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Journal of Modern Optics

The asymptotic behaviour of the spectrum of resonance fluorescence

Martin Bodo Plenio

Published Oct 1, 1996• 2 citations
Publisher

Abstract

The spectrum of resonance fluorescence from laser-driven multi-level systems is investigated and especially its asymptotic frequency dependence in the wings. Analytical results are presented and the transitions within multilevel systems are classified into three categories according to the asymptotic frequency dependence of their spectra. Under certain conditions an arbitrarily fast asymptotic fall-off behaviour of the spectrum is found which, for intermediately strong driving fields, leads to subnatural linewidths. Numerical examples are presented to illustrate the analytical results.

DOI
10.1080/09500349608232878

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The spectrum of resonance fluorescence from laser-driven multi-level systems is investigated and especially its asymptotic frequency dependence in the wings. Analytical results are presented and the transitions within multilevel systems are classified into three categories according to the asymptotic frequency dependence of their spectra. Under certain conditions an arbitrarily fast asymptotic fall-off behaviour of the spectrum is found which, for intermediately strong driving fields, leads to subnatural linewidths. Numerical examples are presented to illustrate the analytical results.
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We study how the spectral properties of resonance fluorescence propagate through a two-atom system. Within the weak-driving-field approximation we find that, as we go from one atom to the next, the power spectrum exhibits both subnatural linewidth narrowing and large asymmetries while the noise spectrum of the squeezed quadrature narrows but remains otherwise unchanged. Analytical results for the observed spectral features of the fluorescence are provided and their origin is thoroughly discussed.
We investigate the spectrum of resonance fluorescence of laser-driven three-level systems in the V or $\ensuremath{\Lambda}$ configuration where one transition is metastable. If the laser driving the weak transition has a sufficiently small Rabi frequency we find an extremely narrow structure in the resonance fluorescence spectrum of the strong transition. Analytical expressions approximating the spectrum are given and the properties of the spectrum are discussed. With the help of a simplified model of resonance fluorescence emitted on the strong transition we are able to show that the origin of the narrow peak can be traced back to electron shelving, i.e., to the existence of light and dark periods in the resonance fluorescence emitted on the strong transition.
The stationary second-order spectrum of the resonance-fluorescence light from a vibronic system is studied in a nonperturbative manner. In the model used the potential energy surfaces for the vibrational motion in the electronic ground state and in the excited state are assumed to be displaced and distorted relative to each other. The calculations are performed for the case when the frequency of the driving laser field is tuned to the vibrationless electronic transition. In particular, in the high-driving-field limit the vibrationless transition exhibits a triplet structure, the sidebands being narrower and higher in comparison with the well-known two-level case. The Raman lines are shifted and split into doublets, the linewidths being determined by the electronic as well as the vibrational relaxation rates.
This study concerns the shape of the resonance fluorescence spectrum emitted by a V-type three-level atom driven by two coherent fields which are resonant with the transitions connecting the ground state and the second and third level, respectively. We are especially interested in monitoring the spontaneous emission from the top level to the ground state. If the field connecting levels 1 and 2 is absent or small, the spontaneous emission from level 3 is characterized by the standard Mollow spectrum. If instead the 1-2 transition is saturated, the spectrum of resonance fluorescence from the top level is characterized by the following signatures: (i) the appearance of sidebands due to Rabi splitting effects, (ii) a reduction of its integrated area because of coherent population trapping1, and (iii) a significant reduction of its linewidth if the natural lifetime of level 2 is longer than level 3. The latter effect is especially interesting and rather unexpected, as the decay properties of an optical transition are being transferred to another by controlling the relative magnitudes of the driving fields. We have carried out our calculations with the help of the regression theorem and also developed a simple physical interpretation in terms of appropriate dressed states2.
Our investigation is focused on obtaining analytical results describing the resonance fluorescence and weak probe absorption spectra of a driver Lambda-system under the Raman resonance condition. For the saturation field limit and within the rotating wave approximation (RWA) the resonance fluorescence and weak probe absorption spectra are calculated for the case of unequal driving fields strengths and non-zero one-photon detunings, generalizing the previously known results. A novel contribution derived is the nonpositive nonlorentzian part of the spectrum, originating from the specific quantum properties of the atomic correlation functions. This contribution is asymptotically small under given conditions and, therefore, determines behavior of the resonance fluorescence spectrum wings and the absorption spectrum in the vicinities of the driving field frequencies. Beyond the RWA, the spectral structures due to the off-resonant four-photon atomic excitations are calculated. They consist of a coherent and two broadened spectral lines centered at the four-photon frequencies 2(omega) L-(omega) 1L and 2(omega) +1)/ - (omega) L4/ respectively, where (omega l and (omega) (superscript 1$L are the driving laser frequencies.