Tunneling rates of single electrons on liquid helium in an extracting field

Abstract

We calculated the tunneling rates of single electrons from the quasi-stationary states on both liquid He-4 and He-3 in an extracting electric field. The rates were obtained from the widths of the resonance lineshapes of the asymptotic amplitude of the wave function for the electron. The calculations were carried out in the limit of strong tunneling which leads to tunneling rates of the order of 1 GHz, and is of recent interest in a proposed quantum-computer system using the electronic states of electrons on helium as qubits. We find that the resonances can, in general, be described by Fano lineshapes. Our results, in addition to presenting quantitative information involving the read-out operations of qubits, clarify that when tunneling is weak the resonances are sharp and more accurately Lorentzian and that the observed Fano lineshapes result from strong tunneling leading to fat resonances and hence asymmetry.