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AIP conference proceedings

Kinetic Description of Feed-Back Non-Resonant Optical Lattices-Gas Interaction

Mikhail N. Shneider, P. F. Barker

Published Jan 1, 2011• 0 citations
Publisher

Abstract

In this paper the effects of coupling a non‐resonant optical lattice to a gas is studied. When the lattice induces a periodic modulation of the gas density, strong Bragg diffraction of light can occur. If a significant fraction of the light used to make the periodic structure is diffracted it can potentially limit the achievable intensities inside the lattice limiting the ability to manipulate the gas with the light. We calculate the evolution of the light fields by finding solutions to the wave equation with a periodic refractive index induced by the lattice. The local gas density perturbation induced by the lattice is determined by solution of the Boltzmann kinetic equation in the collisional regime. This allows us to predict the limits of gas transport within optical lattice. We discuss the maximum energy and momentum transfer to the gas from the lattice.

DOI
10.1063/1.3562746

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In this paper the effects of coupling a non‐resonant optical lattice to a gas is studied. When the lattice induces a periodic modulation of the gas density, strong Bragg diffraction of light can occur. If a significant fraction of the light used to make the periodic structure is diffracted it can potentially limit the achievable intensities inside the lattice limiting the ability to manipulate the gas with the light. We calculate the evolution of the light fields by finding solutions to the wave equation with a periodic refractive index induced by the lattice. The local gas density perturbation induced by the lattice is determined by solution of the Boltzmann kinetic equation in the collisional regime. This allows us to predict the limits of gas transport within optical lattice. We discuss the maximum energy and momentum transfer to the gas from the lattice.
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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 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.
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In this thesis we investigate the diffraction of cold atomic gases by optical lattices. Of particular interest to atom interferometry is the implementation of a high momentum-transfer ``beam-splitter,'' which may be achieved by inducing quantum resonance in such an atomic gas. We use Monte Carlo simulations to investigate these quantum resonances in the regime where the gas receives laser pulses of finite duration, and demonstrate that an ϵ\epsilonϵ-pseudoclassical model for the dynamics of the gas atoms reproduces quantum resonant behavior for both zero-temperature and finite-temperature non-interacting gases. We show that this model agrees well with the fully quantum treatment of the system over a timescale set by the choice of experimental parameters. In similar setups, the depth of a laser lattice may be measured by exposing an atomic gas to a series of off-resonant laser-standing-wave pulses, and fitting theoretical predictions for the population found in each of the allowed momentum states. We present an analytic model for the time evolution of the atomic populations of the lowest momentum-states, which is sufficient for a weak lattice, as well as numerical simulations incorporating higher momentum states for both relatively strong and weak lattices at zero and finite temperature. We propose a new approach to characterizing the depths of optical lattices, in which an atomic gas is given a finite initial momentum, leading to high amplitude oscillations in the zeroth diffraction order which are robust to finite-temperature effects. We present a zero-temperature analytic formula describing such oscillations, extend it to include atoms with initial momenta detuned from our chosen initial value, and analyze the full finite-temperature response.