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We consider the application of a small in-plane magnetic field to electrons on a helium surface in a perpendicular magnetic field. Certain states that were bound to the helium surface then dissolve into the continuum turning into long-lived resonances. As a result microwave absorption lines acquire an asymmetric Fano lineshape that is tunable by varying the microwave polarisation or the in-plane magnetic field. Electrons trapped in a formerly bound state will tunnel off the surface of helium; we show that under suitable circumstances this ``radioactive decay'' can show damped oscillations rather than a simple exponential decay. The mechanism for oscillatory exponential decay is not specific to electrons on Helium and this effect may also be relevant elsewhere in physics.

Nonexponential tunneling and control of microwave absorption lineshapes via Fano resonance for electrons on helium