Abstract

We showed earlier¹ that a single electron in a magnetic field can exhibit hysteretic cyclotron resonance when the frequency of driving EM field is close to the cyclotron frequency (usually in the microwave range). This effect is based on a slightly relativistic mass effect of the electron; recently it has been observed experimentally.² Here we show that based on the same small relativistic dependence, yet another nonlinear optical effect can be predicted: large excitation of microwave (or rf) cyclotron motion of a single electron in the Penning trap by two optical waves, when their respective frequencies ω₁ and ω₂ differ approximately by the double cyclotron frequency ω₀, i.e., |ω₁ − ω₂| ≃ 2ω₀. The critical amplitudes of the optical fields required to attain such an excitation are very low, e.g., E_1,2 ≃ 10⁻²V/cm if λ_1,2 ≃ 10 μm and λ₀ ≃ 2 mm. From the quantum electronics standpoint this effect may be regarded either as a three-photon process (ω₀ = |ω₁ − ω₂| −ω₀) of as a higher-order stimulated Raman scattering. Since the conduction electrons in some semiconductors may also exhibit pseudo-relativistic nonlinear cyclotron resonance,³ the analogous three-photon optical excitation may also be expected in semiconductors.

© 1985 Optical Society of America