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Optics Express

Interference effects induced by non-local spatial filtering

Stephen Patrick Walborn, P. H. Souto Ribeiro, Carlos Henrique Monken

Published Aug 18, 2011• 5 citations
Publisher

Abstract

The spatial correlation between down-converted photons allows for non-local spatial filtering when two-photon coincidences are registered. This allows one to non-locally control the visibility of interference fringes, to observe ghost images and interference patterns, and to "retrieve" a coherent quantum image from an incoherent field distribution. We show theoretically that non-local spatial filtering can lead to counter-intuitive effects when the pump beam is no longer given by a Gaussian profile. Namely, increased non-local filtering can actually decrease the visibility of interference fringes, contrary to what has been observed so far. We explain this behavior through the transverse spatial parity entanglement of the down-converted photons.

DOI
10.1364/oe.19.017308

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The spatial correlation between down-converted photons allows for non-local spatial filtering when two-photon coincidences are registered. This allows one to non-locally control the visibility of interference fringes, to observe ghost images and interference patterns, and to "retrieve" a coherent quantum image from an incoherent field distribution. We show theoretically that non-local spatial filtering can lead to counter-intuitive effects when the pump beam is no longer given by a Gaussian profile. Namely, increased non-local filtering can actually decrease the visibility of interference fringes, contrary to what has been observed so far. We explain this behavior through the transverse spatial parity entanglement of the down-converted photons.
Fourth-order coherence determines the visibility of interference fringes observed in two-photon correlation measurements. In some cases, one photon triggers the presence of its conjugate twin in the interferometer. Therefore, spatial or spectral filtering of the trigger photon may change the visibility of the interference fringes and the degree of fourth-order coherence as well. We show that, contrary to the intuition developed from series of previous experiments, it is possible to increase the fourth-order coherence by reducing the degree of filtering. We present a theoretical approach and experimental results demonstrating this effect and interpret it in terms of spatial mode parity selection.
Ghost interference with entangled photon pairs are studied theoretically. The pump beam in parametric down-conversion is treated as the Gaussian profile, while for the function describing phase matching in the longitudinal direction, both a Gaussian and a sinc function are considered. The numerical results show that the transverse size of the pump beam and transverse coherence width of the parametric fluorescence strongly influence the interference pattern. With the increase of the pump transverse size and the decrease of transverse coherence width, the interference pattern becomes more and more prominent. When the transverse coherence width is small to 0.01 mm category, the Gaussian and sinc models give the same results.
Partially coherent quantum-entangled beams combine quantum correlation with partial coherence, allowing them to maintain quantum characteristics while being more resistant to distortions caused by random media during propagation. In this study, we investigate the effect of coherence variation of such beams on non-local double-slit quantum interference. The spatial coherence variation is achieved by controlling the transverse coherence length of the Gaussian Schell model pump in the spontaneous parametric down conversion process. For a fixed beam size, the momentum correlation width of partially coherent biphotons increases with the decrease in the transverse coherence length. This results in a biphoton beam exhibiting multiple spatial modes, making it more suitable for studying the non-local features of quantum states in imaging, interference, and diffraction experiments. Our findings infer both high-quality and near-unity visibility of nonlocal interference using the partially coherent twin beams, even with the substantial decrease in the coherence of the pump. We believe these results can enhance robustness against the deleterious effects of the medium during propagation and can have potential applications in optical image cryptography, biomedical imaging, quantum lithography, and quantum holography.
Nonlocal shaping effects in the time or spectral profiles of an entangled photon pair emerging from a pulsed parametric down-converter are observed by spectrally or temporally filtering one of the twin beams. In particular, we demonstrate the appearance of fourth-order ("ghost") interference fringes in the spectrum of one beam conditioned by photodetection at the output of an unbalanced Michelson interferometer placed in the path of the other beam. The coherence time of the pump is the limiting factor for the sharpness of the details in the shaped biphoton spectrum.
The quantum state for spontaneous parametric down-conversion was evaluated to include information about the transverse spatial characteristic of the down-conversion fields. This state was used to calculate the angular spectrum of down-conversion in the case of both single-channel and coincidence measurements, while retaining the characteristic nonclassical correlations. Actual transverse profiles for typical experimental parameters were evaluated numerically and measurements were performed with results that compared well with the numerical calculation. This theoretical spatial model was then applied nonrigorously to the case of induced coherence without induced emission. The theoretical results implied that there was a reduction in the degree of induced coherence due strictly to the spatial distribution of the down-conversion beams. This was interpreted as a result of increased distinguishability of the overlapping idler photons. Measurements were conducted which support these results qualitatively. In addition, the present theory explained an unexpected quantitative discrepancy between second- and fourth-order visibilities in previous induced-coherence experiments. This discrepancy was interpreted phenomenologically as a difference between intrinsic and nonintrinsic indistinguishability, and some implications towards quantum measurement theory and the role of the observer were suggested.
We present a theoretical study of coincidence imaging and interference with coherent Gaussian beams. The equations for the coincidence image formation and interference fringes are derived, from which it is clear that the imaging is due to the corresponding focusing in the two paths. The quality and visibility of the images and fringes can be high simultaneously. The nature of the coincidence imaging and interference between with quantum entangled photon pairs and with coherent Gaussian beams are different. The coincidence image with coherent Gaussian beams is due to intensity-intensity correspondence, a classical nature, while that with entangled photon pairs is due to the amplitude correlation, a quantum nature.