Abstract

The classical theory of cyclotron resonance of a single electron (or any other charged particle) suggests giant broadening of resonant cyclotron line due to a hysteresis based on relativistic mass-effect proposed in [1] and observed recently in [2]. The quantum theory of the same phenomenon developed here predicts a multiple-line spectrum of a driven cyclotron resonance with equidistantly-spaced lines which is due to relativistic shift of Landau levels. The spacing ΔΩ_sp between-lines is determined as ΔΩ_sp/Ω_o = ħΩ_o/m_oc², where Ω_o=eH_o/m_oc is the unperturbed cyclotron frequency of electron. The linewidth ΔΩ_R of each of these lines is strictly of radiation nature, with the relative linewidth Γ = ΔΩ_R/Ω_o = (2/3)r_ek_o, where r_e = e²/m_oc² = 2.8×10⁻¹³cm is the classical radius of electron, and k_o = Ω_o/c. In the case of a single electron at λ_o(= 2π/k_o) = 2mm, Γ ≈ 0.7×10⁻¹¹.

© 1988 Optical Society of America