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Physics

Bragging rights

Joseph H. Thywissen

Published May 23, 2011• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physics.4.41

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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.
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.
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.
This thesis reports on new experimental techniques for the study of strongly correlated states of ultracold atoms in optical lattices. We used a high numerical aperture imaging system to probe 87Rb atoms in a two-dimensional lattice with single-site resolution. Fluorescence imaging allows to detect single atoms with a large signal to noise ratio and to reconstruct the atom distribution on the lattice. We applied this new technique to a two-dimensional Mott insulator and directly observed number squeezing and the emerging shell structure. A comparison of the radial density and variance distributions to theory provides a precise in situ temperature and entropy measurement from single images. We find entropies around the critical value for quantum magnetism. In a second series of experiments, we demonstrated two-dimensional single-site spin control in the optical lattice. The differential light shift of a tightly focused laser beam shifts selected atoms into resonance with a microwave field driving a spin flip. In this way, we reach sub-diffraction limited spatial resolution well below the lattice spacing. Starting from a Mott insulator with unity filling we were able to create arbitrary spin patterns. We used this ability to prepare atom distributions to study one-dimensional single-particle tunneling dynamics in a lattice. By discriminating the dynamics of the ground state and of the first excited band, we find that our addressing scheme leaves most atoms in the vibrational ground state. Moreover, we studied coherent light scattering from the atoms in the optical lattice and found diffraction maxima in the far-field. We showed that an antiferromagnetic order leads to additional diffraction peaks which can be used to detect this order also when single-site resolution is not available. The new techniques described in this thesis open the path to a wide range of novel applications from quantum dynamics of spin impurities, entropy transport, implementation of novel cooling schemes, and engineering of quantum many-body phases to quantum information processing.
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 show that light scattering from an ultracold gas reveals not only density correlations, but also matter-field interference at its shortest possible distance in an optical lattice, which defines key properties such as tunneling and matter-field phase gradients. This signal can be enhanced by concentrating probe light between lattice sites rather than at density maxima. As addressing between two single sites is challenging, we focus on global nondestructive scattering, allowing probing order parameters, matter-field quadratures, and their squeezing. The scattering angular distribution displays peaks even if classical diffraction is forbidden and we derive generalized Bragg conditions. Light scattering distinguishes all phases in the Mott insulator--superfluid--Bose glass phase transition.