Coherent Magnon Optics in a Ferromagnetic Spinor BEC

We measure the dispersion relation, gap, and magnetic moment of a magnon in the ferromagnetic \( F=1 \) spinor Bose-Einstein condensate of \( ^{87}\text{Rb} \). From the dispersion relation we measure an average effective mass \( 1.033(2)_\text{stat}(10)_\text{sys} \) times the atomic mass, as determined by interfering standing and running coherent magnon waves within the dense and trapped condensed gas. The measured mass is higher than theoretical predictions of mean-field and beyond-mean-field Beliaev theory for a bulk spinor Bose gas with \(s\)-wave contact interactions. We observe a magnon energy gap of \(h \times 2.5(1)_\text{stat}(2)_\text{sys} \text{Hz} \), which is consistent with the predicted effect of magnetic dipole-dipole interactions. These dipolar interactions may also account for the high magnon mass. The effective magnetic moment of \( −1.04(2)_\text{stat}(8)_\text{sys} \) times the atomic magnetic moment is consistent with mean-field theory.