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arXiv:1406.1982 · Physical Review X

From the Area under the Bessel Excursion to Anomalous Diffusion of Cold Atoms

Eli Barkai, Erez Aghion, David A. Kessler

Published May 28, 2014• 106 citations
arXivHTMLPDF

Abstract

Researchers develop a new theory to characterize anomalous spatial diffusion of an ensemble of cold ${}^{87}$Rb atoms and single ${}^{24}$Mg${}^{+}$ ions in optical lattices. The theory shows how a transition from regular to anomalous diffusion, with a continuous range of anomalous scaling, is obtained with the tuning of the laser intensity.

DOI
10.1103/physrevx.4.021036

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Researchers develop a new theory to characterize anomalous spatial diffusion of an ensemble of cold 87{}^{87}87Rb atoms and single 24{}^{24}24Mg+{}^{+}+ ions in optical lattices. The theory shows how a transition from regular to anomalous diffusion, with a continuous range of anomalous scaling, is obtained with the tuning of the laser intensity.
Recently, anomalous superdiffusion of ultracold 87Rb atoms in an optical lattice has been observed along with a fat-tailed, Lévy type, spatial distribution. The anomalous exponents were found to depend on the depth of the optical potential. We find, within the framework of the semiclassical theory of Sisyphus cooling, three distinct phases of the dynamics as the optical potential depth is lowered: normal diffusion; Lévy diffusion; and x∼t(3/2) scaling, the latter related to Obukhov's model (1959) of turbulence. The process can be formulated as a Lévy walk, with strong correlations between the length and duration of the excursions. We derive a fractional diffusion equation describing the atomic cloud, and the corresponding anomalous diffusion coefficient.
We carry out quantum and semiclassical numerical simulations of the dynamics, particularly diffusion, of atoms in an optical lattice. We consider specifically the situation of a $J=1/2\ensuremath{\leftrightarrow}J=3/2$ atomic transition, whose experimental counterpart can be realized in Mg+{\mathrm{Mg}}^{+}Mg+ experiments. The semiclassical results, which cover a larger range of parameters than would be practical for fully quantum calculations, confirm and extend the work of Marksteiner et al. [Phys. Rev. A 53, 3409 (1996)], characterize the transition from normal to anomalous diffusion and the atomic trajectories which give rise to it, and provide a physical explanation for the difference between these two regimes. The full quantum calculations reveal uniquely quantum features of individual atomic trajectories, and in addition, predict significantly lower diffusion, by a factor of 1.2 to 2, than their semiclassical counterparts.
In this dissertation a cloud of cold rubidium atoms confined in a magnetooptical trap (MOT) has been realized. The laser cooling and trapping technique was implemented in the Laboratory for femtosecond frequency comb spectroscopy at Institute of Physics for the first time, so this work opens a new area of research. The cloud of cold atoms, containing ~ 10^9 87^Rb, F_g = 2, in volume ~ 3 mm3, density of ~ 1011 atom/cm3 in typical MOT operating conditions was obtained. Detailed characterization of the cloud has been done and the Doppler model for the real atomic system of rubidium 87 atoms was applied to describe the radiative force. The main focus of this work is investigation of the coherent continuous (cw) or pulsed (femtosecond) radiation effects on rubidium atoms in MOT. Atomic motion in the trap can be described with a damped harmonic oscillator model. A new technique for monitoring cold cloud center of mass oscillations induced by cw laser, tuned to rubidium resonant transition has been introduced. With this method the basic trap parameters, such are spring constant, damping coefficient and atom temperature are determined. For various trap working conditions an effective saturation intensity of 87^Rb D1 (F_g = 2 → F_e = 2) transition is, for the first time, determined through experimentally and theoretically investigated rubidium excited F_e = 2 state population depending on the probe beam intensity. Also, the radiative force of the probe D1 laser on cold cloud is measured and theoretically modelled. Interaction of cold rubidium cloud with femtosecond (fs) pulses has been studied in three different experimental configurations; interaction of cold atoms with single fs train of pulses, with two in-phase counterpropagating fs pulses and with two out-of-phase counterpropagating fs pulses. In all three described geometries the LIF signal and radiative force are experimentally determined and compared with theoretical model, based on optical Bloch equations (OBE) for two energy level atom.
Field emission (FE) electron sources are made close to atomic-scale to reach the highest spatial resolution as well as stable emission for electron microscopy, electron beam inspection and lithography. At present, no single agreed method exists of using FE current-voltage data to extract the apparent emission area, which is needed for predicting some beam properties. The 1956 theory of Murphy and Good (MG) is better physics than the 1920s theory of Fowler and Nordheim (FN) and colleagues, but many researchers use simplified FN theory to analyse experimental data. The present paper reports an experimental method of finding apparent emission area, based on using field ion and field electron microscopes (FIM-FEM). The discrepancy of emission area between the FIM-FEM method and MG-based analysis is a factor of 7.4, while that with simplified FN-based analysis is about 25, confirming MG theory is better for FE data analysis. The result allows deduction of key indicators, including source energy spread, reduced brightness and emission efficiency. A downloadable program is made available to help analysis. Our work provides a new experimental method of characterizing FE electron sources, especially the atomic-scale cold cathode, for which existing plot-based data-analysis methods are not suitable.