Spin-dependent Bragg spectroscopy of a spinor Bose gas

TL;DR

This paper develops a theoretical framework for spin-dependent Bragg spectroscopy in spinor Bose-Einstein condensates, enabling detailed investigation of their excitation spectra and phases.

Contribution

It introduces a general theory linking Bragg spectroscopy to dynamic structure factors and derives sum rules, with applications to spin-1 condensates using Bogoliubov theory.

Findings

Dynamic structure factors computed for all four phases of a spin-1 condensate.

Spin-dependent Bragg spectroscopy can selectively probe phonon and magnon excitations.

Theoretical framework provides constraints and guides experimental investigations.

Abstract

We develop a general theory of spin-dependent Bragg spectroscopy for spinor Bose-Einstein condensates. This spectroscopy involves using a density and spin-coupled optical probe to excite the system. We show that within the linear response regime the momentum or energy transferred by the probe is determined by a set of density and spin-density dynamic structure factors. We derive a set of $f$-sum rules that provide rigorous constraints for the first energy moments of these structure factors. As an application we compute the dynamic structure factors for cases within all four distinct phases of a spin-1 condensate using Bogoliubov theory. Our results demonstrate that spin-dependent Bragg spectroscopy can be used to selectively investigate the various phonon and magnon excitation branches and will be a useful tool for advancing our understanding of spinor condensates.