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Acta Physica Polonica A

Resonance Fluorescence Spectrum of Two-Level Atoms Driven by Two Noncollinear Classical Fields

Bogdan Lobodzinski

Published Sep 1, 1997• 1 citation
Publisher

Abstract

The resonance fluorescence spectrum of au ensemble of two-level atoms driven by two classical, frequency degenerate and noncollinear laser beams is investigated.It has been found that the spatially-averaged resonance fluorescence spectra differ significantly from the spectra of two-level atoms cal- cula.ted for the single-beam excitation.Tle differences were noticed in the number of peaks, their positions and shapes and in their dependences on au angle between wave vectors of the incident beams.

DOI
10.12693/aphyspola.92.501

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The resonance fluorescence spectrum of au ensemble of two-level atoms driven by two classical, frequency degenerate and noncollinear laser beams is investigated.It has been found that the spatially-averaged resonance fluorescence spectra differ significantly from the spectra of two-level atoms cal- cula.ted for the single-beam excitation.Tle differences were noticed in the number of peaks, their positions and shapes and in their dependences on au angle between wave vectors of the incident beams.
Resonance fluorescence of two two-level atoms driven by a coherent laser field propagating parallel to the interatomic axis is examined, taking into account the dipole-dipole interaction. We show that the number of peaks in the fluorescence intensity depends on the direction of observation with respect to the interatomic axis and on whether the system is driven by a standing-wave or a running-wave laser field. When the system is driven by the standing-wave field the fluorescence intensity shows two peaks and a dip for an observation direction perpendicular to the interatomic axis and three peaks in the direction parallel to it. When the system is driven by the running-wave field only two peaks are observed for the perpendicular direction. We explain these features in terms of the collective states of the system and show that the directional effect can be attributed to the fact that the antisymmetric state of the system does not radiate in the direction perpendicular to the interatomic axis. Photon statistics also demonstrate the directional effect for the standing-wave field. Frequency regimes are found where sub-Poissonian photon statistics occur. Depending on the direction of the observation, a state close to a Fock state can occur for one or two frequencies of the driving field, corresponding to zero-photon-number fluctuations or maximum sub-Poissonian behavior. The fluorescence spectrum is found to depend on the direction of observation and the interatomic separation. For small interatomic separations and a standing-wave driving field the spectrum exhibits seven lines for the perpendicular direction and 13 lines in the direction parallel to the interatomic axis. For the running-wave field the spectrum shows 13 lines independent of the direction of observation. Moreover, we show that for particular interatomic separations dark regimes appear in the spectrum. We discuss the effect of the dipole-dipole interaction on the dark states and explain the spectral features in terms of the dressed-atom model. We also consider the absorption spectrum of a weak probe beam illuminating the two-atom system. We show that apart from a weak dispersion structure, the spectrum shows large peaks as one of the atoms is moved to successive nodes of the field.
Resonance-fluorescence power spectrum of two-level atoms driven by a strong monochromatic laser field is discussed, taking into account effects due to the dipole-dipole interaction between the atoms. For two atoms confined to a region smaller than the wavelength of the driving field, we predict significant deviations of the power spectrum from the single-atom case. The two-atom spectrum is nonsymmetric, the wing peaks are shifted from their Rabi-frequency positions, and additional maxima may appear.
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.
The fluorescence spectrum of a system of a large number of two-level atoms driven by a strong resonant field has been treated, so far, for atoms contained in a region that is small compared to a wavelength. For high laser intensities resonances displaced from the line center by twice the Rabi frequency were predicted1-3 in addition to the usual Stark sidebands.4 We show that the explicit spatial distribution of the two-level atoms affects the shape of the radiation spectra and leads to the appearance of additional sidebands.
The steady-state populations, the fluorescent intensity-intensity correlation function, and the resonance fluorescence and absorption spectra of a two-level atom bichromatically driven by a strong, coherent field and a weak, stochastic field with tunable carrier frequency and wide bandwidth are investigated analytically. Surprisingly, the population is inverted if the stochastic field is appropriately detuned from the coherent field, which is assumed resonant with the atomic transition. The resonance fluorescence spectrum still displays a three-peaked structure, but with linewidths and heights that depend upon the frequency and bandwidth of the stochastic field as well as the intensities of both fields. Asymmetric fluorescence spectra are found when the coherent field is detuned from the atomic resonance frequency. The intensity-intensity correlation function varies dramatically with the carrier frequency of the stochastic field. For appropriate choices of the parameters, the fluorescent emission of the atom is antibunched for all time. The absorption spectral features also deviate significantly from those of the monochromatically driven atom. By appropriately tuning the stochastic field, one finds that a sharp peak (absorption) or hole (gain) can occur at line center and the probe beam can be amplified at either the lower-frequency Rabi sideband or the higher-frequency sideband and the inversionless gain can be enhanced.