Quantifying metarefraction with confocal lenslet arrays

METATOYs can change the direction of light in ways that appear to, but do not actually, contravene the laws of wave optics. This direction change applies only to part of the transmitted light beam; the remainder gets re-directed differently. For a specific example, namely confocal pairs of rectangular lenslet arrays with no dead area between lenslets, we calculate here the fractions of power of a uniform-intensity light beam incident from a specific (but arbitrary) direction that get re-directed in different ways, and we derive an equation describing this redirection. This will facilitate assessment of the suitability of METATOYs for applications such as solar concentration. Finally, we discuss similarities between the multiple refraction of light at the lenslet arrays and multiple refraction and reflection of cold atoms at a barrier in the presence of the light fields.Comment: 24 pages, 15 figure

Magnetically generated spin-orbit coupling for ultracold atoms

We present a new technique for producing two- and three-dimensional Rashba-type spin-orbit couplings for ultracold atoms without involving light. The method relies on a sequence of pulsed inhomogeneous magnetic fields imprinting suitable phase gradients on the atoms. For sufficiently short pulse durations, the time-averaged Hamiltonian well approximates the Rashba Hamiltonian. Higher order corrections to the energy spectrum are calculated exactly for spin-1/2 and perturbatively for higher spins. The pulse sequence does not modify the form of rotationally symmetric atom-atom interactions. Finally, we present a straightforward implementation of this pulse sequence on an atom chip