dorsal/arxiv
View SchemaAtom focusing by far-detuned and resonant standing wave fields: Thin lens regime
| Authors | J. L. Cohen, B. Dubetsky, P. R. Berman |
|---|---|
| Categories | |
| ArXiv ID | physics/9907038 |
| URL | https://arxiv.org/abs/physics/9907038 |
| DOI | 10.1103/PhysRevA.60.4886 |
Abstract
The focusing of atoms interacting with both far-detuned and resonant standing wave fields in the thin lens regime is considered. The thin lens approximation is discussed quantitatively from a quantum perspective. Exact quantum expressions for the Fourier components of the density (that include all spherical aberration) are used to study the focusing numerically. The following lens parameters and density profiles are calculated as functions of the pulsed field area $\theta $: the position of the focal plane, peak atomic density, atomic density pattern at the focus, focal spot size, depth of focus, and background density. The lens parameters are compared to asymptotic, analytical results derived from a scalar diffraction theory for which spherical aberration is small but non-negligible ($\theta \gg 1$). Within the diffraction theory analytical expressions show that the focused atoms in the far detuned case have an approximately constant background density $0.5(1-0.635\theta ^{- 1/2})$ while the peak density behaves as $% 3.83\theta ^{1/2}$, the focal distance or time as $\theta ^{-1}(1+1.27\theta ^{- 1/2})$, the focal spot size as $0.744\theta ^{-3/4}$, and the depth of focus as $1.91\theta ^{- 3/2}$. Focusing by the resonant standing wave field leads to a new effect, a Rabi- like oscillation of the atom density. For the far-detuned lens, chromatic aberration is studied with the exact Fourier results. Similarly, the degradation of the focus that results from angular divergence in beams or thermal velocity distributions in traps is studied quantitatively with the exact Fourier method and understood analytically using the asymptotic results. Overall, we show that strong thin lens focusing is possible with modest laser powers and with currently achievable atomic beam characteristics.
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"abstract": "The focusing of atoms interacting with both far-detuned and resonant standing\nwave fields in the thin lens regime is considered. The thin lens approximation\nis discussed quantitatively from a quantum perspective. Exact quantum\nexpressions for the Fourier components of the density (that include all\nspherical aberration) are used to study the focusing numerically. The following\nlens parameters and density profiles are calculated as functions of the pulsed\nfield area $\\theta $: the position of the focal plane, peak atomic density,\natomic density pattern at the focus, focal spot size, depth of focus, and\nbackground density. The lens parameters are compared to asymptotic, analytical\nresults derived from a scalar diffraction theory for which spherical aberration\nis small but non-negligible ($\\theta \\gg 1$). Within the diffraction theory\nanalytical expressions show that the focused atoms in the far detuned case have\nan approximately constant background density $0.5(1-0.635\\theta ^{- 1/2})$\nwhile the peak density behaves as $% 3.83\\theta ^{1/2}$, the focal distance or\ntime as $\\theta ^{-1}(1+1.27\\theta ^{- 1/2})$, the focal spot size as\n$0.744\\theta ^{-3/4}$, and the depth of focus as $1.91\\theta ^{- 3/2}$.\nFocusing by the resonant standing wave field leads to a new effect, a Rabi-\nlike oscillation of the atom density. For the far-detuned lens, chromatic\naberration is studied with the exact Fourier results. Similarly, the\ndegradation of the focus that results from angular divergence in beams or\nthermal velocity distributions in traps is studied quantitatively with the\nexact Fourier method and understood analytically using the asymptotic results.\nOverall, we show that strong thin lens focusing is possible with modest laser\npowers and with currently achievable atomic beam characteristics.",
"arxiv_id": "physics/9907038",
"authors": [
"J. L. Cohen",
"B. Dubetsky",
"P. R. Berman"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1103/PhysRevA.60.4886",
"title": "Atom focusing by far-detuned and resonant standing wave fields: Thin lens regime",
"url": "https://arxiv.org/abs/physics/9907038"
},
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