Hysteretic and multiphoton optical resonances of a single cyclotron electron

Due to tiny relativistic effects, a host of nonlinear interactions of microwave or optical radiation with a single trapped electron in a strong magnetic field is feasible. This phenomenon, relativistic so-called nonlinear optics of a single electron, includes hysteretic and isolas resonances and various multiphoton excitations, in particular, stimulated cyclo-Raman resonances and subharmonics of any order. The authors develop a unified approach to all these effects. Results valid for arbitrary electron energy and for any order of interaction are obtained, and higher order cyclo-Raman resonances are predicted