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arXiv:0804.1162

Gaussian Schell Source as Model for Slit-Collimated Atomic and Molecular Beams

Ben McMorran, Alex D. Cronin

Published Apr 8, 2008• 3 citations
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Abstract

We derive the spatial coherence and intensity profiles of beams emerging from two consecutive collimating apertures, and compare our results with data. We show how to make a Gaussian Schell-model (GSM) beam by assuming Gaussian apertures. Then we compare the intensity profile, the transverse coherence width and the divergence angle of a GSM beam with those same properties of a beam that is collimated with two hard-edged slits. The GSM beam formulae are simpler, and offer an intuitive way to understand how partially coherent beams interact with interferometers.

DOI
10.48550/arxiv.0804.1162

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We derive the spatial coherence and intensity profiles of beams emerging from two consecutive collimating apertures, and compare our results with data. We show how to make a Gaussian Schell-model (GSM) beam by assuming Gaussian apertures. Then we compare the intensity profile, the transverse coherence width and the divergence angle of a GSM beam with those same properties of a beam that is collimated with two hard-edged slits. The GSM beam formulae are simpler, and offer an intuitive way to understand how partially coherent beams interact with interferometers.
The role of spatial coherence on diffraction intensity is investigated for a partially coherent incident Gaussian Schell-model beam which is diffracted from a two-level atomic grating. It is shown that the performance of the atomic grating is greatly influenced by the spectral coherence width of the partially coherent fields. It is observed that relatively large intensity of the diffracted light can be obtained via spatial coherence, beam width, interaction length, and mode index of partially coherent incident light. The scheme provides possibilities for the potential applications of atomic grating in lensless imaging using the partially coherent light field.
We examine how partial coherence and wavefront curvature of beams affect interference fringes behind diffraction gratings. We simulate (1) the Talbot effect, (2) far-field diffraction, (3) Mach-Zehnader interferometers, (4) Talbot-Lau interferometers, and (5) Lau interferometers using a numerically efficient expression. We show how interference fringes in each case depend on the beam's initial width, its coherence width (transverse coherence length), and its wavefront curvature in directions both parallel and perpendicular to the grating bars. The separation between gratings and the rotational alignment of the gratings about the optical axis are also considered. The formula used for our simulations is derived using the mutual intensity function of a Gaussian Schell-model beam.
The nonparaxial propagation of partially coherent Gaussian Schell-model (GSM) beams in a graded-index waveguide is studied using the coherent states and coherent modes decomposition methods, as well as perturbation theory. Long-scale decoherence and recoherence of the GSM beam occur due to the revival effect caused by mode interference. It is shown that the radius of coherence and the degree of coherence can be determined based on measurements of purely geometric characteristics of the GSM beam. The information entropy and quantum mechanical purity of GSM beams are evaluated.
The quantum theory of the electromagnetic field uncovered that classical forms of light were indeed produced by distinct superpositions of nonclassical multiphoton wave packets. This situation prevails for partially coherent light, the most common kind of classical light. Here, for the first time, to our knowledge, we demonstrate the extraction of the constituent multiphoton quantum systems of a partially coherent light field. We shift from the realm of classical optics to the domain of quantum optics via a quantum representation of partially coherent light using its complex-Gaussian statistical properties. Our formulation of the quantum Gaussian-Schell model (GSM) unveils the possibility of performing photon-number-resolving (PNR) detection to isolate the constituent quantum multiphoton wave packets of a classical light field. We experimentally verified the coherence properties of isolated vacuum systems and wave packets with up to 16 photons. Our findings not only demonstrate the possibility of observing quantum properties of classical macroscopic objects but also establish a fundamental bridge between the classical and quantum worlds.
The recently introduced concept of Stokes fluctuations generalizes both the Hanbury Brown--Twiss effect and the notion of scintillation. Here we apply this new framework to the specific example of a Gaussian Schell-model (GSM) beam. We derive formulas for Stokes scintillations and Stokes fluctuation correlations, which explicitly express the dependence of these quantities on the GSM source parameters. It is found that the normalized Stokes scintillations vary significantly with position. Also, they can be either positively or negatively correlated.
Analytical expression is obtained for the cross-spectral density function of a Gaussian Schell-model (GSM) beam passing through an electromagnetic induced transparency (EIT) atomic vapor. The formula can be used in the study of the changes in the spectral density and spectral degree of coherence of the beam through the EIT atomic vapor. Numerical examples show that both the spectral density and the spectral degree of coherence of the GSM beam can be modulated by the Rabi frequency of the control light.