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arXiv:1108.5408 · Physical Review Letters

Bragg Scattering as a Probe of Atomic Wave Functions and Quantum Phase Transitions in Optical Lattices

Hirokazu Miyake, Georgios A. Siviloglou, Graciana Puentes, David E. Pritchard, Wolfgang Ketterle, David Weld

Published Oct 21, 2011• 56 citations
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Abstract

We have observed Bragg scattering of photons from quantum degenerate ^{87}Rb atoms in a three-dimensional optical lattice. Bragg scattered light directly probes the microscopic crystal structure and atomic wave function whose position and momentum width is Heisenberg limited. The spatial coherence of the wave function leads to revivals in the Bragg scattered light due to the atomic Talbot effect. The decay of revivals across the superfluid to Mott insulator transition indicates the loss of superfluid coherence.

DOI
10.1103/physrevlett.107.175302

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We have observed Bragg scattering of photons from quantum degenerate ^{87}Rb atoms in a three-dimensional optical lattice. Bragg scattered light directly probes the microscopic crystal structure and atomic wave function whose position and momentum width is Heisenberg limited. The spatial coherence of the wave function leads to revivals in the Bragg scattered light due to the atomic Talbot effect. The decay of revivals across the superfluid to Mott insulator transition indicates the loss of superfluid coherence.
We investigate theoretically light scattering of photons by ultracold atoms in an optical lattice in the linear regime. A full quantum theory for the atom-photon interactions is developed as a function of the atomic state in the lattice along the Mott-insulator--superfluid phase transition, and the photonic-scattering cross section is evaluated as a function of the energy and of the direction of emission. The predictions of this theory are compared with the theoretical results of a recent work on Bragg scattering in time-of-flight measurements [A.M. Rey et al., Phys. Rev. A 72, 023407 (2005)]. We show that, when performing Bragg spectroscopy with light scattering, the photon recoil gives rise to an additional atomic site-to-site hopping, which can interfere with ordinary tunneling of matter waves and can significantly affect the photonic-scattering cross section.
Studies of the scattering of light on systems of identical atoms under conditions of their quantum degeneracy have been reviewed. The formation of a periodic spatial structure caused by the interference of material waves is responsible for coherent resonance scattering similar to Bragg diffraction on regular spatial inhomogeneities. The interference of macroscopic material waves that is observed in experiments with a Bose–Einstein condensate forms a dielectric medium in the region of optical transparency of the sample that has the properties of a photonic crystal. Common characteristics and differences between the scattering of light on atomic systems under quantum degeneracy conditions and scattering on one-dimensional atomic lattices where the positions of atoms are described by classical statistics have been discussed.
We report the Bragg spectroscopy of interacting one-dimensional Bose gases loaded in an optical lattice across the superfluid to the Mott-insulator phase transition. Elementary excitations are created with a nonzero momentum and the response of the correlated 1D gases is in the linear regime. The complexity of the strongly correlated quantum phases is directly displayed in the spectra which exhibit novel features. This work paves the way for a precise characterization of the state of correlated gases in optical lattices.
Ultracold atoms loaded on optical lattices can provide unprecedented experimental systems for the quantum simulations and manipulations of many quantum phases. However, so far, how to detect these quantum phases effectively remains an outstanding challenge. Here, we show that the optical Bragg scattering of cold atoms loaded on optical lattices can be used to detect many quantum phases, which include not only the conventional superfluid and Mott insulating phases, but also other important phases, such as various kinds of charge density wave (CDW), valence bond solid (VBS), CDW supersolid (CDW-SS) and Valence bond supersolid (VB-SS).
We experimentally demonstrate coherent light scattering from an atomic Mott insulator in a two-dimensional lattice. The far-field diffraction pattern of small clouds of a few hundred atoms was imaged while simultaneously laser cooling the atoms with the probe beams. We describe the position of the diffraction peaks and the scaling of the peak parameters by a simple analytic model. In contrast to Bragg scattering, scattering from a single plane yields diffraction peaks for any incidence angle. We demonstrate the feasibility of detecting spin correlations via light scattering by artificially creating a one-dimensional antiferromagnetic order as a density wave and observing the appearance of additional diffraction peaks.
Coherence properties are central to quantum systems and are at the heart of phenomena such as superconductivity. In this work, we studied coherence properties of an ultracold Bose gas in a two-dimensional optical lattice across the thermal phase transition. To infer the phase coherence and phase fluctuation profiles, we used direct matter-wave imaging of higher Talbot revivals and introduced a phase microscope based on a site-resolved mapping of phase fluctuations to density fluctuations during matter-wave imaging. We observed the algebraic decay of the phase correlations in the superfluid phase and a linear temperature increase of the exponent. These techniques may enable studying coherence properties in strongly correlated quantum systems with full spatial resolution.