of this model with a $^{87}$Rb spinor Bose-Einstein condensate, which allows us to examine spatially dependent signatures of the Raman beams. The two-photon detuning allows us to precisely control the spin density and imprinted relative phase profiles, as we show with a coreless vortex. With this comprehensive understanding and intuitive geometric interpretation, we use the Raman process to create and tailor as well as study and characterize exotic topological spin textures in spinor BECs.