Slow Diffusion of Light in a Cold Atomic Cloud G. Labeyrie, 1, * E. Vaujour, 1 C. A. Mu ¨ller, 2 D. Delande, 3 C. Miniatura, 1 D. Wilkowski, 1 and R. Kaiser 1 1 Laboratoire Ondes et De ´sordre, FRE 2302 CNRS, 1361 route des Lucioles, F-06560 Valbonne, France 2 Physikalisches Institut, Universita ¨t Bayreuth, D-95440 Bayreuth, Germany 3 Laboratoire Kastler Brossel, Universite ´ Pierre et Marie Curie, 4 Place Jussieu, F-75005 Paris, France (Received 19 May 2003; published 26 November 2003) We study the diffusive propagation of multiply scattered light in an optically thick cloud of cold rubidium atoms illuminated by a quasiresonant laser beam. In the vicinity of a sharp atomic resonance, the energy transport velocity of the scattered light is almost 5 orders of magnitude smaller than the vacuum speed of light, reducing strongly the diffusion constant. We verify the theoretical prediction of a frequency-independent transport time around the resonance. We also observe the effect of the residual velocity of the atoms at long times. DOI: 10.1103/PhysRevLett.91.223904 PACS numbers: 42.25.Dd, 32.80.Pj When light propagates through a multiply scattering medium, two components can be distinguished in the light emerging from the sample: the ‘‘transmitted’’ com- ponent, i.e., the light emerging in the incident mode, and the ‘‘diffuse’’ component corresponding to photons redis- tributed into other modes by the scattering processes. The temporal propagations of these two components are very different. The group velocity, whose behavior is deter- mined by the index of refraction, describes the trans- mitted (and absorbed) component. The possibility to manipulate the refractive index allowed the spectacular observation of slow light [1], or of apparent supraluminal propagation [2] due to a negative group velocity. On the other hand, the diffuse light does not propagate ballisti- cally, but shows a diffusive behavior for optically thick media. In this situation, it is the energy transport velocity v E that accounts for the propagation of energy by the scattered wave [3,4]. In the present paper, we use the versatility of cold atomic vapors to study the temporal propagation of the diffuse light in the interesting situation of strongly resonant scattering, a previously unreachable regime where v E is 5 orders of magnitude smaller than the vacuum speed of light c. This is the first observation of such a dramatic reduction of the energy transport veloc- ity, and thus of the diffusion constant, in multiply scatter- ing media. It is also a first and important step toward the possible strong (Anderson) localization of light in an atomic gas, a regime where interference effects further reduce the diffusion constant until it vanishes at the localization border [5]. Besides the mean-free path, which characterizes the stationary properties of multiple scattering, the diffusion constant is a crucial parameter for its dynamical properties [6,7]. The propagation of quasiresonant light in atomic va- pors has been investigated for a long time under the name of radiation trapping (RT), in a regime where the atomic motion (Doppler effect) or collisions induce frequency redistribution, which completely blurs the effects linked to the atomic resonance [8,9]. In most cases, the inhomo- geneous broadening dominated over the homogeneous one, since vapors with very small velocity spread could not be produced before the advent of laser cooling [10]. Following the pioneering work [11], we present the first systematic study of RT in cold atoms. We measure the light diffusion coefficient and transport velocity and analyze the role of the number of atoms and of the light frequency. We present some experimental evidence for the indepen- dence of the transport time with frequency, a nontrivial prediction of the theory for point scatterers. Finally, we show that the residual motion of the atoms noticeably affects the propagation of light in our sample. The experimental setup and procedure are similar to those employed to observe coherent backscattering [12]. The magneto-optical trap (MOT) producing the cold atomic sample is turned off for 2 ms every 20 ms to allow for RT probing. We obtain a cold cloud of quasi-Gaussian shape (rms radius r 0  2–3 mm) containing up to 7  10 9 atoms, with a maximal optical thickness along a diameter b   2 p r 0 =‘  40 where ‘ is the minimum scattering mean-free path of the light at the center of the atomic cloud. The rms velocity of the atoms is 0:15 m=s.We use a probe light resonant with the F  3 ! F 0  4 transition of the D2 line of Rb 85 (wavelength   780 nm, natural lifetime  nat  1=  27 ns). The optical thickness is determined by measuring the spectral width of the trans- mission curve [13]. Together with a measurement of the density profile of the cloud by fluorescence imaging, this gives access to the scattering mean-free path ‘. We can adjust the effective number of atoms in the cloud by turning off the MOT repumping laser shortly before the trapping laser. The principle of the RT measurement is shown in Fig. 1. Aweak probe beam pulse generated by an acousto-optic modulator is sent through the center of the cloud (beam diameter 2 mm, linewidth 2 MHz FWHM, pulse width typically 4 s, 90%–10% fall time 1:5 nat ). The diffuse light is collected in a solid angle of about 0.1 srd at 17  from the forward direction and is detected by a photomutiplier. The RT signal is averaged over 512 PHYSICAL REVIEW LETTERS week ending 28 NOVEMBER 2003 VOLUME 91, NUMBER 22 223904-1 0031-9007= 03=91(22)=223904(4)$20.00  2003 The American Physical Society 223904-1