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Nonlinear Optics

Nonlinearities of atoms trapped in optical lattices

G. Grynberg

Published Dec 17, 2002• 0 citations
Publisher

Abstract

We present results concerning the transmission and the scattering of a probe beam in optical lattices. We have observed stimulated Raman and Rayleigh gains as large as 70% for a 1 mm/sup 3/ lattice and the occurence of diffraction in the Bragg directions. We discuss the relation between Bragg diffraction and four-wave mixing.>
DOI
10.1109/nlo.1994.470894

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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 present a study of pump-probe spectroscopy experiments in an optical lattice. The probe transmission spectrum contains three types of resonances similar to those found in usual nonlinear media: Raman, Brillouin and Rayleigh resonances. We show evidence of the existence of a propagating elementary excitation in the lattice which involves no interaction between the particles and lead to a Brillouin-like scattering. We discuss the central Rayleigh resonance and show that its shape is sensitive to the radiation pressure.
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.
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.
Selected topics related to the fundamentals of nonlinear optics are discussed. First, a brief description on the theory of nonlinear optical susceptibilities is given. Emphasis is on the basic properties, on the recently developed bond theory, and on the dispersion of nonlinear susceptibilities. Then the coupled wave approach is discussed. It is shown that the transverse resonant excitation in material can be treated as a material excitational wave, and most nonlinear optics problems can be understood as results of coupling between em waves or em and material excitational waves. A number of examples of current interest are presented. These include sum- and difference-frequency generation, Raman scattering by coherent excitation, stimulated Raman and stimulated polariton scattering, four-wave mixing, and vibrational relaxation measurements. Finally, the physical distinction between laser emission and resonant stimulated Raman scattering in an optically pumped three-level system are considered. A similar problem on the distinction of hot luminescence and resonant Raman scattering has recently attracted much attention. It is shown that the hot laser action is connected directly with the population inversion, while the resonant stimulated Raman scattering is connected with transverse excitation. The problem is, however, more complicated for a multi-level system. (auth)