Four-Wave Mixing at peV Energy Scales

We measure the nonlinear magnetic susceptibility χ^{(3)} of the disordered quantum Ising magnet LiHo_{0.045}Y_{0.955}F_{4} and demonstrate four-wave mixing due to coherent (anti-)Stokes Raman scattering at ∼100 Hz (peV) energy scales. The temperature dependence of χ^{(3)} approximately follows a (1/T) form, with a high-T cutoff that can be linked to dissipation in the coherent spin clusters. χ^{(3)} also decreases monotonically with a transverse field, approaching a constant offset above a few kOe, suggesting the presence of both coherent and spontaneous Raman scattering.