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Physical Review Letters

Observing the Position Spread of Atomic Wave Packets

Axel Görlitz, Matthias Weidemüller, Theodor W. Hänsch, Andreas Hemmerich

Published Mar 17, 1997• 43 citations
Publisher

Abstract

We report on a novel method to measure the spatial extension of atomic wave packets confined in the microscopic light traps of a three-dimensional optical lattice. We compare the powers Bragg scattered by two different classes of lattice planes from two blue light beams incident on the atomic lattice under different Bragg angles. We have used this technique to explore unusual atomic vibrational modes which display a position spread oscillating at twice the fundamental vibrational frequency.

DOI
10.1103/physrevlett.78.2096

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We report on a novel method to measure the spatial extension of atomic wave packets confined in the microscopic light traps of a three-dimensional optical lattice. We compare the powers Bragg scattered by two different classes of lattice planes from two blue light beams incident on the atomic lattice under different Bragg angles. We have used this technique to explore unusual atomic vibrational modes which display a position spread oscillating at twice the fundamental vibrational frequency.
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 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 have observed Bragg scattering of photons from quantum degenerate ^{87}Rb atoms in a three-dimensional optical lattice. Bragg scattered light directly probes the microscopic crystal structure and atomic wave function whose position and momentum width is Heisenberg limited. The spatial coherence of the wave function leads to revivals in the Bragg scattered light due to the atomic Talbot effect. The decay of revivals across the superfluid to Mott insulator transition indicates the loss of superfluid coherence.
We study, experimentally and with quantum Monte-Carlo wave-function simulations, the effects of dispersion and dissipation on two types of spatial wave-packets of atoms in 1D and 3D optical lattices. Breathing-mode oscillations are excited by suddenly changing the potential depth after equilibration of the atoms at the lattice sites. The subsequent breathing-mode oscillations are measured using Bragg scattering. The second type of oscillations is prepared by suddenly shifting the lattice, thus exciting coherent-state-like wave-packets. These sloshing-type oscillations manifest themselves in a periodic photon redistribution between the lattice beams. We measure the resultant intensity exchange, which is a sensitive probe for the wave-packet evolution. For both types of wave-packets we observe an initial collapse within about three to six oscillation periods, a fact which we attribute to dephasing of the components of the wave-packets caused by the anharmonicity of the lattice potential. The initial collapse is followed by revivals of the wave-packets. Dissipation not only reduces the amplitude of these revivals but also modifies their shape and time of occurrence. In shallow lattices we observe that tunneling of the atoms between neighboring potential wells influences the wave-packet oscillations.
We study photonic band gaps in a one-dimensional optical lattice of laser-cooled trapped atoms. We solve for the self-consistent equilibrium positions of the atoms, accounting for the backaction of the atoms on the trapping beams. This solution depends strongly on the sign of the trapping laser detuning. For red-detuned trapping lasers, the resulting lattice exhibits a one-dimensional photonic band gap for frequencies between the trapping laser frequency and the atomic resonance. For blue detuning the stop band extends symmetrically about resonance, typically for hundreds of atomic linewidths, except for the small region between atomic resonance and the lattice frequency, which is excluded. We calculate the reflection spectrum for a lattice of Cs atoms for various trapping laser detunings and interpret its behavior as a function of the lattice size and density. For a mean density of 1011{10}^{11}1011 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, and 1000 planes, 55% reflection of a weak probe beam should be observed. We also consider Bragg scattering in a three-dimensional optical lattice as a means of probing the long-range order in the atomic density correlation function.