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Journal of Modern Optics

Fluorescence quenching and spectral narrowing from a two-level atom driven by a weak, narrow band, light field

William Smyth, S. Swain

Published Jul 1, 1999• 1 citation
Publisher

Abstract

We consider a single two-level atom driven by the output from a degenerate optical parametric oscillator. For squeezing bandwidths of the order of the natural atomic width and smaller, we report remarkable spectral profiles for the scattered light, including the existence of a narrow hole at line-centre. Under appropriate conditions, the spectrum may be both subnatural and narrower than the spectrum of the incident field, a phenomenon which does not depend upon strong coupling. To explain the role of the classical or non-classical nature of the driving field plays, we consider an alternative system which enables the atom to be driven by an arbitrary bandwidth light field with arbitrary two-photon correlations. Both numerical and analytic solutions are employed to provide physical insight. Surprisingly, spectral narrowing does not require squeezing: narrowed spectra appear for driving with a blackbody field. Then the atomic fluorescence can be expressed as the product of the atomic response with the incident spectrum. The resulting narrowing is maximized for incident bandwidths of the order of the natural width. However, the narrow hole at line-centre does require a non-classical driving field. For ideal squeezing, the fluorescence at line-centre vanishes. We test how robust the effects are to changes in experimentally pertinent factors such as the solid angle of coupling.

