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Topical Meeting on Optical Bistability (OB)

Cyclotron Bistability of Electrons in Vacuum and Semiconductors

A. E. Kaplan

Published Jan 1, 1983• 0 citations
Publisher

Abstract

The feasibility of an optical cyclotron bistability of free electrons in vacuum as well as of conductive electrons in semiconductors is discussed. It was recently shown by us1 that the cyclotron bistability of the free electrons can be based on the dependence of a cyclotron frequency of forced oscillations on the relativistic mass of the electron and, hence, on its momentum (or kinetic energy). It was also suggested that1 the analogous effect could be feasible in semiconductors whose conductive electrons have a particularly strong dependence of their effective masses on energy (or momentum) of their excitation. The main advantageous features of the cyclotron bistability in semiconductors is that (i) the effective mass of electrons in some semiconductors (e.g. InSb) is very small which results in a considerable decrease of a required magnet field for a given resonant frequency, and (ii) the nonlinearity associated with conductive electrons in semiconductors is by many orders of magnitude larger than the relativistic nonlinearity of free electrons, which allows for a fairly low critical pumping intensity, even if taking into consideration a faster relaxation time in semiconductors.

DOI
10.1364/obi.1983.thb19

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The feasibility of an optical cyclotron bistability of free electrons in vacuum as well as of conductive electrons in semiconductors is discussed. It was recently shown by us1 that the cyclotron bistability of the free electrons can be based on the dependence of a cyclotron frequency of forced oscillations on the relativistic mass of the electron and, hence, on its momentum (or kinetic energy). It was also suggested that1 the analogous effect could be feasible in semiconductors whose conductive electrons have a particularly strong dependence of their effective masses on energy (or momentum) of their excitation. The main advantageous features of the cyclotron bistability in semiconductors is that (i) the effective mass of electrons in some semiconductors (e.g. InSb) is very small which results in a considerable decrease of a required magnet field for a given resonant frequency, and (ii) the nonlinearity associated with conductive electrons in semiconductors is by many orders of magnitude larger than the relativistic nonlinearity of free electrons, which allows for a fairly low critical pumping intensity, even if taking into consideration a faster relaxation time in semiconductors.
It was recently predicted by us that cyclotron resonance of free electrons in vacuum and conduction electrons in semiconductors may exhibit bistable and hysteretic behavior which is due to the relativistic mass-effect (or pseudo relativistic-in semiconductors). Consistent with this prediction, the hysteretic cyclotron resonance of a trapped single electron in vacuum has recently been experimentally observed by Gabrielse et al. A preliminary estimate shows that their experimental results are consistent with the relativistic nature of the observed hysteresis. In this paper we consider this phenomenon as ultimate bistability since it is based on the most fundamental mechanism of nonlinearity (the relativistic mass-effect), involves the interaction of an EM wave with the simplest single elementary particle, and exhibits the first known intrinsic bistability with no macroscopic optical feedback. We also show that a hysteretic resonance of a Single electron based on relativistic effects is feasible also in a parabolic potential (with no magnetic field required to attain a resonance).
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.
Semiconductors exhibit large optical nonlinearities near the band edge because of resonance enhancement. Optical bistability occurs when the optical nonlinearities are coupled with feedback. In bulk GaAs and GaAs–AlGaAs multiple-quantum-well superlattices, the nonlinearity arising from the presence of the free-exciton resonance has produced room-temperature optical bistability with a few milliwatts of power. The formation of biexcitons in CuCl, the saturation of the bound exciton on CdS, and band-filling effects in InSb, InAs, and HgCdTe lead to observation of bistability in these materials. A bistable etalon can be operated in an optical-gate mode to generate optical analogs of electronic gates such as and, or, and nor. It has been demonstrated that a GaAs optical NOR gate responds in ∼1 psec, using only ≲3 pJ of energy. However, because of the carrier lifetime of a few nanoseconds, the repetition rate of the NOR gate is now limited to a few hundred megahertz.
Relaxation cavityless optical bistability is studied when a semiconductor is exposed to light quanta with an energy exceeding the transition energy and the free-electron relaxation time depends on temperature. The numerical analysis of dynamic equations for temperature and free-electron density demonstrates that 11 regimes of light-semiconductor interaction are possible. The regimes are classified in terms of the features of temperature-intensity characteristic curves, namely, by the number and arrangement of instability and quasistability segments and by the presence or absence of bistability. It is found that both the upper and the lower branch of a bistable characteristic curve may be unstable, which results in spontaneous switchings between the respective states. Similarly, if the upper state is unstable and the lower state is stable, a small perturbation of the parameters (free-electron temperature and density) near the former causes the transition to the oscillatory regime. If the upper state is unstable and a small perturbation of the lower (stable) state excites a damped oscillation, spontaneous switchings result if the fluctuating temperature exceeds some critical value for the lower state.
The cyclotron and spin resonance of free electrons field confined in a small volume in ultrahigh vacuum have been observed via the rapid loss of electrons when their cyclotron motion is excited by the rf field and spin-dependent collision processes with polarized Na atoms in a beam, respectively. The electrons were polarized by spin exchange and then monitored through the spin dependence of the excitation process $e+\mathrm{Na}(3S)\ensuremath{\rightarrow}e+{\mathrm{Na}}^{*}(3P)$ and hence of their cooling rate.