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arXiv:quant-ph/0410177 · Physical Review Letters

Phase-Sensitive Detection of Bragg Scattering at 1D Optical Lattices

Sebastian Slama, C. von Cube, Benjamin Deh, A. Ludewig, Claus Zimmermann, Ph. W. Courteille

Published May 17, 2005• 42 citations
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Abstract

We report on the observation of Bragg scattering at 1D atomic lattices. Cold atoms are confined by optical dipole forces at the antinodes of a standing wave generated by the two counterpropagating modes of a laser-driven high-finesse ring cavity. By heterodyning the Bragg-scattered light with a reference beam, we obtain detailed information on phase shifts imparted by the Bragg scattering process. Being deep in the Lamb-Dicke regime, the scattered light is not broadened by the motion of individual atoms.

DOI
10.1103/physrevlett.94.193901

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We report on the observation of Bragg scattering at 1D atomic lattices. Cold atoms are confined by optical dipole forces at the antinodes of a standing wave generated by the two counterpropagating modes of a laser-driven high-finesse ring cavity. By heterodyning the Bragg-scattered light with a reference beam, we obtain detailed information on phase shifts imparted by the Bragg scattering process. Being deep in the Lamb-Dicke regime, the scattered light is not broadened by the motion of individual atoms.
We study Bragg scattering at one-dimensional (1D) optical lattices. Cold atoms are confined by the optical dipole force at the antinodes of a standing wave generated inside a laser-driven high-finesse cavity. The atoms arrange themselves into a chain of pancake-shaped layers located at the antinodes of the standing wave. Laser light incident on this chain is partially Bragg reflected. We observe an angular dependence of this Bragg reflection which is different from what is known from crystalline solids. In solids, the scattering layers can be taken to be infinitely spread (three-dimensional limit). This is not generally true for an optical lattice consistent of a 1D linear chain of pointlike scattering sites. By an explicit structure factor calculation, we derive a generalized Bragg condition, which is valid in the intermediate regime. This enables us to determine the aspect ratio of the atomic lattice from the angular dependance of the Bragg scattered light.
We study Bragg scattering at one-dimensional atomic lattices. Cold atoms are confined by optical dipole forces at the antinodes of a standing wave generated inside a laser-driven cavity. The atoms arrange themselves into an array of lens-shaped layers located at the antinodes of the standing wave. Light incident on this array at a well-defined angle is partially Bragg reflected. We measure reflectivities as high as 3030%30. In contrast to a previous experiment devoted to the thin grating limit [S. Slama et al., Phys. Rev. Lett. 94, 193901 (2005)] we now investigate the thick grating limit characterized by multiple reflections of the light beam between the atomic layers. In principle, multiple reflections give rise to a photonic stop band, which manifests itself in the Bragg diffraction spectra as asymmetries and minima due to destructive interference between different reflection paths. We show that close to resonance however disorder favors diffuse scattering, hinders coherent multiple scattering and impedes the characteristic suppression of spontaneous emission inside a photonic band gap.
Abstract Ultracold atoms interacting with the optical modes of a high‐Q optical ring cavity can synchronize their motion. The collective behavior makes the system interesting for quantum computing applications. This paper is devoted to the study of the collective coupling. We report on the first observation of a collective dynamics and on the realization of a laser, the gain mechanism of which is based on collective atomic recoil. We show that, if the atoms are subject to a friction force, starting from an unordered distribution they spontaneously form a moving density grating. Furthermore, we demonstrate that a 1D atomic density grating can be probed via Bragg scattering. By heterodyning the Bragg‐reflected light with a reference beam, we obtain detailed information on phase shifts induced by the Bragg scattering process.
In this thesis we investigate the dynamics of cold atoms in optical cavities. We study how the scattering properties of laser driven atoms are modified by the presence of an optical resonator. This investigation can be divided into two parts. First, we study the scaling of the scattering properties with the number of atoms, and we show in particular how Bragg scattering by an atomic lattice is modified by the presence of the resonator. In this case, the atoms are trapped at the antinodes of the cavity mode function by the mechanical potential induced by the resonator. In a second part, we show how this modification of the scattering properties can be used for efficiently cooling single atoms to the ground state of a harmonic trap. In particular, we find that the motion is critically affected by quantum correlations induced by the mechanical coupling with the resonator, which may lead to selective suppression of certain transitions for the appropriate parameters regimes, thereby increasing the cooling efficiency.
Bragg diffraction of an atomic wave packet in a retroreflective geometry with two counterpropagating optical lattices exhibits a light shift induced phase. We show that the temporal shape of the light pulse determines the behavior of this phase shift: In contrast to Raman diffraction, Bragg diffraction with Gaussian pulses leads to a significant suppression of the intrinsic phase shift due to a scaling with the third power of the inverse Doppler frequency. However, for box-shaped laser pulses, the corresponding shift is twice as large as for Raman diffraction. Our results are based on approximate but analytical expressions as well as a numerical integration of the corresponding Schr\"odinger equation.
Bragg diffraction of atoms at thick standing light waves requires that the wave-matching condition is fulfilled. This usually means that the atomic beam crosses the light wave exactly at the Bragg angle. Nevertheless, our experiments also demonstrate Bragg diffraction at detuned angles if the amplitude of the standing light wave is temporally modulated with an appropriate frequency. If, on the other hand, the phase of the light wave is modulated no diffraction is observed. Both modulation processes produce frequency sidebands which set up `slowly travelling standing waves' in front of a retro-reflection mirror. Atoms are diffracted at these `almost standing' light waves in a similar way to photons at the travelling sound waves in an acousto-optic modulator. The frequency of the diffracted de Broglie waves is assumed to be shifted by the intensity modulation frequency. The different results using amplitude- and phase-modulated light waves are due to interference between the diffraction contributions of the individual frequency sidebands contained in the standing light wave.