  Polarized inelastic neutron scattering experiments recently identified the
amplitude (Higgs) mode in C$_9$H$_{18}$N$_2$CuBr$_4$, a two-dimensional
near-quantum-critical spin-1/2 two-leg ladder compound, which exhibits a weak
easy-axis exchange anisotropy. Here, we theoretically examine the dynamic spin
structure factor of such planar coupled spin-ladder systems using large-scale
quantum Monte Carlo simulations. This allows us to provide a quantitative
account of the experimental neutron scattering data within a consistent quantum
spin model. Moreover, we trance the details of the continuous evolution of the
amplitude mode from a two-particle bound state of coupled ladders in the
classical Ising limit all the way to the quantum spin-1/2 Heisenberg limit with
fully restored SU(2) symmetry, where it gets overdamped by the two-magnon
continuum in neutron scattering.
