We report the first observation of Bragg scattering of sodium atoms from a standing light wave. We also present a theory which quantitatively predicts the amplitude of the various Bragg orders as a function of the light's detuning and power, and the interaction time. The analog of the Pendello'sung eff'ect, previously observed in Bragg scattering of neutrons from crystals, is predicted and qualitatively observed for first-order Bragg scattering of atoms from a standing light wave PACS numbers: 42.50.Vk Bragg scattering of x rays from crystal planes was demonstrated by W. H. Bragg and his son W. L. Bragg in 1912, in a series of experiments' which won them a Nobel prize in 1915. Bragg scattering of neutron de Broglie waves from crystal planes was first observed in 1946, leading to the Geld of neutron interferometry. This Letter presents the first experimental observation of Bragg scattering of atoms from a standing light wave.This observation provides a beautiful example of the complementarity of particles and waves in that we treat the atomic beam as a wave and the intensity maxima of the standing light wave as crystal planes. Our observation also represents a breakthrough in the coherent manipulation of atoms, completing the technology necessary to construct an atomic interferometer (i.e. , one which acts by interference of atomic-matter waves). Momentum transfer to atoms by light in the absence of spontaneous emission results from an interaction of the induced dipole moment of the atom with the field gradient of the standing light wave. Quantum mechanically, the atom trades a photon via absorption and stimulated emission between the counterpropagating traveling waves which compose the standing light wave, thus gaining momentum in discrete units of 26k, along the k vector of the standing light wave. One can also view this phenomenon as diffraction of an atomic de Broglie wave (Ada =It/p) from the intensity grating (periodicity dl;sbt A, l;sbt/2) of the standing light wave. Thus, constructive interference occurs at discrete angles given by p=kdtt/dl;sh, which again results in momentum transfer to the atom in discrete units of 26k.The difference between Bragg scattering, in which the atoms scatter mainly into one order (i.e. , final momentum state), and the previously observed Kapitza-Dirac scattering, in which a large number of momentum states are populated, results from energy-momentum conservation. The absorption and stitnulated emission of photon pairs changes the momentum but not the laboratory kinetic energy of the atom. The final momentum vectors must lie on a circle of radius p; in momentum space as shown in Fig. 1. The focused waist of a Gaussian light beam has a minimum Heisenberg uncertainty 50'. QW 5mm / P I FIG. l. Comparison of Kapitza-Dirac and Bragg scattering. A tightly focused waist (left) has a large angular uncertainty in the direction of its photons, thus allowing energy conservation for many final momentum states pf -this is the Kapitza-Dirac regime.The observation of Bragg scattering requires...

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We have studied the statistics of the absorption of photons by atoms by measuring the momentum distribution of an atomic beam that is deflected by a laser beam. We observe the transition from a Poissonian to a sub-Poissonian distribution, as we vary the detuning of the laser. The largest observed fractional deviation of the variance from Poissonian statistics is ^ =-0.51 ±0.05, in agreement with theoretical predictions for our experimental conditions. PACS numbers: 32.80. 33.80.Ps, 42.50.Dv The basic interactions between a two-state atom and a coherent, traveling, laser wave have been studied for many years. The processes of absorption and spontaneous emission continue to be of fundamental interest because they display quantum statistics features that have no classical analog. In 1979, MandeP predicted that pin), the probability of observing n fluorescent photons in a given time interval 7, could display ''sub-Poissonian" statistics, in the sense that {(An)^) <{n}. This can be understood in terms of successively emitted photons. After emitting a photon, the atom must be excited before emitting another. Successive emissions are therefore correlated and not statistically independent. Mandel quantified his analysis by defining Q=l{(An)'}-{n)]/{n).(1)Several experimental observations of negative ^'s, using photon-coincidence counting, have been reported. ^"^ The largest value of Q which is measured directly in these experiments is about 7xlO~^, due to the inherent photon detector inefficiency. The detection efficiency has been increased to 95% using shelving and a minimum Q = -0.25 was inferred although not directly observed.^ The work reported here is the first measurement of the dependence of Q on the laser's detuning from the atomic transition frequency.'^ We use a method proposed by Cook^ in 1980 and employed by Wang et al.^ in 1985 to obtain preliminary data demonstrating the eff'ect. Cook pointed out that the statistics of the resonancefluorescence photon emissions in time are connected to the statistics of the momentum transferred to the atom from the exciting laser field. He proposed observing the momentum distribution of an atomic beam after it had been deflected by a laser as a diff'erent way to observe sub-Poissonian statistics. The deflection occurs because absorption followed by spontaneous emission changes the atom's momentum, decreases the incident wave's photon number by 1, and provides a fluorescent photon in a random direction. Regardless of the detector eflSciency, the amount of deflection of an atom necessarily reflects all of the photons that the atom has absorbed that are followed by spontaneous emission. Using this technique, we measure a minimum g = -0.51 ±0.05. This value and the dependence of Q on the detuning from exact resonance are in agreement with theoretical predictions for the conditions of our experiment.The dependence of the Q parameter on the laser frequency is not only important in its own right, but is also an important consideration in theories for the laser cooling and trap...

The United States Association for Young Physicists Tournaments (USAYPT) held its annual February Tournaments on Feb. 9–10, 2007, at the North Carolina School for Science and Mathematics, Durham, NC. Young physicists' tournaments are theoretical and experimental research-based team competitions described more fully at the USAYPT website: http://www.usaypt.org.

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The United States Association for Young Physicists Tournaments (USAYPT) held its annual U.S. Invitational Young Physicists Tournament Feb. 8–9, 2008, at the North Carolina School for Science and Mathematics in Durham, NC. Young physicists tournaments are theoretical and experimental research-based team competitions described more fully at the USAYPT website: http://www.usaypt.org.

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