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Physical Review A

Projection of diffraction patterns for use in cold-neutral-atom trapping

Katharina Gillen-Christandl, Glen D. Gillen

Published Dec 29, 2010• 6 citations
Publisher

Abstract

Scalar diffraction theory is combined with beam-propagation techniques to investigate the projection of near-field diffraction patterns to spatial locations away from the aperture for use in optically trapping cold neutral alkali-metal atoms. Calculations show that intensity distributions with localized bright and dark spots usually found within a millimeter of the diffracting aperture can be projected to a region free from optical components such as a cloud of cold atoms within a vacuum chamber. Calculations also predict that the critical properties of the optical dipole atom traps are not only maintained for the projected intensity patterns but also can be manipulated and improved by adjustment of the optical components outside the vacuum chamber.

DOI
10.1103/physreva.82.063420

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Physical Review A•Feb 9, 2011•13 citations
Scalar diffraction theory is combined with beam-propagation techniques to investigate the projection of near-field diffraction patterns to spatial locations away from the aperture for use in optically trapping cold neutral alkali-metal atoms. Calculations show that intensity distributions with localized bright and dark spots usually found within a millimeter of the diffracting aperture can be projected to a region free from optical components such as a cloud of cold atoms within a vacuum chamber. Calculations also predict that the critical properties of the optical dipole atom traps are not only maintained for the projected intensity patterns but also can be manipulated and improved by adjustment of the optical components outside the vacuum chamber.
In this chapter we present an interesting application of the propagation of laser light through linear optical media: the ability to spatially confine (trap) cold atoms within localized light intensity patterns. We first present some of the fundamentals for understanding how light can trap an atom. Depending upon the relationship between the properties of the atom and the properties of the laser light, atoms can be trapped in either localized dark spots, or localized bright spots. We will describe several light patterns for trapping atoms: The tightly localized bright and dark regions in the near-field diffraction patterns presented in Chapters 7 and 8 , The near-field patterns projected to a location far away from the diffracting aperture, and Polarization-dependent movable light field traps based on the near-field diffraction patterns.
We theoretically investigate the feasibility of using intensity distributions of light of a single laser beam diffracted by a circular aperture as optical dipole traps for cold neutral atoms. Localized and cylindrically symmetric traps on the central axis of the circular aperture exist for both blue- and red-detuned laser light. Experimental mapping of the spots of interest using CO2{\mathrm{CO}}_{2}CO2​ laser light demonstrates the existence of these light distributions for laboratory conditions and their agreement with theoretical predictions.
We propose and present a quantitative analysis of neutral atom microtraps based on optical near fields produced by the diffraction of a laser wave on small apertures in a thin screen. We show that near-field atom microtraps are capable of storing atoms in micron-sized regions, with estimated trap lifetimes of about 1s1\phantom{\rule{0.3em}{0ex}}\mathrm{s}1s, when using a moderate laser intensity of about 10W∕cm210\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}10W∕cm2. The depth of the proposed Fresnel atom microtraps is about 0.1mK0.1\phantom{\rule{0.3em}{0ex}}\mathrm{mK}0.1mK. An array of such atom microtraps could have applications to site-selective manipulation of cold atoms.
Theoretical calculations were performed for the projection of a diffraction pattern created by a pinhole through a single-lens system using vector diffraction theory and a combination of programs (MathCAD, Igor, etc.). The projected diffraction patterns were then experimentally created, recorded, and analyzed. This work is part of a larger collaboration with Dr. Kat Gillen, to trap and manipulate atoms in a Magneto Optical Trap (MOT) and to make further steps in the direction of Quantum Computing using trapped neutral atoms.
Summary form only given. Recently, atom manipulation by using optical near fields has been attracting a lot of interests. Optical near field can be localized in a nanometric region, being free from the diffraction limit in contrast to propagation light. The intensity distribution of optical near field decays rapidly as an exponential-like function. Because such a spatially inhomogeneous light field can affect the resonant force on an atom (the so called dipole force), the optical near field produces the strong dipole force. Using the dipole force of the optical near field, we can expect to manipulate an atom with high spatial accuracy. Moreover, due to the resonant character of the dipole force, we can manipulate an atom species- and state-selectively. The optical near field localized in a nanometric region can be generated on the tip of a sharpened fiber-probe. This kind of fiber probe can be used for deflection of the atomic motion, and then trapping of an atom. To this end, it is very important to fabricate the fiber probe suitable for the atoms used. In this case, we must consider several parameters: a size and a shape of the tip, light intensity, frequency detuning, etc. In order to examine the optimal conditions for the fabrication, we measured and evaluated the optical near-field intensity distribution of the fiber-probe.
The neutral-atom quantum computing community has successfully implemented almost all necessary steps for constructing a neutral-atom quantum computer. We present computational results of a study aimed at solving the remaining problem of creating a quantum memory with individually addressable sites for quantum computing. The basis of this quantum memory is the diffraction pattern formed by laser light incident on a circular aperture. Very close to the aperture, the diffraction pattern has localized bright and dark spots that can serve as red-detuned or blue-detuned atomic dipole traps. These traps are suitable for quantum computing even for moderate laser powers. In particular, for moderate laser intensities ( 100~100 100 W/cm2{\mathrm{cm}}^{2}cm2) and comparatively small detunings ( 1000~1000 1000--10 000 linewidths), trap depths of  1~1 1 mK and trap frequencies of several to tens of kilohertz are achieved. Our results indicate that these dipole traps can be moved by tilting the incident laser beams without significantly changing the trap properties. We also explored the polarization dependence of these dipole traps. We developed a code that calculates the trapping potential energy for any magnetic substate of any hyperfine ground state of any alkali-metal atom for any laser detuning much smaller than the fine-structure splitting for any given electric field distribution. We describe details of our calculations and include a summary of different notations and conventions for the reduced matrix element and how to convert it to SI units. We applied this code to these traps and found a method for bringing two traps together and apart controllably without expelling the atoms from the trap and without significant tunneling probability between the traps. This approach can be scaled up to a two-dimensional array of many pinholes, forming a quantum memory with single-site addressability, in which pairs of atoms can be brought together and apart for two-qubit gates for quantum computing.