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arXiv:1208.1884 · Physical Review A

Steady-state signatures of radiation trapping by cold multilevel atoms

Quentin Baudouin, Nicolas Mercadier, Robin Kaiser

Published Jan 16, 2013• 6 citations
arXivHTMLPDF

Abstract

In this paper, we use steady-state measurements to obtain evidence of radiation trapping in an optically thick cloud of cold rubidium atoms. We investigate the fluorescence properties of our sample, pumped on opened transitions. This fluorescence exhibits a nontrivial dependence on the optical thickness of the media. A simplified model, based on rate equations, self-consistently coupled to a diffusive model of light transport, is used to explain the experimental observations in terms of incoherent radiation trapping on one spectral line. Measurements of the atomic populations and the fluorescence spectrum qualitatively agree with this interpretation.

DOI
10.1103/physreva.87.013412

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In this paper, we use steady-state measurements to obtain evidence of radiation trapping in an optically thick cloud of cold rubidium atoms. We investigate the fluorescence properties of our sample, pumped on opened transitions. This fluorescence exhibits a nontrivial dependence on the optical thickness of the media. A simplified model, based on rate equations, self-consistently coupled to a diffusive model of light transport, is used to explain the experimental observations in terms of incoherent radiation trapping on one spectral line. Measurements of the atomic populations and the fluorescence spectrum qualitatively agree with this interpretation.
We have measured the change of fluorescence from cold 87Rb atoms after magnetic field of the magneto-optic trap is turn off. A rise in fluorescence within several tens of milliseconds was observed. Analyzing this phenomenon in connection with the experimental conditions, we found that incoherent pumping field due to radiation trapping in the high density cold-atom cloud was the reason of fluorescence weakening under tight confinement by the magneto-optic trap. We have also performed a simple numerical simulation, which indicated that the calculations agree with experimental results only when the effect of frequency redistribution of scattered light is taken into account.
We experimentally and numerically study the temporal dynamics of light scattered by large clouds of cold atoms after the exciting laser is switched off, in the low intensity (linear-optics) regime. Radiation trapping due to multiple scattering as well as subradiance lead to decay much slower than the single atom fluorescence decay. These two effects have already been observed separately, but the interplay between them remained to be understood. Here, we show that with well chosen parameters of the driving field, the two effects can occur at the same time, but follow different scaling behaviors. The subradiant decay is observed at late time and its rate is independent of the detuning, while the radiation trapping decay is observed at intermediate time and depends on the detuning through the optical depth of the sample. Numerical simulations based on random walk process and coupled-dipole equations support our interpretations. Our study clarifies the different interpretations and physical mechanisms at the origin of slow temporal dynamics of light in cold atoms.
We study the emergence of a collective optical response of a cold and dense 87Rb^{87}\mathrm{Rb}87Rb atomic cloud to a near-resonant low-intensity light when the atom number is gradually increased. Experimental observations are compared with microscopic stochastic simulations of recurrent scattering processes between the atoms that incorporate the atomic multilevel structure and the optical measurement setup. We analyze the optical response of an inhomogeneously broadened gas and find that the experimental observations of the resonance line shifts and the total collected scattered light intensity in cold atom clouds substantially deviate from those of thermal atomic ensembles, indicating strong light-induced resonant dipole-dipole interactions between the atoms. At high densities, the simulations also predict a significantly slower decay of light-induced excitations in cold than in thermal atom clouds. The role of dipole-dipole interactions is discussed in terms of resonant coupling examples and the collective radiative excitation eigenmodes of the system.
We present experimental evidence that the intensity correlations of light scattered from a cold-atom cloud are sensitive to the presence of small amounts of radiation trapping in an atomic sample of density 6 x 10(8)/cm3, with an optical depth (for a resonant light beam) of 0.4. This density and optical depth are approximately an order of magnitude less than the density and on-resonance optical depth at which effects of multiple scattering in cold-atom clouds have been previously observed [Phys. Rev. Lett. 64, 408 (1990)].
The problem of the interaction of N atoms with a laser beam and vacuum modes can give rise to many interesting phenomena concerning the spontaneous emission of light and its propagation in the medium. The cooperative effects, for example, such as superadiance and subradiance, are effects related to the coherence created between the atoms when a photon is emitted spontaneously by a single excited atom. Superradiance can be defined as the enhancement of the spontaneous emission due to constructive interference of the scattered light. Its counterpart, subradiance, is the trapping of some remaining light due to destructive interference. In cold atoms, some previous theoretical works predict and characterize these two cooperative effects in a large and diluted atomic cloud, in the regime of low intensities and large detunings of the incident laser. The theoretical model is a coupled-dipole model for two-level atoms driven by a low-intensity field and in the scalar approach. The experiment consists in measuring the super- and subradiant decay rates from the temporal emitted intensity after the switch off of the incident laser in the steady state. Our experimental setup consists in a magneto-optical trap of rubidium 87 atoms at large resonant optical thicknesses. A probe beam excites the atoms close to the D2 line. The intensity emitted is detected by a single photon detector with no afterpulsing and a calibration procedure allows us to determine the resonant optical thickness of the cloud and its temperature. In this work, we report the experimental observation of super- and subradiance in a large cloud of cold atoms. For subradiance, the main result is the linear evolution of the characteristic time with the resonant optical thickness of the cloud and its independence of the detuning. For superradiance, we observe superradiance out of the forward direction. We verify the validity of our interpretations with the predictions of the coupled-dipole model. Finally, we discuss the interplay of subradiance and radiation trapping, as well as theoretical predictions for: a setup of a phased cloud, to control the subradiant amplitude emission; and temperature effects, where subradiance is shown to be robust in a large range of temperatures.
We have measured the time-dependent fluorescence of the sodium DDD lines following pulsed excitation of one DDD line, in the presence of radiation trapping with optical depths k0L{k}_{0}Lk0​L of \ensuremath{\sim}10 to 2000. When collisional coupling of the 3P123{P}_{\frac{1}{2}}3P21​​ and 3P323{P}_{\frac{3}{2}}3P23​​ levels and different radiative-escape probabilities for each DDD line are taken into account, we obtain excellent agreement with Holstein's theory for the effective radiative decay rates in the Doppler region (${k}_{0}L\ensuremath{\sim}10\ensuremath{-}300$) and in the redistributed Lorentzian region (k0L>1000{k}_{0}L>1000k0​L>1000). For k0L{k}_{0}Lk0​L between these two regions, we observe an abrupt transition between the two limiting formulas. The buildup rate of the sensitized fluorescence signal also yields a $3{P}_{\frac{3}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}$ excitation transfer cross section in agreement with our previously reported cw measurement. Additionally, we have measured the dependence of the 3P3P3P fluorescence on laser power and beam diameter, and we explain the observed approach to saturation. We suggest that the previously reported "anomalous" approaches to saturation may be explained in terms of the laser beam burning through the optically thick vapor. Laser-beam spatial intensity variations and self-focusing also contribute to fluorescence signals that deviate from the usual single-atom saturation behavior.