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Journal of Qinghai Normal University

Response of a two-Level Atom to a Narrow Bandwidth Squeezed Vacuum Excitation

Hailiang Yang

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Using the coupled-system approach we calculate the optical spectra of the fluorescenceand transmitted field of a two-level atom driven by a squeezed vacuum of bandwidths smaller than the natural atomic linewidth.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.

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Journal of Modern Optics•Jul 1, 1999•1 citation
Using the coupled-system approach we calculate the optical spectra of the fluorescenceand transmitted field of a two-level atom driven by a squeezed vacuum of bandwidths smaller than the natural atomic linewidth.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.
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.
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.
The fluorescence spectrum of a strongly driven two-level atom located inside an optical cavity damped by a narrow-bandwidth squeezed vacuum is studied. We use a dressed atom model approach, first applied to squeezed vacuum problems by Yeoman and Barnett, to derive the master equation of the system and discuss the role of the cavity and the squeezed vacuum in the narrowing of the spectral lines and the population trapping effect. We find that in the presence of a single-mode cavity the effect of squeezing on the fluorescence spectrum is more evident in the linewidths of the Rabi sidebands rather than in the linewidth of the central component. Even in the absence of squeezing, the cavity can reduce the linewidth of the central component almost to zero, whereas the Rabi sidebands can be narrowed only to some finite value. In the presence of a two-mode cavity and a two-mode squeezed vacuum the signature of squeezing is evident in the linewidths of all spectral lines. We also establish that the narrowing of the spectral lines is very sensitive to the detuning of the driving field from the atomic resonance. Moreover, we find that the population trapping effect, predicted for the broadband squeezed vacuum case, may appear in a narrow-bandwidth case only if the input squeezed modes are perfectly matched to the cavity modes and if there is non-zero squeezing at the Rabi sidebands.
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 system consisting of a two-level atom coupled strongly to a cavity mode behaves as a two-state system when excited near one of the ``vacuum'' Rabi resonances. With finite-bandwidth squeezed light incident upon the cavity and tuned to one of these resonances, we show that it is possible to realize a two-state system coupled to a squeezed vacuum. This system exhibits subnatural linewidths in the emitted spectra, as described by Gardiner [Phys. Rev. Lett. 56, 1917 (1986)] in a study of spontaneous emission of a two-level atom in a squeezed vacuum, but requires that only a single cavity mode be subject to squeezing rather than the entire three-dimensional vacuum.
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.