Relativistic nonlinear optics of a single cyclotron electron

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Abstract
Because of relativistic nonlinear effects large amplitude cyclotron motion of a free electron can be excited by two laser beams with frequencies much higher than the cyclotron frequency Ω. The laser frequencies can differ either by Ω (three-photon resonance) or 2Ω (four-photon resonance). The excited cyclotron motion displays a hysteretic resonance based solely on the relativistic mass effect. To observe three-photon hysteretic excitation, a He-Ne laser with a few microwatts of power is sufficient.