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Chinese Physics Letters

The effects of transverse relaxation and optical pumping on the resonance fluorescence

TAN WEI-HAN, Weiping Zhang

Published Jul 1, 1985• 4 citations
Publisher

Abstract

Although the resonance fluorescence spectrum of coherent light scattering from a two-level atom has been discussed in many papers, the effects of longitudinal, transverse relaxation and optical pumping have not yet been considered simultaneously in the motion equations. By solving the optical Bloch equations including the longitudinal relaxation time T 1 , transverse relaxation time T 2 and optical pumping parameter Δ 0 , in the case T 2 /T 1 <<1, we obtain the spectrum with dip in the central peak besides the familiar spectrum of three peaks. In addition, we find that the parameter Δ 0 and detuning Δω have influence on the symmetry, height and width of the spectrum of the three peaks.

DOI
10.1088/0256-307x/2/7/006

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Although the resonance fluorescence spectrum of coherent light scattering from a two-level atom has been discussed in many papers, the effects of longitudinal, transverse relaxation and optical pumping have not yet been considered simultaneously in the motion equations. By solving the optical Bloch equations including the longitudinal relaxation time T 1 , transverse relaxation time T 2 and optical pumping parameter Δ 0 , in the case T 2 /T 1 <<1, we obtain the spectrum with dip in the central peak besides the familiar spectrum of three peaks. In addition, we find that the parameter Δ 0 and detuning Δω have influence on the symmetry, height and width of the spectrum of the three peaks.
A beam of two-level atoms or ions excited by the resonant laser radiation orthogonal to the beam is observed from the third orthogonal direction. The well known resonance fluorescence three-peaked spectrum is deformed when the atoms or ions forming the beam oscillate at the Rabi frequency in the direction of the laser radiation wavevector, and the characteristic feature appears on the spectrum. The calculation based on the Bloch equations is presented and possible applications of the effect are discussed.
A quantum statistical theory of resonant optical phenomena is developed for the case when the fluctuations of the laser, used for exciting transitions, are important. The general equations describing the dynamics of a relaxing two-level atom (TLA) are solved exactly for different types of mean values and the two-time amplitude and intensity correlations. The phase-diffusion model is adopted for laser fluctuations. The exact results are used to analyze the effect of laser fluctuations on a number of optical effects-optical free-induction decay, adiabatic following, the spectrum of the scattered light from a relaxing TLA, the energy-absorption spectrum from a weak field, Hanle resonances, etc. In each case, the laser fluctuations are found to affect in an important way the characteristics of the above optical-resonance phenomena. For example, the spectrum of scattered radiation from a TLA has the usual three-peak structure for fields at resonance and with strengths $\ensuremath{\alpha}$ above the threshold and for $\ensuremath{\alpha}\ensuremath{\gg}{\ensuremath{\gamma}}_{c}$; however, now the peak heights (widths) are in the ratio 3x3x3x (23x\frac{2}{3x}3x2​), $x=\frac{[{\ensuremath{\gamma}}_{c}+\frac{({T}_{1}^{\ensuremath{-}1}+{T}_{2}^{\ensuremath{-}1})}{3}]}{[2{\ensuremath{\gamma}}_{c}+{T}_{2}^{\ensuremath{-}1}]}$, where ${\ensuremath{\gamma}}_{c}^{\ensuremath{-}1}$ is the correlation time for laser phase fluctuations. For ${\ensuremath{\gamma}}_{c}\ensuremath{\gg}\ensuremath{\alpha}$, one gets a single-peak spectrum. The laser field is treated as a second-quantized field with excitation in either a coherent state or a Fock state. The results, obtained by straightforward perturbation theory, but valid for arbitrary values of the relaxation parameters, detuning, and the laser correlation time, are also presented.
The effects of different laser line shapes on the intensity and spectrum of resonance fluorescence from a two-level atom are investigated. The laser model considered is that of an ideal single-mode laser operating high above threshold, with constant amplitude and undergoing phase-frequency fluctuations analogous to Brownian motion. As the correlation time of the frequency fluctuations increases from zero to infinity, the laser line shape changes from Lorentzian to Gaussian in a continuous way. It is shown that for intermediate and strong fields, the average intensity of fluorescence in the case of a resonant broadband Lorentzian line shape is higher than that in the case of a Gaussian line shape with the same bandwidth and total power. This is in contrast to the weak-field case where the higher peak power of the Gaussian line shape makes it more effective than the Lorentzian line shape. It is also shown that in the case of a nonzero frequency correlation time (non-Lorentzian line shape) the intensity of fluorescence undergoes non-Markovian fluctuations. In relation to the spectrum of resonance fluorescence, it is shown that as the line shape is varied from Lorentzian to Gaussian the following changes take place: In the case of off-resonance excitation, the asymmetry of the spectrum decreases. In the case of resonant excitation, the center-peak to side-peak height ratio for the triplet structure increases. Moreover, the recently predicted center-line dip, which develops in the spectrum in the case of broadband excitation when the Rabi frequency and the bandwidth are nearly equal, becomes increasingly deeper.
Quantum fluctuations in a laser with two different relaxation times are considered, i.e., transverse (polarization relaxation) and longitudinal (population relaxation) in the case in which the cavity transmission band half-width is much smaller than the transverse width and much larger than the longitudinal one. The lasing frequency detuning from the transition frequency of a two-level system is assumed to be arbitrary in this case, and it is necessary to take into account the contribution of two-particle correlators into the dispersion and laser linewidth. The results are considered as applied to a semiconductor laser.