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arXiv:quant-ph/0702193 · Physical Review A

Light scattering from ultracold atoms in optical lattices as an optical probe of quantum statistics

Igor B. Mekhov, Christoph Maschler, Helmut Ritsch

Published Nov 21, 2007• 56 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.76.053618

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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.
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 consider collective light scattering from ultracold atoms trapped in a deep optical lattice. Different atomic quantum states were shown to exhibit qualitatively different light scattering. This suggests a novel nondestructive method to probe atomic quantum statistics and characterize quantum phase transitions, e.g., between Mott insulator and superfluid states. The method is based on measurements of light fields only, in contrast to the standard methods based on matter-field interference, which destroys the system.
Light transmission or diffraction from different quantum phases of cold atoms in an optical lattice has recently come up as a useful tool to probe such ultracold atomic systems. The periodic nature of the optical lattice potential closely resembles the structure of a diffraction grating in real space but is loaded with a strongly correlated quantum many-body state which interacts with the incident electromagnetic wave, a feature that controls the nature of light transmission or dispersion through such quantum media. In this paper we show that, as one varies the relative angle between the cavity mode and the optical lattice, the peak of the transmission spectrum through such cavities also changes, which reflects the statistical distribution of the atoms in the illuminated sites. Consequently, the angle-resolved transmission spectrum of such quantum diffraction gratings can provide a plethora of information about the Fock-space structure of the many-body quantum state of ultracold atoms in such an optical cavity that can be explored in current state-of-the-art experiments.
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 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.
We consider light scattering from ultracold quantum gas in optical lattices into a cavity. The measurement of photons leaking out of the cavity enables a quantum nondemolition access to various atomic variables. The time resolved light detection projects the motional state to various atom-number squeezed and macroscopic superposition states that strongly depend on the geometry. Modifications of the atomic and light properties at a single quantum trajectory are demonstrated. The quantum structure of final states can be revealed by further observations of the same sample.