Abstract

We showed earlier¹ that, due to a small relativistic change of mass, a single electron can exhibit pronounced hysteretic cyclotron resonance when the frequency of driving the electromagnetic field is near the cyclotron frequency (usually in a microwave range). Consistent with this prediction, this effect has recently been observed in experiment² with a single electron trapped for 10 months in a Penning trap. Here we show that, due to the combination of the relativistic mass effect and two other fundamental effects (the Doppler effect and the Lorentz force), still another group of nonlinear optical effects is feasible, the large excitation of (microwave) cyclotron motion of an electron by two optical waves with their respective frequencies ω₁ and ω₂ (ω₁ > ω₂) being much higher than the cyclotron frequency Ω (ω₁, ω₂ ≫Ω) and differing by either Ω or 2Ω.

© 1986 Optical Society of America