  Doppler broadening in thermal ensembles degrades the absorption cross-section
and the coherence time of collective excitations. In two photon transitions, it
is common to assume that this problem becomes worse with larger wavelength
mismatch. Here we identify an opposite mechanism, where such wavelength
mismatch leads to cancellation of Doppler broadening via the counteracting
effects of velocity-dependent light-shifts and Doppler shifts. We show that
this effect is general, common to both absorption and transparency resonances,
and favorably scales with wavelength mismatch. We experimentally confirm the
enhancement of transitions for different low-lying orbitals in rubidium atoms
and use calculations to extrapolate to high-lying Rydberg orbitals. These
calculations predict a dramatic enhancement of up to 20-fold increase in
absorption, even in the presence of large homogeneous broadening. More general
configurations, where an auxiliary dressing field is used to counteract Doppler
broadening, are also discussed and experimentally demonstrated. The mechanism
we study can be applied as well for rephasing of spin waves and increasing the
coherence time of quantum memories.
