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Scientific Reports

Two-dimensional Talbot self-imaging via Electromagnetically induced lattice

Feng Wen, Wei Qiang Wang, Irfan Ahmed, Hongxing Wang, Yiqi Zhang, Yanpeng Zhang, Abdul Rasheed Mahesar, Min Xiao

Published Feb 6, 2017• 18 citations
Publisher

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.

DOI
10.1038/srep41790

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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.
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Abstract By modulating the emission characteristics of a twin-correlated bright beam in a parametric amplification of the four-wave mixing process, a nondestructive and lensless imaging scheme to image ultra-cold atoms or molecules is proposed. The optical lattice state, which is induced via the coupling between ultra-cold atoms and a standing wave, is used to effectively modulate the dressing-suppressed/enhanced nonlinear susceptibility, and an emission-intensity-modulated grating of a correlated bright beam is formed. The intensity fluctuations of the correlated bright beam are taken as the imaging light to implement second-order coincidence measurement. As an important complementary scheme to a previous self-imaging scheme with spontaneous parametric down-conversion, our scheme has the characteristic of an efficient generation and detection rate. In addition, the visibility of the imaging can be significantly improved by enhanced nonlinear susceptibility. Our work may offer a nondestructive and lensless way to image ultra-cold atoms or molecules.
The nonlinear Talbot effect means formation of self-imaging of the periodic structure by utilizing the harmonic wave instead of the fundamental one. Electromagnetically induced optical lattices established in atomic ensembles by optical induction technique have received great attention in recent years. Here, we experimentally demonstrate the nonlinear four wave mixing (FWM) Talbot effect in the Rubidium medium, where the third-order susceptibility χ(3) has periodic distribution due to the modulation from the incident pump light. Two kinds of periodic structure, the square lattice and hexagonal lattice, are employed to investigate the nonlinear FWM Talbot effect. The integer and fractional Talbot images produced by the FWM field are all obtained. The experimental results are qualitatively consistent with theoretical simulations. Different from the self-imaging of the refractive index in the linear optics, the FWM Talbot effect is the self-imaging of the periodic χ(3). The results may offer a high-resolution lensless way for imaging various optical periodic structures.
Lenses play a key role in quantum imaging but inevitably constrain the spatial resolution and working wavelength. In this work we develop and demonstrate a lensless quantum ghost imaging by engineering quadratic nonlinear photonic crystals. With a transverse parabolic domain modulation introduced into the lithium tantalate crystal, the entangled photon pairs generated from parametric down-conversion will self-focus. Therefore we can dispense with additional lenses to construct imaging in a nonlocal way. The lensless imaging is found to follow a specific imaging formula where the effective focal length is determined by the domain modulation and pump wavelength. Additionally, two nonlocal images can be retrieved when the entangled photon pair is generated under two concurrent noncollinear phase-matching geometries. Our work provides a principle and method to realize lensless ghost imaging, which may be extended to other wavelengths and stimulate new types of practical quantum technologies.
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.