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Journal of Modern Optics

Dynamics and spatial order of atoms confined in an optical lattice

Axel Görlitz, Theodor W. Hänsch, Andreas Hemmerich

Published Oct 1, 1997• 3 citations
Publisher

Abstract

This paper discusses how Bragg diffraction can be applied to measure the position spread of atomic wave packets localized in the light-induced periodic potential wells of an optical lattice. We describe an observation method which is solely based on monitoring light powers. No hard-to-access system parameters are referred to. We discuss the application of this method in the observation of unusual atomic vibrational modes with a position spread oscillating at twice the fundamental harmonic frequency. We also discuss the influence of the number of trapped atoms on the lattice geometry. We give experimental evidence for a contraction of the optical lattice as the filling factor is increased.

DOI
10.1080/09500349708231851

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This paper discusses how Bragg diffraction can be applied to measure the position spread of atomic wave packets localized in the light-induced periodic potential wells of an optical lattice. We describe an observation method which is solely based on monitoring light powers. No hard-to-access system parameters are referred to. We discuss the application of this method in the observation of unusual atomic vibrational modes with a position spread oscillating at twice the fundamental harmonic frequency. We also discuss the influence of the number of trapped atoms on the lattice geometry. We give experimental evidence for a contraction of the optical lattice as the filling factor is increased.
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.
We observe coherently enhanced reflection (Bragg scattering) of a near resonant laser beam from cesium atoms ordered by a periodic array of optical potential wells known as an optical lattice. The reflected light is enhanced by a factor of $\ensuremath{\sim}{10}^{5}$ over scattering from a disordered atomic sample. We measure the magnitude of the reflectivity and its detuning dependence as functions of the density and the degree of localization of the atoms. The change in lattice constant due to the frequency-dependent effective index of refraction seen by the lattice light field is observed.
Optical lattices are formed when cold atoms get trapped in the periodic array of optical potential wells created by a number of traveling light waves. Exact periodicity is guaranteed when the number of traveling waves exceeds the number of dimensions by no more than one. We present a few simple exactly solvable models for the transport of atoms over a lattice in the tight-binding limit. One model concerns the spreading of an atom by tunneling through the barriers and by momentum recoil induced by optical pumping. Another model gives results for the amplitude of Bloch oscillations, which occur when a uniform is added to the periodic potential. Finally the dissipative spreading of the quasimomentum due to optical pumping is modeled.
We observe Bragg diffraction of blue (422 nm) radiation from ultracold rubidium atoms bound in an infrared (780 nm) optical lattice thus demonstrating the long range periodic order in these atomic lattices. The blue light is reflected from the [201] planes of a cubic body-centered lattice at an incidence angle of 57\ifmmode^\circ\else\textdegree\fi{}. The angular breadth of the Bragg resonance is limited by the size of the atomic lattice to less than 0.26 mrad. We use Bragg diffraction in combination with an additional weak infrared probe beam as a novel tool to selectively study the motion of atoms deeply bound in the potential wells.
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.