Near-ionization-threshold emission in atomic gases driven by intense sub-cycle pulses

We study theoretically the dipole radiation of a hydrogen atom driven by an intense sub-cycle pulse. The time-dependent Schr\"odinger equation for the system is solved by ab initio calculation to obtain the dipole response. Remarkably, a narrowband emission lasting longer than the driving pulse appears at a frequency just above the ionization threshold. An additional calculation using the strong field approximation also recovers this emission, which suggests that it corresponds to the oscillation of nearly-bound electrons that behave similarly to Rydberg electrons. The predicted phenomenon is unique to ultrashort driving pulses but not specific to any particular atomic structure.