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arXiv:0910.2450 · Physical Review A

Detecting antiferromagnetism of atoms in an optical lattice via optical Bragg scattering

Theodore A. Corcovilos, Stefan K. Baur, J. M. Hitchcock, Erich J. Mueller, Randall G. Hulet

Published Jan 26, 2010• 97 citations
arXivHTMLPDF

Abstract

Antiferromagnetism of ultracold fermions in an optical lattice can be detected by Bragg diffraction of light, in analogy to the diffraction of neutrons from solid-state materials. A finite sublattice magnetization will lead to a Bragg peak from the $(\frac{1}{2}\frac{1}{2}\frac{1}{2})$ crystal plane with an intensity depending on details of the atomic states, the frequency and polarization of the probe beam, the direction and magnitude of the sublattice magnetization, and the finite optical density of the sample. Accounting for these effects we make quantitative predictions about the scattering intensity and find that with experimentally feasible parameters the signal can be readily measured with a CCD camera or a photodiode and used to detect antiferromagnetic order.

DOI
10.1103/physreva.81.013415

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Antiferromagnetism of ultracold fermions in an optical lattice can be detected by Bragg diffraction of light, in analogy to the diffraction of neutrons from solid-state materials. A finite sublattice magnetization will lead to a Bragg peak from the (121212)(\frac{1}{2}\frac{1}{2}\frac{1}{2})(21​21​21​) crystal plane with an intensity depending on details of the atomic states, the frequency and polarization of the probe beam, the direction and magnitude of the sublattice magnetization, and the finite optical density of the sample. Accounting for these effects we make quantitative predictions about the scattering intensity and find that with experimentally feasible parameters the signal can be readily measured with a CCD camera or a photodiode and used to detect antiferromagnetic order.
We show how off-resonant light scattering can provide quantitative information on antiferromagnetic ordering of a two-species fermionic atomic gas in a tightly-confined two-dimensional optical lattice.We analyze the emerging magnetic ordering of atoms in the mean-field and in random phase approximations and show how the many-body static and dynamic correlations, evaluated in the standard Feynman-Dyson perturbation series, can be detected in the scattered light signal.The staggered magnetization reveals itself in the magnetic Bragg peaks of the individual spin components.These magnetic peaks, however, can be considerably suppressed in the absence of a true long-range antiferromagnetic order.The light scattered outside the diffraction orders can be collected by a lens with highly improved signal-to-shot-noise ratio when the diffraction maxima are blocked.The collective and single-particle excitations are identified in the spectrum of the scattered light.We find that the spin-conserving and spin-exchanging atomic transitions convey information on density, longitudinal spin, and transverse spin correlations.The different correlations and scattering processes exhibit characteristic angular distribution profiles for the scattered light, and e.g., the diagnostic signal of transverse spin correlations could be separated from the optical response by the scattering direction, frequency, or polarization.We also analyze the detection accuracy by estimating the number of required measurements, constrained by the heating rate that is determined by inelastic light-scattering events.The imaging technique could be extended to the two-species fermionic states in other regions of the phase diagram where the ground-state properties are still not fully understood.
We use ultracold spin--1/2 atomic fermions (6^66Li) to realize the Hubbard model on a three-dimensional (3D) optical lattice. At relatively high temperatures and at densities near half-filling, we show that the gas forms a Mott insulator with unordered spins. To observe antiferromagnetic order that is predicted to occur at lower temperatures, we developed the compensated optical lattice method to evaporatively cool atoms in the lattice. This cooling has enabled the detection of short-range magnetic order by spin-sensitive Bragg scattering of light.
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.
We experimentally demonstrate coherent light scattering from an atomic Mott insulator in a twodimensional 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.
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 observe coherently enhanced reflection (Bragg scattering) of a near resonant laser beam from cesium atoms ordered by a periodic array of optical potential wells known as an optical lattice. The reflected light is enhanced by a factor of $\ensuremath{\sim}{10}^{5}$ over scattering from a disordered atomic sample. We measure the magnitude of the reflectivity and its detuning dependence as functions of the density and the degree of localization of the atoms. The change in lattice constant due to the frequency-dependent effective index of refraction seen by the lattice light field is observed.