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Optics Communications

Resonance fluorescence of linear and nonlinear oscillators. An insight into vacuum fluctuations

I. R. Senitzky

Published Jun 1, 1989• 0 citations
Publisher
DOI
10.1016/0030-4018(89)90006-0

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Resonance fluorescence of linear and nonlinear oscillators according to classical and quantum theories: An insight into vacuum fluctuations

I. R. Senitzky

The resonance fluorescence spectrum of linear and nonlinear oscillators driven by a monochromatic field of frequency ${\ensuremath{\omega}}_{0}$, near the resonant frequency \ensuremath{\omega}, is calculated both classically and quantum mechanically. The result for the linear oscillator is the same in both calculations: a \ensuremath{\delta} function at ${\ensuremath{\omega}}_{0}$. For the nonlinear oscillator, however, the classical and quantum-mechanical spectra near resonance are qualitatively different: Classically, a \ensuremath{\delta} function at ${\ensuremath{\omega}}_{0}$ is obtained; quantum mechanically, a weak-field calculation leads to a \ensuremath{\delta} function at ${\ensuremath{\omega}}_{0}$ together with finite-width peaks nearby. An intuitive explanation for the difference is suggested by the examination of the quantum-mechanical energy-correlation function for the linear oscillator. This function describes energy oscillations with frequencies within a band centered at ${\ensuremath{\omega}}_{0}$-\ensuremath{\omega}. The oscillations can be interpreted as the beating of the driven oscillation with those produced by the vacuum fluctuations (the latter having a frequency spread of the order of the relaxation constant). Because of the nonlinearity, the energy oscillation modulates the effect of the driving field to produce sidebands. Higher-order processes produce additional peaks. A heuristic picture of vacuum fluctuations is developed.

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We investigate the resonance fluorescence spectrum of a bulk semiconductor subject to an injection current and an arbitrarily intense electromagnetic wave. We assume that the electronhole system is in quasiequilibrium due to the rapid carrier-carrier intraband scattering. The analysis is based on the generalized Bloch equations1 for semiconductors. Although the fast carrier scattering heavily damps the electronic coherence, it nevertheless allows the medium to follow adiabatically the relatively slowly varying field fluctuations. As a consequence, the resonance fluorescence spectra reveal asymmetric dips generated by pump scattering off carrier-density pulsations induced by the interference between the pump and vacuum mode. Similar to the two-level resonance fluorescence and probe absorption, the semiconductor probe absorption coefficient equals the difference between the resonance fluorescence and reabsorption coefficients. The results are important for nonlinear semiconductor spectroscopy and semiconductor laser instabilities.

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The resonance fluorescence spectrum of linear and nonlinear oscillators driven by a monochromatic field of frequency ${\ensuremath{\omega}}_{0}$, near the resonant frequency \ensuremath{\omega}, is calculated both classically and quantum mechanically. The result for the linear oscillator is the same in both calculations: a \ensuremath{\delta} function at ${\ensuremath{\omega}}_{0}$. For the nonlinear oscillator, however, the classical and quantum-mechanical spectra near resonance are qualitatively different: Classically, a \ensuremath{\delta} function at ${\ensuremath{\omega}}_{0}$ is obtained; quantum mechanically, a weak-field calculation leads to a \ensuremath{\delta} function at ${\ensuremath{\omega}}_{0}$ together with finite-width peaks nearby. An intuitive explanation for the difference is suggested by the examination of the quantum-mechanical energy-correlation function for the linear oscillator. This function describes energy oscillations with frequencies within a band centered at ${\ensuremath{\omega}}_{0}$-\ensuremath{\omega}. The oscillations can be interpreted as the beating of the driven oscillation with those produced by the vacuum fluctuations (the latter having a frequency spread of the order of the relaxation constant). Because of the nonlinearity, the energy oscillation modulates the effect of the driving field to produce sidebands. Higher-order processes produce additional peaks. A heuristic picture of vacuum fluctuations is developed.
Noise that can be attributed to vacuum fluctuations, usually referred to as quantum noise, is examined. It is shown that vacuum fluctuations of a single uncoupled mode do not constitute noise, in the sense of a random process, but the superposition of the fluctuations of a large number of modes does constitute, formally, noise. The effect of vacuum fluctuations of the free-space radiation field on a harmonic oscillator, a nondegenerate parametric amplifier, and a degenerate parametric amplifier, all driven by a prescribed sinusoidal field, is compared with the effect of classical noise. It is found that the coordinates of all systems respond in a formally similar manner to both vacuum fluctuations and classical noise. However, the resonance fluorescence spectrum---the evidence of ``detection''---is completely different for the two kinds of noise. The spectrum of the harmonic oscillator does not exhibit noise in response to vacuum fluctuations, but does so in response to classical noise. The spectra of the two types of parametric amplifiers do exhibit noise in response to vacuum fluctuations, but this noise differs from that in the classical case. An explanation for the difference is offered, based on the fact that the quantum fluctuations cannot do work, but can noise-modulate power from an outside source, which, for the parametric amplifiers, is the pump. In the analysis of noise from the degenerate parametric amplifier, it is shown that squeezed noise, viewed as an oscillation of the dispersion with a sufficiently low minimum, is generated in the same manner in the case of classical noise as in the case of quantum noise, and is due to phase conjugation.
We investigate the resonance fluorescence spectrum of a bulk semiconductor subject to an injection current and an arbitrarily intense electromagnetic wave. We assume that the electronhole system is in quasiequilibrium due to the rapid carrier-carrier intraband scattering. The analysis is based on the generalized Bloch equations1 for semiconductors. Although the fast carrier scattering heavily damps the electronic coherence, it nevertheless allows the medium to follow adiabatically the relatively slowly varying field fluctuations. As a consequence, the resonance fluorescence spectra reveal asymmetric dips generated by pump scattering off carrier-density pulsations induced by the interference between the pump and vacuum mode. Similar to the two-level resonance fluorescence and probe absorption, the semiconductor probe absorption coefficient equals the difference between the resonance fluorescence and reabsorption coefficients. The results are important for nonlinear semiconductor spectroscopy and semiconductor laser instabilities.