Atom focusing by far-detuned and resonant standing wave fields: Thin lens regime

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 $$, 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.Comment: 21 pages, 11 figure

A step towards global key distribution

Large random bit-strings known as 'keys' are used to encode and decode sensitive data, and the secure distribution of these keys is essential to secure communications across the globe1. Absolutely secure key exchange2 between two sites has now been demonstrated over fibre3 and free-space4, 5, 6 optical links. Here we describe the secure exchange of keys over a free-space path of 23.4 kilometres between two mountains. This marks a step towards accomplishing key exchange with a near-Earth orbiting satellite and hence a global key-distribution system.Large random bit-strings known as 'keys' are used to encode and decode sensitive data, and the secure distribution of these keys is essential to secure communications across the globe1. Absolutely secure key exchange2 between two sites has now been demonstrated over fibre3 and free-space4, 5, 6 optical links. Here we describe the secure exchange of keys over a free-space path of 23.4 kilometres between two mountains. This marks a step towards accomplishing key exchange with a near-Earth orbiting satellite and hence a global key-distribution system