  When atomic gases are laser driven to Rydberg states in an off resonant way,
a single Rydberg atom may enhance the excitation rate of surrounding atoms.
This leads to a facilitated excitation referred to as Rydberg anti-blockade. In
the usual facilitation scenario, the detuning of the laser from resonance
compensates the interaction shift. Here, we discuss a different excitation
mechanism, which we call anomalous facilitation. This occurs on the "wrong
side" of the resonance and originates from inhomogeneous broadening. The
anomalous facilitation may be seen in experiments of attractively interacting
atoms on the blue detuned side, where facilitation is not expected to appear.
