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Journal of Physics B Atomic Molecular and Optical Physics

Spectral and statistical properties of collective resonance fluorescence in a squeezed vacuum

A.S. Shumovsky, Tran Ouang

Published Jan 14, 1989• 27 citations
Publisher

Abstract

The authors discuss the problem of collective resonance fluorescence of N driven atoms which are damped by a white squeezed noise. Analytical formulae for the spectrum of resonance fluorescence and for the degree of second-order coherence for spectral lines are calculated. The narrowing or expansion of linewidths and the asymmetry of the spectrum caused by the squeezed vacuum are shown.

DOI
10.1088/0953-4075/22/1/015

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The authors discuss the problem of collective resonance fluorescence of N driven atoms which are damped by a white squeezed noise. Analytical formulae for the spectrum of resonance fluorescence and for the degree of second-order coherence for spectral lines are calculated. The narrowing or expansion of linewidths and the asymmetry of the spectrum caused by the squeezed vacuum are shown.
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 study the system of a single two-level atom interacting with a braodband squeezed vacuum and a classical applied field. The atom is subject to collisions, and the applied field may possess a finite linewidth. The atomic populations, coherences, resonance fluorescence spectrum, and intensity fluctuation spectrum are calculated. Wherever practicable, analytic expressions are obtained that show the dependence of these quantities on the damping parameters. Numerical plots are presented. Two qualitative results that we obtain are the following: (a) we show that the dependence of the populations on the squeezing phase is increased by increasing the damping parameters, contrary to what might at first have been expected, and (b) we show that, in the absence of external damping, the squeezing induces strong asymmetries in the off-resonant resonance fluorescence spectra.
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.
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 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.