Measurement of the atom number distribution in an optical tweezer using single photon counting

We demonstrate in this paper a method to reconstruct the atom number distribution of a cloud containing a few tens of cold atoms. The atoms are first loaded from a magneto-optical trap into a microscopic optical dipole trap and then released in a resonant light probe where they undergo a Brownian motion and scatter photons. We count the number of photon events detected on an image intensifier. Using the response of our detection system to a single atom as a calibration, we extract the atom number distribution when the trap is loaded with more than one atom. The atom number distribution is found to be compatible with a Poisson distribution.Comment: 6 pages, 5 figure

Study of light-assisted collisions between a few cold atoms in a microscopic dipole trap

We study light-assisted collisions in an ensemble containing a small number (~3) of cold Rb87 atoms trapped in a microscopic dipole trap. Using our ability to operate with one atom exactly in the trap, we measure the one-body heating rate associated to a near-resonant laser excitation, and we use this measurement to extract the two-body loss rate associated to light-assisted collisions when a few atoms are present in the trap. Our measurements indicate that the two-body loss rate can reach surprisingly large values beta>10^{-8} cm^{3}.s^{-1} and varies rapidly with the trap depth and the parameters of the excitation light.Comment: 6 pages, 7 figure

Propagation of light through small clouds of cold interacting atoms

We demonstrate experimentally that a cloud of cold atoms with a size comparable to the wavelength of light can induce large group delays on a laser pulse when the laser is tightly focused on it and is close to an atomic resonance. Delays as large as -10 ns are observed, corresponding to "superluminal" propagation with negative group velocities as low as -300 m/s. Strikingly, this large delay is associated with a moderate extinction owing to the very small size of the cloud and to the light-induced interactions between atoms. It implies that a large phase shift is imprinted on the continuous laser beam, and opens interesting perspectives for applications to quantum technologies.Comment: 5 pages, 3 figures Supplemental Material : 2 pages, 2 Figure

Evaporative cooling of a small number of atoms in a single-beam microscopic dipole trap

We demonstrate experimentally the evaporative cooling of a few hundred rubidium 87 atoms in a single-beam microscopic dipole trap. Starting from 800 atoms at a temperature of 125microKelvins, we produce an unpolarized sample of 40 atoms at 110nK, within 3s. The phase-space density at the end of the evaporation reaches unity, close to quantum degeneracy. The gain in phase-space density after evaporation is 10^3. We find that the scaling laws used for much larger numbers of atoms are still valid despite the small number of atoms involved in the evaporative cooling process. We also compare our results to a simple kinetic model describing the evaporation process and find good agreement with the data.Comment: 7 pages, 5 figure

Sub-Poissonian atom number fluctuations using light-assisted collisions

We investigate experimentally the number statistics of a mesoscopic ensemble of cold atoms in a microscopic dipole trap loaded from a magneto-optical trap, and find that the atom number fluctuations are reduced with respect to a Poisson distribution due to light-assisted two-body collisions. For numbers of atoms N>2, we measure a reduction factor (Fano factor) of 0.72+/-0.07, which differs from 1 by more than 4 standard deviations. We analyze this fact by a general stochastic model describing the competition between the loading of the trap from a reservoir of cold atoms and multi-atom losses, which leads to a master equation. Applied to our experimental regime, this model indicates an asymptotic value of 3/4 for the Fano factor at large N and in steady state. We thus show that we have reached the ultimate level of reduction in number fluctuations in our system.Comment: 4 pages, 3 figure

Homogenization of an ensemble of interacting resonant scatterers

We study theoretically the concept of homogenization in optics using an ensemble of randomly distributed resonant stationary atoms with density $\rho$. The ensemble is dense enough for the usual condition for homogenization, viz. $\rho\lambda^3 \gg 1$, to be reached. Introducing the coherent and incoherent scattered powers, we define two criteria to define the homogenization regime. We find that when the excitation field is tuned in a broad frequency range around the resonance, none of the criteria for homogenization is fulfilled, meaning that the condition $\rho\lambda^3\gg 1$ is not sufficient to characterize the homogenized regime around the atomic resonance. We interpret these results as a consequence of the light-induced dipole-dipole interactions between the atoms, which implies a description of scattering in terms of collective modes rather than as a sequence of individual scattering events. Finally, we show that, although homogenization can never be reached for a dense ensemble of randomly positioned laser-cooled atoms around resonance, it becomes possible if one introduces spatial correlations in the positions of the atoms or non-radiative losses, such as would be the case for organic molecules or quantum dots coupled to a phonon bath.Comment: 9 pages, 5 figures. Corrected mistakes in reference

Analysis of the entanglement between two individual atoms using global Raman rotations

Making use of the Rydberg blockade, we generate entanglement between two atoms individually trapped in two optical tweezers. In this paper we detail the analysis of the data and show that we can determine the amount of entanglement between the atoms in the presence of atom losses during the entangling sequence. Our model takes into account states outside the qubit basis and allows us to perform a partial reconstruction of the density matrix describing the two atom state. With this method we extract the amount of entanglement between pairs of atoms still trapped after the entangling sequence and measure the fidelity with respect to the expected Bell state. We find a fidelity $F_{\rm pairs} =0.74(7)$ for the 62% of atom pairs remaining in the traps at the end of the entangling sequence

Imaging a single atom in a time-of-flight experiment

We perform fluorescence imaging of a single 87Rb atom after its release from an optical dipole trap. The time-of-flight expansion of the atomic spatial density distribution is observed by accumulating many single atom images. The position of the atom is revealed with a spatial resolution close to 1 micrometer by a single photon event, induced by a short resonant probe. The expansion yields a measure of the temperature of a single atom, which is in very good agreement with the value obtained by an independent measurement based on a release-and-recapture method. The analysis presented in this paper provides a way of calibrating an imaging system useful for experimental studies involving a few atoms confined in a dipole trap.Comment: 14 pages, 8 figure

Entanglement of two individual neutral atoms using Rydberg blockade

We report the generation of entanglement between two individual $^{87}$Rb atoms in hyperfine ground states $|F=1,M=1>$ and $|F=2,M=2>$ which are held in two optical tweezers separated by 4 $\mu$m. Our scheme relies on the Rydberg blockade effect which prevents the simultaneous excitation of the two atoms to a Rydberg state. The entangled state is generated in about 200 ns using pulsed two-photon excitation. We quantify the entanglement by applying global Raman rotations on both atoms. We measure that 61% of the initial pairs of atoms are still present at the end of the entangling sequence. These pairs are in the target entangled state with a fidelity of 0.75.Comment: text revised, with additional reference