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arXiv:1109.0493 · Physical Review A

Imaging of quantum Hall states in ultracold atomic gases

James S. Douglas, Keith R. Burnett

Published Nov 11, 2011• 17 citations
arXivHTMLPDF

Abstract

We examine off-resonant light scattering from ultracold atoms in the quantum Hall regime. When the light scattering is spin dependent, we show that images formed in the far field can be used to distinguish states of the system. The spatial dependence of the far-field images is determined by the two-particle spin-correlation functions, which the images are related to by a transformation. Quasiholes in the system appear in images of the density formed by collecting the scattered light with a microscope, where the quasihole statistics are revealed by the reduction in density at the quasihole position.

DOI
10.1103/physreva.84.053608

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We examine off-resonant light scattering from ultracold atoms in the quantum Hall regime. When the light scattering is spin dependent, we show that images formed in the far field can be used to distinguish states of the system. The spatial dependence of the far-field images is determined by the two-particle spin-correlation functions, which the images are related to by a transformation. Quasiholes in the system appear in images of the density formed by collecting the scattered light with a microscope, where the quasihole statistics are revealed by the reduction in density at the quasihole position.
Systems of ultracold atoms in optical potentials have taken a place at the forefront of research into many-body atomic systems because of the clean experimental environment they exist in and the tunability of the system parameters. In this thesis we study how light scattered from these ultracold atomic gases reveals information about the state of the atomic gas and also leads to changes in that state.We begin by investigating the angular dependence of light scattered from atoms in optical lattices at finite temperature. We demonstrate how correlations in the superfluid and Mott insulator states affect the scattering pattern, and we show that temperature affects the number of photons scattered. This effect could be used to measure the temperature of the gas, however, we show that when the lattice band structure is taken into account the efficiency of this temperature measurement is reduced.We then investigate light scattering from small optical lattices where the Bose-Hubbard Hamiltonian can be solved exactly. For small lattices, scattering a photon from the atomic system significantly perturbs the atomic system. We develop a model of the evolution of the many-body state that results from the consecutive scattering and detection of photons. This model shows that light scattering pushes the system towards eigenstates of the light scattering measurement process, in some cases leading to a superposition of atomic states.In the second half of this thesis we study light scattering that depends on the internal hyperfine spin state of the atoms, in which case the scattered light can form images of the spatial atomic spin distribution. We demonstrate how scattering spatially correlated light from the atoms can result in spin state images with enhanced spatial resolution. We also show how using spatially correlated light can lead to direct measurement of the spatial correlations of the atomic spin distribution.We then apply this theory of spin-dependent light scattering to the detection of different spin states of ultracold gases in synthetic magnetic fields. We show that it is possible to distinguish between ground states in the quantum Hall regime using light scattering. Moreover, we show how noise correlation analysis of the spin state images can be used to identify the correlations between atoms and how a variant on phase-contrast imaging can reveal the relationship between the atomic spins.
We study off-resonant collective light scattering from ultracold atoms trapped in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the spatial intensity distribution, quadrature variances, photon statistics, or spectral measurements. In particular, angle-resolved intensity measurements reflect global statistics of atoms (total number of radiating atoms) as well as local statistical quantities (single-site statistics even without optical access to a single site) and pair correlations between different sites. As a striking example we consider scattering from transversally illuminated atoms into an optical cavity mode. For the Mott-insulator state, similar to classical diffraction, the number of photons scattered into a cavity is zero due to destructive interference, while for the superfluid state it is nonzero and proportional to the number of atoms. Moreover, we demonstrate that light scattering into a standing-wave cavity has a nontrivial angle dependence, including the appearance of narrow features at angles, where classical diffraction predicts zero. The measurement procedure corresponds to the quantum nondemolition measurement of various atomic variables by observing light.
The quantum optical response of high-density ultracold atomic systems is important to a wide range of fundamentally and technically important physical processes. We present here a microscopic analysis of the light scattering on such a system and compare it with a corresponding description based on macroscopic Maxwell theory. Results are discussed in the context of the spectral resonance structure of the scattering cross section, the time-dependent response under a range of conditions, and evolution of these quantities as the atomic density is varied. For high atomic densities, the microscopic theoretical treatment reveals a distributed and configuration-dependent narrow resonance structure. This structure is attributed to microcavity spatial structures associated with the dense and ultracold atomic gases.
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 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.
The author proposes a minimal setup to create and observe a fractional quantum Hall (FQH) quasihole state of a few ultracold atoms in a small optical lattice under a synthetic magnetic field with additional pinning and harmonic confinement potentials. It is shown by exact diagonalization and an extensive parameter-space search that a joint observation of two density-dependent indicators, namely the mean-square-radii ratio of particle clouds and the density depletion around a pinned quasihole, yield signatures of the underlying FQH physics.