Coherent magnon optics in a ferromagnetic spinor Bose-Einstein condensate

We measure the mass, gap, and magnetic moment of a magnon in the ferromagnetic $F=1$ spinor Bose-Einstein condensate of ${}^{87}$Rb. We find an unusually heavy magnon mass of $1.038(2{)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}(8{)}_{\mathrm{s}\mathrm{y}\mathrm{s}}$ times the atomic mass, as determined by interfering standing and running coherent magnon waves within the dense and trapped condensed gas. This measurement is shifted significantly from theoretical estimates. The magnon energy gap of $h\times 2.5(1{)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}(2{)}_{\mathrm{s}\mathrm{y}\mathrm{s}}\mathrm{H}\mathrm{z}$ and the effective magnetic moment of $-1.04(2{)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}(8){\mu }_{\text{bare}}$ times the atomic magnetic moment are consistent with mean-field predictions. The nonzero energy gap arises from magnetic dipole-dipole interactions.