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arXiv:0909.4382 · Physical Review A

Second-order Talbot effect with entangled photon pairs

Kai-Hong Luo, Jianming Wen, Xi-Hao Chen, Qian Liu, Min Xiao, Ling-An Wu

Published Oct 19, 2009• 47 citations
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Abstract

The second-order Talbot effect is analyzed for a periodic object illuminated by entangled photon pairs in both the quantum imaging and quantum lithography configurations. The Klyshko picture is applied to describe the quantum imaging scheme, in which self-images of the object that may or may not be magnified can be observed nonlocally in the photon coincidences but not in the singles count rate. In the quantum lithography setup, we find that the second-order Talbot length is half that of the classical first-order case, thus the resolution may be improved by a factor of 2.

DOI
10.1103/physreva.80.043820

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The second-order Talbot effect is analyzed for a periodic object illuminated by entangled photon pairs in both the quantum imaging and quantum lithography configurations. The Klyshko picture is applied to describe the quantum imaging scheme, in which self-images of the object that may or may not be magnified can be observed nonlocally in the photon coincidences but not in the singles count rate. In the quantum lithography setup, we find that the second-order Talbot length is half that of the classical first-order case, thus the resolution may be improved by a factor of 2.
We report the first experimental observation of quantum Talbot effects with single photons and entangled photon pairs. Both the first- and second-order quantum Talbot self-images are observed experimentally. They exhibit unique properties, which are different from those produced by coherent and incoherent classical light sources. In particular, our experiments show that the revival distance of two-photon Talbot imaging is twice the usual classical Talbot length and there is no net improvement in the resolution, due to the near-field effect of Fresnel diffraction, which is different from the case of previous proof-of-principle quantum lithography experiments in the far field.
\n\nThe electromagnetically induced Talbot effect (EITE) offers a nondestructive and lensless way to image ultracold atoms or molecules (Wen J. M. et al., Appl. Phys. Lett., 98 (2011) 081108). We study an atomic imaging scheme based on the second-order two-photon EITE. Entangled photon pairs are taken as the imaging light to realize coincidence recording. Compared to the previous self-imaging scheme, the present one has the characteristic of imaging nonlocally and of the controllable image variation in size, and thus, it is useful for facilitating the EITE application in imaging techniques.\n
We theoretically demonstrate second-order Talbot effect (SOTE) based on entangled photon pairs. The photon pairs are generated from the spontaneous parametric four-wave mixing (SPFWM) process in a cold atomic medium and can be taken as the imaging light in order to realize coincidence recording. A strong standing wave is used to create the electromagnetically induced grating in the entangled photon pairs channels. By changing the frequency detuning of the standing wave or the other optical fields participating in the process, we can manipulate the contrast of the second-order Talbot image. We use the second-order correlation function and the dressed-state picture to explain the SOTE occurring in the SPFWM process. Moreover, we demonstrate the scheme for SOTE based on the spatially correlated twin beams generated from the SPFWM process with injection. This scheme provides a convenient detection proposal for the SOTE at the cost of the image contrast. Compared to the previous self-imaging schemes, the present schemes have the characteristic of controllable image contrast and of nonlocal imaging, and thus, they might broaden their applications in imaging techniques and find applications in quantum lithography.
Two‐photon “ghost” imaging, based on the second‐order intensity correlation, was first realized with entangled light, but has now been demonstrated with true thermal light. Following our work on lensless and high‐order ghost imaging with thermal light, we have recently shown that both entangled and thermal light may be used to produce two‐photon correlation Talbot effects. In the Talbot effect, first observed in 1836, a periodic object illuminated with coherent light can give rise to repeated self‐images at specific positions within the Fresnel diffraction field without any lens. Using an incoherent thermal light source, we have experimentally observed second and higher order Talbot self‐images, including fractional and phase‐reversal images, at multiples of the Talbot length in a lensless setup containing two optical paths. We have also recently observed another surprising imaging phenomenon which does not depend on the second‐order correlation function, and can produce both negative and positive images of a nonlocal object. It is expected that these types of imaging will find novel applications in both the microscopic and macroscopic regimes.
Different from classical Talbot self-imaging, second-order spatial Talbot effect is a kind of second-order imaging, in which the self-imaging of an object is observed through intensity correlation measurement. Here, in terms of space-time duality, we investigate the temporal counterpart of second-order Talbot self-imaging with temporally incoherent light. Our work shows that second-order Talbot effect in the time domain is related to the joint dispersion of light pulse in dispersive medium. Particularly, based on the discrete Fourier transformation, the fractional Talbot self-imaging via intensity correlation doesn't generally possess a definite fractional period, which contradicts some articles' results. Our results may be useful for implementing the repetition-rate-multiplication technique and remotely transmitting the periodic temporal signals robustly.