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arXiv:quant-ph/9907093 · Physical Review A

Two-level atom in an optical parametric oscillator: Spectra of transmitted and fluorescent fields in the weak-driving-field limit

James Clemens, Perry R. Rice, P. K. Rungta, Robert J. Brecha

Published Aug 8, 2000• 14 citations
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Abstract

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.

DOI
10.1103/physreva.62.033802

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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.
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.
Summary form only given. We consider a single two-level atom inside a resonant optical cavity, with cavity loss rate K, atomic fluorescence rate into noncavity modes A, and atom-field coupling g. For large atom cavity coupling (g>A, K) and weak driving fields, the fluorescence from this system exhibits a splitting of the spectral line, known as vacuum-Rabi splitting. When the cavity loss rate is the largest rate in the problem (K>A, g), the fluorescent spectrum is Lorentzian with a cavity-enhanced width. We examine the regime where A>g>K, and find that the spectrum exhibits a hole at line center as a result of quantum interference effects. This effect is formally identical to the phenomenon of electromagnetically induced transparency (EIT) in multilevel atomic systems. We discuss the relationship of these spectral holes to the presence of squeezing in the intracavity field, and present results also for the emission spectra, and incoherent spectra in transmission and fluorescence.
The dynamics of a strongly driven two-level atom are examined for the case that the atom is coupled to a ``two-mode'' squeezed vacuum. The source of squeezed light is taken to be a (frequency) nondegenerate parametric oscillator. We consider the situation in which the Rabi sidebands produced by the coherent driving field coincide with the spectral peaks of the parametric oscillator. Approximate analytical results are presented and checked against numerical simulations of the exact equations. For a suitable choice of relative phase, all three spectral lines in the fluorescence triplet are found to exhibit subnatural linewidths. Significant modifications to the fluorescence spectrum are also possible with a nonzero laser-atom detuning.
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.
Resonance fluorescence from a single two-level atom driven by a beam of squeezed light is studied in the weak field limit. We consider the situation where the atom is coupled to the ordinary vacuum and only a few field modes corresponding to the driving field are squeezed. The field produced by the degenerate optical parametric oscillator is used as the driving field. This driving field can be described in terms of two real independent Gaussian processes. Heisenberg equations of motion are solved in the steady-state, and analytic expressions for the fluorescent light intensity and the spectrum of fluorescent light are derived. We also consider photon statistics of fluorescent light. In particular, squeezing, antibunching, and sub-Poissonian statistics of fluorescent photons are discussed and analytic expressions for the quadrature variance and the two-time intensity correlation function are presented. Contrary to the case of coherent excitation the second-order intensity correlation function does not factorize.