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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Influence of the Mollow triplet on the spectrum of the scattered radiation by a multiatom system

B. B. Averbukh

Published Jan 30, 2007• 0 citations
Publisher

Abstract

It is well known, that for large Rabi frequencies the spectrum of resonance fluorescence of a single two-level atom contains three separate lines (Mollow triplet). Question naturally arise as to what effect sidebands of this triplet might have on the spectrum of the scattered radiation in the multiatom case. The purpose of the present paper, therefore, is to obtain a space-frequency dependent spectrum of the scattered radiation in backward direction (reflection) by a system of N noninteracting atoms. We neglect the translational motion of the atoms and multiple scattering and concentrate on the effects of the collective scattering. It is shown that spectral energy of the scattered radiation consists of two different parts. One is the incoherent and isotropic emission of fluorescence. The energy of radiation in this case is the sum of the atomic energies and then is proportional to N . The other is the collective emission (interference effect). The energy of radiation in this case is spatially focused in a small solid angles about three propagation directions and then is proportional to N2. Thus the frequency Mollow triplet is transformed into the space-frequency dependent triplet.

DOI
10.1117/12.726607

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It is well known, that for large Rabi frequencies the spectrum of resonance fluorescence of a single two-level atom contains three separate lines (Mollow triplet). Question naturally arise as to what effect sidebands of this triplet might have on the spectrum of the scattered radiation in the multiatom case. The purpose of the present paper, therefore, is to obtain a space-frequency dependent spectrum of the scattered radiation in backward direction (reflection) by a system of N noninteracting atoms. We neglect the translational motion of the atoms and multiple scattering and concentrate on the effects of the collective scattering. It is shown that spectral energy of the scattered radiation consists of two different parts. One is the incoherent and isotropic emission of fluorescence. The energy of radiation in this case is the sum of the atomic energies and then is proportional to N . The other is the collective emission (interference effect). The energy of radiation in this case is spatially focused in a small solid angles about three propagation directions and then is proportional to N2. Thus the frequency Mollow triplet is transformed into the space-frequency dependent triplet.
We investigate the fluorescence spectrum of a two-level atom driven by a multiple amplitude-modulated field. The driving field is modeled as a polychromatic field composed of a strong central (resonant) component and a large number of symmetrically detuned sideband fields displaced from the central component by integer multiples of a constant detuning. Spectra obtained here differ qualitatively from those observed for a single pair of modulating fields [B. Blind, P.R. Fontana, and P. Thomann, J. Phys. B 13, 2717 (1980)]. In the case of a small number of the modulating fields, a multipeaked spectrum is obtained with the spectral features located at fixed frequencies that are independent of the number of modulating fields and their Rabi frequencies. As the number of the modulating fields increases, the spectrum ultimately evolves to the well-known Mollow triplet with the sidebands shifted from the central component by an effective Rabi frequency whose magnitude depends on the initial relative phases of the components of the driving field. For equal relative phases, the effective Rabi frequency of the driving field can be reduced to zero resulting in the disappearance of fluorescence spectrum, i.e., the atom can stop interacting with the field. When the central component and the modulating fields are $180\ifmmode^\circ\else\textdegree\fi{}$ out of phase, the spectrum retains its triplet structure with the sidebands located at frequencies equal to the sum of the Rabi frequencies of the component of the driving field. Moreover, we show that the frequency of spontaneous emission can be controlled and switched from one frequency to another when the Rabi frequency or initial phase of the modulating fields are varied.
This paper is concerned with two rather basic phenomena: the incoherent fluorescence spectrum of an atom driven by an intense laser field and the coupling of the atom to the (empty) modes of the radiation field. The sum of the many-photon processes gives rise to the inelastic part of the atomic fluorescence, which, for a two-level system, has a well-known characteristic three-peak structure known as the Mollow spectrum. From a theoretical point of view, the Mollow spectrum finds a natural interpretation in terms of transitions among laser-dressed states which are the energy eigenstates of a second-quantized two-level system strongly coupled to a driving laser field. As recently shown, the quasi-energies of the laser-dressed states receive radiative corrections which are nontrivially different from the results which one would expect from an investigation of the coupling of the bare states to the vacuum modes. In this article, we briefly review the basic elements required for the analysis of the dynamic radiative corrections, and we generalize the treatment of the radiative corrections to the incoherent part of the steady-state fluorescence to a three-level system consisting of 1S, 3P and 2S states.
The effect of collisions on the resonance fluorescence spectrum of two-level atoms excited by monochromatic resonance radiation is studied. Analysis is performed for systems where the Doppler broadening is small compared to the collision frequency (high buffer gas pressures) and for the general case where collisions arbitrarily change the phase of the radiation-induced dipole moment (from completely interrupted to completely unaffected phase of the dipole moment). Both at a relatively low and at a high excitation radiation intensity, the resonance fluorescence spectrum is shown to depend on whether the two-level system is closed or open. This is especially true for the narrow unshifted Rayleigh scattering line. It is shown that, although the absorption line is homogeneously broadened, the resonance fluorescence spectrum exhibits a clearly pronounced anisotropy. In a direction close to the direction of propagation of the excitation radiation, the Rayleigh scattering line is maximally narrowed. Under certain conditions (that can easily be created in experiments), the width of this line is proportional to the diffusion coefficient of atoms interacting with the radiation.
It is demonstrated that both the Mollow triplet and Mandelshtam-Brillouin splitting must be manifested in the indicatrix of light scattering from a system of atoms. Frequency shifts in the Mollow triplet are independent of the observation direction. The magnitude of splitting in the Mandelshtam-Brillouin doublet depends on the angle of scattering and, under certain conditions, can be equal to that in the Mollow triplet. Under these conditions, the scattered light spectrum exhibits five components instead of the six observed in the general case.
The resonance fluorescence spectrum of a two-level atom in a classical light field, whose phase is changed by a feedback system by π after the detection of each spontaneous photon, has been calculated. The spectrum resembles the well-known Rautian-Mollow triplet. However, the sidebands become sharply asymmetric at a nonzero frequency detuning of the light field from the atomic resonance transition. In addition, the spectrum retains the pronounced triplet shape even beyond the secular approximation, when the sidebands of the Rautian-Mollow structure become unresolved in the absence of the feedback.
The calculation is given of the spectral distribution of resonance fluorescence from an atom that is driven near a j=12j=\frac{1}{2}j=21​ to j=12j=\frac{1}{2}j=21​ transition by a monochromatic, xxx-polarized electric field and that is subject to radiation damping only. In accordance with Mollow's results for a two-level system, the power spectrum of the scattered radiation corresponding to the xxx component of the dipole moment contains a coherent part for all driving-field intensities. The coherent part is absent in the fluorescence radiation corresponding to the yyy and zzz components of the dipole moment. For weak driving fields all power scattered by these latter components is present in a narrow Lorentzian. Consistent with energy conservation, the width of the Lorentzian corresponds to the probability of excitation of the atom out of its ground level due to the presence of the driving field. For strong driving fields the power spectra corresponding to the xxx component and to the yyy or zzz component mainly differ in the heights and widths of their central incoherent band and their Rabi-precession-frequency-shifted side bands.