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Transmission of Near-Resonant Light Through a Dense Slab of Cold Atoms

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Transmission of Near-Resonant Light Through a Dense Slab of Cold Atoms PHYSICAL REVIEW A 96, 053629 (2017) Transmission of near-resonant light through a dense slab of cold atoms L. Corman,* J. L. Ville, R. Saint-Jalm, M. Aidelsburger,† T. Bienaimé, S. Nascimbène, J. Dalibard, and J. Beugnon‡ Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, UPMC-Sorbonne Universités, 11 place Marcelin-Berthelot, 75005 Paris, France (Received 30 June 2017; revised manuscript received 4 October 2017; published 27 November 2017) The optical properties of randomly positioned, resonant scatterers is a fundamentally difficult problem to address across a wide range of densities and geometries. We investigate it experimentally using a dense cloud of rubidium atoms probed with near-resonant light. The atoms are confined in a slab geometry with a subwavelength thickness. We probe the optical response of the cloud as its density and hence the strength of the light-induced dipole-dipole interactions are increased. We also describe a theoretical study based on a coupled dipole simulation which is further complemented by a perturbative approach. This model reproduces qualitatively the experimental observation of a saturation of the optical depth, a broadening of the transition, and a blueshift of the resonance. DOI: 10.1103/PhysRevA.96.053629 I. INTRODUCTION than solid-state systems, strong attenuation of the transmission can be observed at resonance. Third, inhomogeneous Doppler The interaction of light with matter is a fundamental broadening can be made negligible using ultracold atomic problem which is relevant for simple systems, such as an atom clouds. Finally, the geometry and the density of the gases strongly coupled to photons [1–3], as well as for complex can be varied over a broad range. materials, whose optical properties provide information on In the dilute limit, such that the three-dimensional (3D) their electronic structure and geometry [4]. This interaction − atomic density ρ and the light wave number k verify ρk 3 1, can also be harnessed to create materials and devices with and for low optical depths, a photon entering the atomic tailored properties, from quantum information systems such medium does not recurrently interact with the same atom. as memories [5] and nanophotonic optical isolators [6] to solar Then, for a two-level atom, the transmission of a resonant cells combining highly absorptive materials with transparent probe beam propagating along the z axis is given by the electrodes [7]. − − Beer-Lambert law: |T |2 = e σ0 ρdz, where σ = 6πk 2 is The slab geometry is especially appropriate to study 0 the light cross section at the optical resonance [20]. At larger light-matter interaction [8,9]. In the limit of a monolayer, densities the transmission is strongly affected by the light- two-dimensional (2D) materials exhibit fascinating optical induced dipole-dipole coupling between neighboring atoms. properties. For simple direct band gap 2D semiconductors, Modification of the atomic resonance line shape or super- the single-particle band structure implies that the transmission and subradiance in dilute (but usually optically dense) and cold coefficient takes a universal value [10,11]. This was first atomic samples have been largely investigated experimentally measured for single-layer graphene samples [12], which have [21–30]. Recently, experiments have been performed in the an optical transmission independent of the light frequency in dense regime studying nanometer-thick hot vapors [31] and the eV range, |T |2 = 1 − πα, where α is the fine-structure mesoscopic cold clouds [32–35]. Interestingly, it has been constant [13,14]. The same value was recovered in InAs found that the mean-field Lorentz-Lorenz shift is absent in semiconductors [15]. This universality does not hold for cold systems where the scatterers remain fixed during the more complex 2D materials, for instance when the Coulomb measurement. A small redshift is still observed for dense interaction plays a more important role [16]. clouds in Refs. [32,34] but could be specific to the geometry Atomic gases represent in many respects an ideal test bed of the system. for investigating light-matter interaction. First, they can be Achieving large densities is concomitant with a vanishingly arranged in regular arrays [17,18] or randomly placed [19]to small transmission T . It is therefore desirable to switch tailor the optical properties of the system. Second, an atom to a 2D or thin slab geometry in order to investigate the always scatters light, in contrast with solid-state materials physical consequences of these resonant interaction effects where the optical excitation can be absorbed and dissipated in a at the macroscopic level. Using a 2D geometry also raises nonradiative way. Even for thin and much more dilute samples a fundamental question inspired by the monolayer semi- conductor case: can the light extinction through a plane of randomly positioned atoms be made arbitrarily large when *Also at Institute for Quantum Electronics, ETH Zurich, 8093 increasing the atom density or does it remain finite, potentially Zurich, Switzerland. †Also at Fakultät für Physik, Ludwig-Maximilians-Universität introducing a maximum of light extinction through 2D random München, Schellingstr. 