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arXiv:quant-ph/0006002 · Physical Review A

Strongly focused light beams interacting with single atoms in free space

S. J. van Enk, Harry J. Kimble

Published Jan 12, 2001• 79 citations
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Abstract

We construct three-dimensional solutions of Maxwell's equations that describe Gaussian light beams focused by a strong lens. We investigate the interaction of such beams with single atoms in free space and the interplay between angular and quantum properties of the scattered radiation. We compare the exact results with those obtained with paraxial light beams and from a standard input-output formalism. We put our results in the context of quantum information processing with single atoms.

DOI
10.1103/physreva.63.023809

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We construct three-dimensional solutions of Maxwell's equations that describe Gaussian light beams focused by a strong lens. We investigate the interaction of such beams with single atoms in free space and the interplay between angular and quantum properties of the scattered radiation. We compare the exact results with those obtained with paraxial light beams and from a standard input-output formalism. We put our results in the context of quantum information processing with single atoms.
Abstract. We investigate the interaction between a single atom and a light field in the strong focusing regime. Such a configuration is subject to recent experimental work not only with atoms but also molecules and other atom-like systems as quantum dots. We derive the scattering probability for a photon from such a microscopic object modeled by a two-level system, starting with a Gaussian beam as the spatial mode of the light field. The focusing by an ideal lens is modeled using spherical wave fronts of a field compatible with Maxwell equations. Using a semi-classical approach for the atom-field interaction, we predict scattering probability of photons by a single atom of up to 98% for realistic focusing parameters. Experimental results for different focusing strengths are compared with our theoretical model. PACS numbers: 42.50Ct, 42.50Ex, 42.25BsInterfacing light and single atoms with a lens 2 1.
We characterize the interaction between a single atom or similar microscopic system and a light field via the scattering ratio. For this, we first derive the electrical field in a strongly focused Gaussian light beam, and then consider the atomic response. Following the simple scattering model, the fraction of scattered optical power for a weak coherent probe field leads to unphysical scattering ratios above 1 in the strong focusing regime. A refined model considering interference between the exciting and scattered field into finite-sized detectors or optical fibers is presented, and compared with experimental extinction measurements for various focusing strengths.
We measured the extinction of a focused light beam by a single 87Rb atom localized in an optical dipole trap and found a value of 7.2% for a focused Gaussian beam resonantly interacting with an atomic two-level system. Various models describing interaction of an atom with a focused light field are compared to explain our experimental result. Our experiment suggests that a strong coupling may be achieved without cavity assistance. This opens new perspectives for a development of an efficient atom-photon interface for Quantum Information processing.
The focusing of atoms to nanometer-scale dimensions by a near-resonant standing-wave light field is examined from a particle optics perspective. The classical equation of motion for atoms traveling through the lens formed by a node of the standing wave is derived and converted to a spatial trajectory equation. A paraxial solution is obtained, which results in simple expressions for the focal properties of the lens, useful for estimating its behavior. Aberrations are also discussed, and an exact numerical solution of the trajectory equation is presented. The effects on focal linewidth of angular collimation and velocity spread in the atomic beam are investigated, and it is shown that angular collimation has a much more significant effect than velocity spread, even when the velocity spread is thermal.
The focusing of an atomic beam using near-resonant laser light is considered. Path-integral techniques are employed to transform the problem into a standard diffraction integral. This approach is general and allows us to deal with thick laser lenses. Starting from the basic form of the potential energy for an atom in a laser beam, we derive the propagation kernel for the atomic wave function for the particular case of a TEM01*, or doughnut, mode laser beam. Both the full three-dimensional propagation kernel and its paraxial approximation are discussed. We show that the paraxial case can be obtained from the three-dimensional case by a stationary-phase approximation of the propagation equation. Numerical results for the focusing of a Gaussian atomic beam are presented. These results show that spot diameters on the order of 20 Å are obtainable for many reasonable choices of laser and atomic beam parameters and that for most of these cases the thin-lens approximation is not valid. The effects of the lowest-order aberrations are also briefly discussed. Spherical aberration is found to contribute significantly to the focal spot diameter, at least for the doughnut mode laser beam considered here.