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Physical Review A

Resonance fluorescence spectrum in a broadband squeezed vacuum: Sideband narrowing

Arup Banerjee

Published Sep 1, 1995• 12 citations
Publisher

Abstract

We show, in contrast to what has hitherto been believed, that the linewidth of the side peaks in the resonance fluorescence spectrum of an atom interacting with broadband squeezed fields and driven by a strong pump can be reduced below the normal vacuum value. In particular, for squeezing parameter N in the range 0N0.125 and relative phase \ensuremath{\theta}=0 we observe narrowing of the linewidth, and for N=0.125 the linewidth is identical to that of the normal vacuum case. For N>0.125, side peaks always broaden.

DOI
10.1103/physreva.52.2472

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We show, in contrast to what has hitherto been believed, that the linewidth of the side peaks in the resonance fluorescence spectrum of an atom interacting with broadband squeezed fields and driven by a strong pump can be reduced below the normal vacuum value. In particular, for squeezing parameter N in the range 0N0.125 and relative phase \ensuremath{\theta}=0 we observe narrowing of the linewidth, and for N=0.125 the linewidth is identical to that of the normal vacuum case. For N>0.125, side peaks always broaden.
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.
We examine resonance fluorescence of a two-level atom in a squeezed vacuum, under the condition that the squeezing bandwidth is much narrower than the Rabi splitting of the Mollow triplet. For a suitable choice of the relative phase between the squeezed vacuum and coherent driving field, we find significant narrowing of the Rabi peaks and inhibited population decay. These results are in marked contrast to previous broadband squeezing analyses, which predict strong broadening of the Rabi peaks and enhanced population decay. We explore the connection between our work and that on the dynamical suppression of spontaneous emission via strongly driven resonance fluorescence in a cavity [Lewenstein, Mossberg, and Glauber, Phys. Rev. Lett. 59, 775 (1987)]. By modifying this work to incorporate squeezing of the cavity modes, we are able to combine the features of both systems, and thereby predict strong inhibition of the decay of all three components of the Bloch vector in a possible experimental configuration.
Fluorescence from a coherently driven two-level atom that is damped by a squeezed vacuum is studied. We show that the mean atomic polarization depends on the relative phases of the squeezed vacuum and the coherent driving field. The fluorescent spectrum is calculated and shows several modifications over the spectrum for normal resonance fluorescence. In particular, the central peak of the Mollow triplet has a linewidth that depends on the phase of the driving field. For strong squeezing this peak can either be much narrower or much broader than the natural linewidth of the atom.
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.
We present an analytical technique for investigating the behaviour of a coherently driven atom damped by a squeezed vacuum with finite squeezing bandwidth. A master equation and analytic expressions for the fluorescent spectrum are derived for the simple case of a two-level atom exactly resonant with the frequencies of both the squeezed field and the driving field. Suitable choices of driving strength, phase and squeezing source lead to either sub-natural lincwidths of the Rabi sidebands or a sub-natural linewidth of the central spectral peak or indeed sub-natural linewidths of all three spectral peaks when squeezing bandwidths are taken into account. We also establish the remarkable result that in the strong driving regime, the width of the central peak of the fluorescent spectrum depends solely on the squeezing found at the Rabi sideband frequencies.
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.