4, 80799 Munich, Germany. atomic samples independent of the atomic species of identical ‡[email protected] electronic spin? In this article, we study the transmission of nearly resonant Published by the American Physical Society under the terms of the light through uniform slabs of atoms. We report experiments Creative Commons Attribution 4.0 International license. Further realized on a dense layer of atoms with a tunable density distribution of this work must maintain attribution to the author(s) and thickness. For dense clouds, the transmission is strongly and the published article’s title, journal citation, and DOI. enhanced compared to the one expected from the single-atom 2469-9926/2017/96(5)/053629(11) 053629-1 Published by the American Physical Society L. CORMAN et al. PHYSICAL REVIEW A 96, 053629 (2017) response. We also observe a broadening and a blueshift of (a) the resonance line on the order of the natural linewidth. This blueshift contrasts with the mean-field Lorentz-Lorenz redshift and is a signature of the stronglycorrelated regime reached in our system because of dipole-dipole interactions [36]. In addition, we observe deviations of the resonance line shape from the single-atom Lorentzian behavior, especially in the wings where the transmission decays more slowly. We model (b) this system with coupled dipole simulations complemented by a perturbative approach which qualitatively supports our observations. After describing our experimental system in Sec. II, we investigate theoretically light scattering for the geometry explored in the experiment in Sec. III. In Sec. IV we present our experimental results and compare them with theory. We conclude in Sec. V. II. EXPERIMENTAL METHODS FIG. 1. (a) Schematic representation of the imaging setup. The atoms are confined by a single, disk-shaped potential which is imaged A. Cloud preparation using a microscope objective onto a back-illuminated CCD camera. We prepare a cloud of 87Rb atoms with typically N = The numerical aperture of the system is limited to ≈0.2 using an iris in 5 the Fourier plane of the atoms to limit the collected fluorescence light. 1.3(2) × 10 atoms in the |F = 1,mF =−1 state. The atoms are confined in an all-optical trap, described in more detail (b) Typical in situ image obtained on a back illuminated CCD camera in [37], with a strong harmonic confinement in the vertical of the in-plane density distribution averaged over three individual = measurements. For this example, the atom surface density is n = direction z with frequency ωz/2π 2.3(2) kHz leading to a −2 Gaussian density profile along this direction. The transverse 25 μm . We extract a region of interest with uniform density for our analysis with a typical area of 200 μm2. confinement along the x and y directions is produced by a flat-bottom disk-shaped potential of diameter 2R = 40 μm. For our initial cloud temperature 300 nK, there is no τ = 10 μs that the thickness averaged over the pulse duration extended phase coherence in the cloud [38]. Taking into is increased by ∼20%. In some experiments, in which the account this finite temperature, we compute for an ideal Bose signal is large enough, we limit this effect by reducing the gas a rms thickness z = 0.25(1) μm, or equivalently kz = probe duration τ to 3 μs. 2.0(1). This situation corresponds to nk−2 ≈ 1.5, where n = N/(πR2) is the surface density and to a maximum density ρk−3 ≈ 0.3 at the trap center along z where ρ is the volume B. Transmission measurement density. We tune the number of atoms that interact with light We probe the response of the cloud by measuring the trans- by partially transferring them to the |F = 2,mF =−2 state mission of a laser beam propagating along the z direction (See using a resonant microwave transition. Atoms in this state Fig. 1). The light is linearly polarized along the x axis and tuned are sensitive to the probe excitation, contrary to the ones in the close to the |F = 2→|F = 3 D2 transition. The duration |F = 1,mF =−1 state. In this temperature range the Doppler of the light pulse is fixed to 10 μs for most experiments and we broadening is about three orders of magnitude smaller than the limit the imaging intensity I to the weakly saturating regime 2 natural linewidth of the atomic transition. with 0.075 <I/Isat < 0.2, where Isat 1.67 mW/cm is the The cloud thickness is varied in a controlled way using resonant saturation intensity. We define ν as the detuning of mainly the following two techniques.
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