  The inelastic scatterings of matter systems, such as Raman scattering,
contain rich information on mechanical vibrations like as resonant frequencies,
which lead to various applications, for example, a sensor for specific
molecules. However, observing output signals requires a sensitive setup because
an inelastic signal is inherently weak and is disturbed by strong input. In
this study, we theoretically investigate a physical scheme to avoid detrimental
impact of the input by distancing it from the emitter and greatly enhancing the
output signals. If two bodies are coupled mechanically and direct optical
communication is forbidden, the nonlocal inelastic scattering signals can be
considerably boosted. We demonstrate this mechanism by considering coupled
optomechanical systems as a typical example that enables control of the
two-body interaction strength. The results present a general scheme to boost
nonlocal inelastic scattering for noiseless and pure signals.