DOI
10.1080/09500349908231332

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We consider a single two-level atom driven by the output from a degenerate optical parametric oscillator. For squeezing bandwidths of the order of the natural atomic width and smaller, we report remarkable spectral profiles for the scattered light, including the existence of a narrow hole at line-centre. Under appropriate conditions, the spectrum may be both subnatural and narrower than the spectrum of the incident field, a phenomenon which does not depend upon strong coupling. To explain the role of the classical or non-classical nature of the driving field plays, we consider an alternative system which enables the atom to be driven by an arbitrary bandwidth light field with arbitrary two-photon correlations. Both numerical and analytic solutions are employed to provide physical insight. Surprisingly, spectral narrowing does not require squeezing: narrowed spectra appear for driving with a blackbody field. Then the atomic fluorescence can be expressed as the product of the atomic response with the incident spectrum. The resulting narrowing is maximized for incident bandwidths of the order of the natural width. However, the narrow hole at line-centre does require a non-classical driving field. For ideal squeezing, the fluorescence at line-centre vanishes. We test how robust the effects are to changes in experimentally pertinent factors such as the solid angle of coupling.
We consider a two-level atom driven by an ideal degenerate optical parametric oscillator. For squeezing bandwidths of the order of the natural width $\ensuremath{\gamma},$ and smaller, we report remarkable spectral profiles for the scattered light. We also consider a system where the atom is driven by arbitrarily correlated light of arbitrary bandwidth. Employing analytic and numerical solutions, we find different spectral features depending on the classical or nonclassical nature of the driving field. The spectral linewidth can be both subnatural and narrower than the incident field linewidth, an effect that does not require nonclassical light. However, nonclassical light is essential for the appearance of a narrow hole at line center. It is a unique signature of the quantum nature of the field, and for ideal squeezing, the fluorescence at line center vanishes.
We consider the interaction of a two-level atom inside an optical parametric oscillator. In the weak-driving-field limit, we essentially have an atom-cavity system driven by the occasional pair of correlated photons, or weakly squeezed light. We find that we may have holes, or dips, in the spectrum of the fluorescent and transmitted light. This occurs even in the strong-coupling limit when we find holes in the vacuum-Rabi doublet. Also, spectra with a subnatural linewidth may occur. These effects disappear for larger driving fields, unlike the spectral narrowing obtained in resonance fluorescence in a squeezed vacuum; here it is important that the squeezing parameter N tends to zero so that the system interacts with only one correlated pair of photons at a time. We show that a previous explanation for spectral narrowing and spectral holes for incoherent scattering is not applicable in the present case, and propose an alternative explanation. We attribute these anomalous effects to quantum interference in the two-photon scattering of the system.
Using the coupled-system approach we calculate the optical spectra of the fluorescence and transmitted fields of a two-level atom driven by a squeezed vacuum of bandwidths smaller than the natural atomic linewidth. We find that in this regime of squeezing bandwidths the spectra exhibit unique features, such as a hole burning and a three-peak structure, which do not appear for a broadband excitation. We show that the features are unique to the quantum nature of the driving squeezed vacuum field and do not appear when the atom is driven by a classically squeezed field. We find that a quantum squeezed-vacuum field produces squeezing in the emitted fluorescence field which appears only in the squeezing spectrum while there is no squeezing in the total field. We also discuss a nonresonant excitation and find that depending on the squeezing bandwidth there is a peak or a hole in the spectrum at a frequency corresponding to a three-wave-mixing process. The hole appears only for a broadband excitation and results from the strong correlations between squeezed-vacuum photons.
The resonance fluorescence of a two-level atom driven by a coherent laser field and damped by a finite bandwidth squeezed vacuum is analysed. We extend the Yeoman and Barnett technique to a non-zero detuning of the driving field from the atomic resonance and discuss the role of squeezing bandwidth and the detuning in the level shifts, widths and intensities of the spectral lines. The approach is valid for arbitrary values of the Rabi frequency and detuning but for the squeezing bandwidths larger than the natural line-width in order to satisfy the Markoff approximation. The narrowing of the spectral lines is interpreted in terms of the quadrature-noise spectrum. We find that, depending on the Rabi frequency, detuning and the squeezing phase, different factors contribute to the line narrowing. For a strong resonant driving field there is no squeezing in the emitted field and the fluorescence spectrum exactly reveals the noise spectrum. In this case the narrowing of the spectral lines arises from the noise reduction in the input squeezed vacuum. For a weak or detuned driving field the fluorescence exhibits a large squeezing and, as a consequence, the spectral lines have narrowed linewidths. Moreover, the fluorescence spectrum can be asymmetric about the central frequency despite the symmetrical distribution of the noise. The asymmetry arises from the absorption of photons by the squeezed vacuum which reduces the spontaneous emission. For an appropriate choice of the detuning some of the spectral lines can vanish despite that there is no population trapping. Again this process can be interpreted as arising from the absorption of photons by the squeezed vacuum. When the absorption is large it may compensate the spontaneous emission resulting in the vanishing of the fluorescence lines.
The incoherent part of the Mollow spectrum for resonance fluorescence has a subnatural linewidth in the weak-field limit. We show that this is due to squeezing of the fluctuations in the induced atomic dipole. The reduced linewidth persists for driving field intensities of approximately 12% of the saturation intensity, where Rabi sidebands begin to appear. We find a similar linewidth narrowing in the transmitted and fluorescent spectra for a single atom in a weakly driven resonant cavity. In this system single-quantum frequency splitting can produce a two-peaked spectrum. Both peaks have a narrowed linewidth. The spectrum of the transmitted light shows a second nonclassical effect that is due to squeezing. A spectral hole may appear at line center, giving a two-peaked spectrum even when there is no frequency splitting.
We analyze the linewidth narrowing in the fluorescence spectrum of a two-level atom driven by a squeezed vacuum field of a finite bandwidth. It is found that the fluorescence spectrum in a low-intensity squeezed field can exhibit a $(\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{0}{)}^{\ensuremath{-}6}$ frequency dependence in the wings. We show that this fast fall-off behavior is intimately related to the properties of a narrow-bandwidth squeezed field and does not extend into the region of broadband excitation. We apply the linear response model and find that the narrowing results from a convolution of the atom response with the spectrum of the incident field. On the experimental side, we emphasize that the linewidth narrowing is not sensitive to the solid angle of the squeezed modes coupled to the atom. We also compare the fluorescence spectrum with the quadrature-noise spectrum and find that the fluorescence spectrum for an off-resonance excitation does not reveal the noise spectrum. We show that this difference arises from the competing three-photon scattering processes.