Nonlinear Excitation of a Single Trapped Electron

One of the most fundamental systems in which to investigate nonlinear physical effects is the interaction of a single bound electron with a time-varying electromagnetic field. If the field is spatially inhomogeneous and the amplitude of the electron's motion is non-zero, then the dipole approximation for the interaction is no longer strictly correct. The force exerted on the electron by the field must be evaluated at the instantaneous position of the electron, resulting in a nonlinear interaction. One effect of this nonlinearity is that resonant excitation of the electron's motion can occur when the frequency of the field is an integer multiple of the electron's oscillation frequency. This is called subharmonic excitation of the electron's motion. The nonlinear interaction between an electron and spatially inhomogeneous field was investigated both theoretically and experimentally in this project. A Penning trap system was constructed which allowed single electrons to be stably bound and the response of their motion to external fields measured. The Penning trap was operated in a cryogenic environment and the oscillation frequencies of the trapped electron's motion were adjusted to be in the radio and microwave frequency spectrum. A number of low order nonlinear effects were observed and will be discussed, including subharmonic excitation, hysteresis, bistability, frequency mixing, and parametric processes. These effects are related to theories of multipole excitation, stimulated Raman scattering, and multi-wave mixing. This nonlinear system has potential future applications in the field of optical frequency metrology.