Abstract
We propose a lensless optical method for imaging two-dimensional ultra-cold atoms (or molecules) in which the image can be non-locally observed by coincidence recording of entangled photon pairs. In particular, we focus on the transverse and longitudinal resolutions of images under various scanning methods. In addition, the role of the induced nonmaterial lattice on the image contrast is investigated. Our work shows a non-destructive and lensless way to image ultra-cold atoms or molecules that can be further used for two-dimensional atomic super-resolution optical testing and sub-wavelength lithography.
Highlights
MethodsEvolution of the Probe Field in an Atomic Ensemble
May broaden the variety of applications used in imaging techniques and prove to be useful for two-dimensional atomic super-resolution optical testing and sub-wavelength lithography as well
To perform lensless imaging of an ultra-cold atomic ensemble sample, we utilize two perpendicular standing-wave fields to modify the optical response of the medium to the weak probe field
Summary
Evolution of the Probe Field in an Atomic Ensemble. Hamiltonian under the electric-dipole approximation and the rotating-wave approximation is expressed as (ħ = 1). H = G1e−i∆1t 0 1 + G2e−i∆2t 1 2 + G3e−i∆3t 1 3 + h.c. Where Gi =μijEi/ħ are the Rabi frequencies of the optical pumping field, and the laser-field detunings from the transitions |0〉→|1〉, |1〉→|2〉and |1〉→|3〉are defined as Δ1 =ω1 −ω10, Δ2 =ω2 −ω21 and Δ3 =ω3 −ω31, respectively, with ωij =ωi −ωj, (i, j = 0, 1, 2, 3). By using the Liouville equation, the coupled system equations are obtained:.
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