  Magnetic excitations of the recently discovered frustrated spin-1/2 two-leg
ladder system Li$_2$Cu$_2$O(SO$_4$)$_2$ are investigated using inelastic
neutron scattering, magnetic susceptibility and infrared absorption
measurements. Despite the presence of a magnetic dimerization concomitant with
the tetragonal-to-triclinic structural distortion occurring below 125 K,
neutron scattering experiments reveal the presence of dispersive triplet
excitations above a spin gap of $\Delta = 10.6$ meV at 1.5 K, a value
consistent with the estimates extracted from magnetic susceptibility. The
likely detection of these spin excitations in infrared spectroscopy is
explained by invoking a dynamic Dzyaloshinskii-Moriya mechanism in which light
is coupled to the dimer singlet-to-triplet transition through an optical
phonon. These results are qualitatively explained by exact diagonalization and
higher-order perturbation calculations carried out on the basis of the
dimerized spin Hamiltonian derived from first-principles.
