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Physical Review A

Resonance fluorescence spectra of three-level atoms in a squeezed vacuum

M. R. Ferguson, Z. Ficek, Bryan J. Dalton

Published Sep 1, 1996• 48 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.54.2379

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Physical Review A•Mar 1, 1997•13 citations
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 examine subnatural phase-dependent linewidths in the fluorescence spectrum of a three-level atom damped by a narrow-bandwidth squeezed vacuum in a cavity. Using the dressed-atom model approach of a strongly driven three-level cascade system, we derive the master equation of the system from which we obtain simple analytical expressions for the fluorescence spectrum. We show that the phase effects depend on the bandwidths of the squeezed vacuum and the cavity relative to the Rabi frequency of the driving fields. When the squeezing bandwidth is much larger than the Rabi frequency, the spectrum consists of five lines with only the central and outer sidebands dependent on the phase. For a squeezing bandwidth much smaller than the Rabi frequency the number of lines in the spectrum and their phase properties depend on the frequency at which the squeezing and cavity modes are centered. When the squeezing and cavity modes are centered on the inner Rabi sidebands, the spectrum exhibits five lines that are completely independent of the squeezing phase with only the inner Rabi sidebands dependent on the squeezing correlations. Matching the squeezing and cavity modes to the outer Rabi sidebands leads to the disappearance of the inner Rabi sidebands and a strong phase dependence of the central line and the outer Rabi sidebands. We find that in this case the system behaves as an individual two-level system that reveals exactly the noise distribution in the input squeezed vacuum.
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 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 authors investigate the dipole-dipole interaction role in the resonance fluorescence of two identical two-level atoms, which are confined to a region much smaller than the resonant wavelength and which are damped by a squeezed vacuum. The spectrum consists of seven or five lines, depending on the relative phase between the driving field and the squeezed vacuum, whereas the spectrum without the dipole-dipole interaction displays three lines. The widths of these lines depend on the parameters of the squeezed vacuum and can be subnatural or supernatural depending on the phase. The central line and additional sidebands at double the Rabi frequency can have intensities larger than in the normal vacuum but the intensities of lines at one Rabi frequency are always less than in the normal vacuum.
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 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.