Survival of the fittest in the coherent evolution of quantum ensembles

We report two effects in an inhomogeneous ensemble of two-level systems driven by an external field. First, we observe a rigidity of the oscillation frequency: the dominant Rabi oscillation frequency does not change with the frequency of the driving field, in contrast to the well-known law of Rabi frequency increase with growing detuning of the driving field. Second, we observe a time-dependent frequency shift of the ensemble-averaged oscillation. We show that these effects follow from the inhomogeneity of the two-level splitting across the ensemble, allowing for a distribution of local oscillations in which those with high frequencies interfere destructively and decay faster than those with a low frequency, which are the only ones to survive in the output signal. Hence, coherence emerges from long-lived oscillations in an inhomogeneous ensemble. We analyze the Fourier spectrum of the time-dependent oscillation signal and find a nontrivial spectral structure that is double peaked for certain parameters. We show that the effects observed in alkali vapor are universal and expected in any system with a moderate inhomogeneity driven by an external field.