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arXiv:physics/0011033 · Physical Review Letters

Random Scattering by Atomic Density Fluctuations in Optical Lattices

M. Blaauboer, Gershon Kurizki, V. M. Akulin

Published Apr 16, 2001• 3 citations
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Abstract

We investigate hitherto unexplored regimes of probe scattering by atoms trapped in optical lattices: weak scattering by effectively random atomic density distributions and multiple scattering by arbitrary atomic distributions. Both regimes are predicted to exhibit a universal semicircular scattering line shape for large density fluctuations, which depend on temperature and quantum statistics.

DOI
10.1103/physrevlett.86.3518

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We investigate hitherto unexplored regimes of probe scattering by atoms trapped in optical lattices: weak scattering by effectively random atomic density distributions and multiple scattering by arbitrary atomic distributions. Both regimes are predicted to exhibit a universal semicircular scattering line shape for large density fluctuations, which depend on temperature and quantum statistics.
In this paper, we study the problem of multiple scattering of light from a randomly occupied optical lattice, thereby extending the first-order Born analysis of the previous paper. A full multiple-scattering analysis is essential to a complete understanding of the nature of light propagation inside a medium. Our calculations show that the incident wave, when resonant with the atomic medium, is rapidly extinguished due to multiple scattering. The decay constant depends critically on the incident wavelength, the lattice constant, the average number density of atoms, and their polarizability. Both the Bragg scattering amplitudes and directions are modified as a result of multiple scattering. Because of the random site occupation of an otherwise regular lattice structure, a coherent enhancement of the scattering cross section is also predicted to occur along a discrete set of directions that are related to the strictly backward direction by reciprocal lattice vectors.
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.
Randomly diffusing atoms confined in a dissipative optical lattice are illuminated by a weak probe of light. The probe transmission spectrum reveals directed atomic propagation that occurs perpendicular to the direction of probe beam propagation. Resonant enhancement of this directed propagation is observed as we vary the random photon scattering rate. We experimentally characterize this stochastic resonance as a function of probe intensity and lattice well depth. A simple model reveals how the probe-excited atomic density waves and optical pumping rates conspire to create directed atomic propagation within a randomly diffusing sample.
A theoretical study of the scattering of light from a randomly occupied optical lattice of resonant atoms is presented to reveal both the characteristics of the lattice and the properties of light scattered from the lattice. In the first-order Born approximation we discuss here, a number of interesting effects are established, including sideband Stokes scattering, a finite angular coherence of the scattered light, and spectral line narrowing. Specifically, the degree of angular coherence of the scattered light is calculated, and it is shown that such coherence is strongly influenced by the regularity and size of the underlying lattice structure. The previously observed phenomenon of the sideband spectral line narrowing is also explained in terms of the localization of atoms in the trapping potential wells. Important information about the lattice can thus be recovered by analyzing the scattered light in the Born approximation.
Different quantum states of atoms in optical lattices can be nondestructively monitored by off-resonant collective light scattering into a cavity. Angle resolved measurements of photon number and variance give information about atom-number fluctuations and pair correlations without single-site access. Observation at angles of diffraction minima provides information on quantum fluctuations insensitive to classical noise. For transverse probing, no photon is scattered into a cavity from a Mott insulator phase, while the photon number is proportional to the atom number for a superfluid.
We study the influence of quantum density fluctuations in ultracold atoms in an optical lattice on the scattering of matter waves. Such fluctuations are characteristic of the superfluid phase and vanish due to increased interactions in the Mott insulating phase. We employ an analytical treatment of the scattering and demonstrate that the fluctuations lead to incoherent processes, which we propose to observe via decoherence of the fringes in a Mach-Zender interferometer. In this way we extract the purely coherent part of the scattering. Further, we show that the quantum density fluctuations can also be observed directly in the differential angular scattering cross section for an atomic beam scattered from the atoms in a lattice. Here we find an explicit dependence of the scale of the inelastic scattering on the quantum density fluctuations.