When an attosecond XUV pulse propagates through a medium, the spectrum of the transmitted light shows narrow absorption lines characteristic of the medium. For example, in hydrogen the spectrum would show absorption lines at the 1s-2p transition. This is paradoxical, since the uncertainty principle says that a short duration and a narrow linewidth cannot both be achieved. What really happens is that the attosecond pulse creates a superposition of quantum states in the atom, leading to a long free induction decay. The emission from the decay is long in time, and hence narrow in frequency.

At NRC, we showed that we could control this process in molecular hydrogen by creating a coherence between two rotational states. Depending on the relative phase between the states, the absorption line shape could be changed from Lorentzian to Fano.

We also showed that we could achieve optical gain, i.e. lasing without a population inversion.

Peng Peng, Yonghao Mi, Marianna Lytova, Mathew Britton, Xiaoyan Ding, A. Yu Naumov, P. B. Corkum, D. M. Villeneuve,
Coherent Control of Ultrafast Extreme Ultraviolet Transient Absorption,
Nature Photonics 16, 45–51 (2022)DOI PDF