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Physical Review A

High-order cyclo-Raman scattering of a laser by a single electron

Yujie J. Ding, A. E. Kaplan

Published Sep 1, 1988• 7 citations
Publisher

Abstract

``Cyclo-Raman resonance'' of a single electron (i.e., cyclotron motion of an electron driven by optical fields) in the nth order at the cyclotron frequency ${\ensuremath{\Omega}}_{c}$ can be excited by biharmonic laser beams with their frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ such that ${\ensuremath{\omega}}_{1}$-${\ensuremath{\omega}}_{2}$\ensuremath{\approxeq}n${\ensuremath{\Omega}}_{c}$. This effect exhibits hysteresis, ``prohibited'' and ``allowed'' orbits of excitation, phase multistability, and the optical Stark effect.

DOI
10.1103/physreva.38.3109

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Cyclo-Raman resonance'' of a single electron (i.e., cyclotron motion of an electron driven by optical fields) in the nth order at the cyclotron frequency ${\ensuremath{\Omega}}_{c}$ can be excited by biharmonic laser beams with their frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ such that ${\ensuremath{\omega}}_{1}$-${\ensuremath{\omega}}_{2}$\ensuremath{\approxeq}n${\ensuremath{\Omega}}_{c}$. This effect exhibits hysteresis, prohibited'' and ``allowed'' orbits of excitation, phase multistability, and the optical Stark effect.
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., E1,2 ≃ 10−2V/cm if λ1,2 ≃ 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.
Optical nutation at the Raman-active transition 6P 1/2−6P 3/2 of thallium atoms (ω R /2πc=7793 cm −1) under resonant Raman excitation by a biharmonic picosecond pulsed field, giving rise to substantial motion of the population, is detected. Optical nutation appears as an oscillatory behavior of the energy of the anti-Stokes scattering of probe pulses, which follow with a fixed delay, as a function of the product of the energies of the excitation pulses. As a result of the dynamic Stark effect, which decreases the frequency of the transition under study, resonance excitation conditions are satisfied for negative initial detunings of the Raman excitation frequency from resonance. The Raman scattering cross section for the transition under study is estimated by comparing the experimental data with the calculations.
The hysteresis curve of the bistable cyclotron motion of a single electron in a magnetic field driven by external microwave radiation is obtained by only varying the phase of a phase-sensitive back-action-evading experimental setup. Thus the steady-state solution of the cyclotron motion includes two branches which could be switched by only changing the phase of the device. This effect is of particular interest as an example of the influence of the noise properties of the measurement apparatus on a microscopic system subjected to measurement.