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Physical Review A

Self-induced Bragg-type scattering in dark optical superlattices

Péter Horák, Helmut Ritsch

Published Mar 1, 1997• 5 citations
Publisher

Abstract

We show that the coherent part of the atomic fluorescence spectrum in a dark optical superlattice can be interpreted as a new type of Bragg scattering of the trapping lasers by the periodic atomic distribution. We explicitly solve the 1D problem to demonstrate that this built-in mechanism provides a diagnostic tool to determine the atomic position and energy distribution without any extra disturbance of the system. Hence, in principle, this method allows one to gain important information on atom-atom interactions and quantum statistics in the case of several atoms confined within a single optical (super)well.

DOI
10.1103/physreva.55.2176

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We show that the coherent part of the atomic fluorescence spectrum in a dark optical superlattice can be interpreted as a new type of Bragg scattering of the trapping lasers by the periodic atomic distribution. We explicitly solve the 1D problem to demonstrate that this built-in mechanism provides a diagnostic tool to determine the atomic position and energy distribution without any extra disturbance of the system. Hence, in principle, this method allows one to gain important information on atom-atom interactions and quantum statistics in the case of several atoms confined within a single optical (super)well.
We calculate the spectrum of resonance fluorescence and the weak-field absorption spectrum obtained from atoms cooled and trapped in a one-dimensional dark optical superlattice, which is formed by a bichromatic laser field in double-Λ configuration. These spectra provide an experimentally accessible tool to gain important information about the trapping mechanism and the steady-state density matrix. A rate-equation approach is used to discuss the dependence of the spectra on various model parameters.
We study Bragg scattering at one-dimensional (1D) optical lattices. Cold atoms are confined by the optical dipole force at the antinodes of a standing wave generated inside a laser-driven high-finesse cavity. The atoms arrange themselves into a chain of pancake-shaped layers located at the antinodes of the standing wave. Laser light incident on this chain is partially Bragg reflected. We observe an angular dependence of this Bragg reflection which is different from what is known from crystalline solids. In solids, the scattering layers can be taken to be infinitely spread (three-dimensional limit). This is not generally true for an optical lattice consistent of a 1D linear chain of pointlike scattering sites. By an explicit structure factor calculation, we derive a generalized Bragg condition, which is valid in the intermediate regime. This enables us to determine the aspect ratio of the atomic lattice from the angular dependance of the Bragg scattered light.
We study a new type of optical lattice in which the localized atoms experience a much reduced optical pumping and fluorescence rate. An optical standing wave is tuned to the blue of the F = 2 ? F = 2 transition of the (87)Rb D(2) line and induces periodic optical potentials by coupling the F = 2 ground state to both the F = 2 and F = 3 excited states. A Sisyphus mechanism efficiently cools the atoms into the lattice sites. We adiabatically release the atoms from the optical lattice and measure their momentum distribution with a resolution of one third of a single photon recoil. This allows us to determine the population of the two lowest energy bands in the optical lattice (44% and 20%).
We report on the observation of Bragg scattering at 1D atomic lattices. Cold atoms are confined by optical dipole forces at the antinodes of a standing wave generated by the two counterpropagating modes of a laser-driven high-finesse ring cavity. By heterodyning the Bragg-scattered light with a reference beam, we obtain detailed information on phase shifts imparted by the Bragg scattering process. Being deep in the Lamb-Dicke regime, the scattered light is not broadened by the motion of individual atoms.
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 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.