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Physical Review A

Response of a two-level atom to a narrow-bandwidth squeezed-vacuum excitation

Azeddine Messikh, R. Tanaś, Z. Ficek

Published Feb 15, 2000• 14 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.61.033811

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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 field from one of the two allowed transitions in a three-level atom can sense squeezed fluctuations of a vacuum field coupled to the other transition. We examine the fluorescence spectra of strongly driven three-level atoms in \ensuremath{\Lambda}, V, and cascade configurations in which one of the two one-photon transitions is coupled to a finite-bandwidth squeezed vacuum field, when the bandwidth is much smaller than the difference in the atomic transition frequencies, though much larger than atomic decay rates and Rabi frequencies of the driving fields. The driving fields are on one-photon resonance, and the squeezed vacuum field is generated by a degenerate parameter oscillator. Details are only given for the \ensuremath{\Lambda} configuration. The extension to the V and cascade configurations is straightforward. We find that in all configurations the fluorescence spectra of the transition not coupled to the squeezed vacuum field are composed of five lines, one central and two pairs of sidebands, with intensities and widths strongly influenced by the squeezed vacuum field. However, only the central component and the outer sidebands exhibit a dependence on the squeezing phase. We also examine the fluorescence spectrum for the cascade configuration with a squeezed vacuum field on resonance with the two-photon transition between the ground and the most excited states and now generated by a nondegenerate parametric oscillator. In this case, where the squeezed vacuum field can be made coupled to both transitions, all spectral lines depend on the squeezing phase. The spectral features are explained in terms of the dressed-atom model of the system. We show that the coherent mixing of the atomic states by the strong driving fields modifies transition rates between the dressed states, which results in the selective phase dependence of the spectral features. \textcopyright{} 1996 The American Physical Society.
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.
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 steady-state resonance fluorescence spectrum of a two-level atom driven by a bichromatic field in a broadband squeezed vacuum is studied. When the carrier frequency of the squeezed vacuum is tuned to the frequency of the central spectral line, anomalous spectral features, such as hole burning and dispersive profiles, can occur at the central line. We show that these features appear for wider, and experimentally more convenient, ranges of the parameters than in the case of monochromatic excitation. The absence of a coherent spectral component at the central line makes any experimental attempt to observe these features much easier. We also discuss the general features of the spectrum. When the carrier frequency of the squeezed vacuum is tuned to the first odd or even sidebands, the spectrum is asymmetric and only the sidebands are sensitive to phase. For appropriate choices of the phase the linewidths of only the odd or even sidebands can be reduced. A dressed-state interpretation is provided.