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arXiv:quant-ph/9909066 · Optics Express

Spatial correlation diagnostics for atoms in optical lattices

J. Grondalski, Paul M. Alsing, Ivan Deutsch

Published Nov 22, 1999• 23 citations
arXivHTMLPDF

Abstract

We explore the use of first and second order same-time atomic spatial correlation functions as a diagnostic for probing the small scale spatial structure of atomic samples trapped in optical lattices. Assuming an ensemble of equivalent atoms, properties of the local wave function at a given lattice site can be measured using same-position first-order correlations. Statistics of atomic distributions over the lattice can be measured via two-point correlations, generally requiring the averaging of multiple realizations of statistically similar but distinct realizations in order to obtain sufficient signal to noise. Whereas two-point first order correlations are fragile due to phase fluctuations from shot-to-shot in the ensemble, second order correlations are robust. We perform numerical simulations to demonstrate these diagnostic tools.

DOI
10.1364/oe.5.000249

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We explore the use of first and second order same-time atomic spatial correlation functions as a diagnostic for probing the small scale spatial structure of atomic samples trapped in optical lattices. Assuming an ensemble of equivalent atoms, properties of the local wave function at a given lattice site can be measured using same-position first-order correlations. Statistics of atomic distributions over the lattice can be measured via two-point correlations, generally requiring the averaging of multiple realizations of statistically similar but distinct realizations in order to obtain sufficient signal to noise. Whereas two-point first order correlations are fragile due to phase fluctuations from shot-to-shot in the ensemble, second order correlations are robust. We perform numerical simulations to demonstrate these diagnostic tools.
Summary form only given. Atom-atom interactions play an important role in the dynamics of cold atoms trapped in optical lattices, and may be crucial to the formation of small scale structure within the lattice. Spatial distributions of atoms trapped in optical lattices are normally probed by absorption or fluorescence spectroscopy. We investigate the possibility of deducing spatial information from the Hanbury-Brown Twiss stellar-interferometric techniques of coincidence counts. This is analogous to the time-delayed coincidence counting employed in analyzing degenerate Bose and Fermi gases.
The paper reports on measurement on a Mott insulator released from an optical lattice trap. We show that strong periodic quantum correlations exist at the atomic shot noise level between density fluctuations in the expanding atom cloud, reflecting the underlying spatial ordering in the lattice. These spatial correlations find a natural interpretation in terms of a multiple wave HBT interference effect, and provide a unique tool to identify novel quantum phases of ultracold bosonic or fermionic atoms.
We study first- and second-order coherence of trapped dilute Bose gases using appropriate correlation functions. Special attention is given to the discussion of second-order or density correlations. Except for a small region around the surface of a Bose-Einstein condensate the correlations can be accurately described as those of a locally homogeneous gas with a spatially varying chemical potential. The degrees of first- and second-order coherence are therefore functions of temperature, chemical potential, and position. The second-order correlation function is governed both by the tendency of bosonic atoms to cluster and by a strong repulsion at small distances due to atomic interactions. In present experiments both effects are of comparable magnitude. Below the critical temperature the range of the bosonic correlation is affected by the presence of collective quasiparticle excitations. The results of some recent experiments on second- and third-order coherence are discussed. It is shown that the relation between the measured quantities and the correlation functions is much weaker than previously assumed.
We propose and demonstrate real-time subwavelength cavity QED measurements of the spatial distribution of atoms in an optical lattice. Atoms initially confined in one ``trap'' standing wave of an optical cavity mode are probed with a second ``probe'' standing wave. With frequencies offset by one free spectral range, the nodes of the trap fall on the antinodes of the probe in the $\ensuremath{\approx}{10}^{4}$ lattice sites around the center of the cavity. This lattice site independent atom-cavity coupling enables high sensitivity detection of atom dynamics even with atoms spread over many lattice sites. To demonstrate, we measure the temperature of $20--70\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$ atom ensembles in $<10\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$ by monitoring their expansion by $\ensuremath{\approx}100$ nm after sudden release from the trap lattice. Atom-cavity coupling imprints the atom dynamics on the probe transmission. The technique will enable improved nondestructive detection of Bloch oscillations and other atom dynamics in optical lattices.
We explore Bragg diffraction from atomic lattices bound by light as a diagnostic tool for studying properties of optical lattices not accessible so far. A weak laser beam at a wavelength of about half the wavelength of the lattice field is diffracted from the (100) and (130) lattice planes of a Rb optical lattice. The observation of well-defined Bragg spots confirms the long-range order in optical lattices. From the acceptance angle for Bragg diffraction we deduce the range over which crystalline order is preserved. The comparison of two Bragg spots diffracted from different lattice planes allows us to directly measure the position spread of the atomic wave packets oscillating in the light-induced potential wells. By combining conventional probe transmission spectroscopy with Bragg diffraction we study the motion of atoms that are deeply bound inside the potential wells. We show experimentally and theoretically how backaction of the bound atoms on the trapping field influences the lattice constant. We develop a model for the modification of the refractive index by the highly ordered atomic medium. Based on first-order scattering theory the model explicitly includes the influence of atomic localization on the resulting lattice constant. By measuring the change of the Bragg angle, we observe a decrease of the lattice plane separation for increasing atomic density. We report experimental evidence for the correction to the refractive index due to the finite position spread of the atoms.