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Physical Review A

Dressed four-wave mixing second-order Talbot effect

Haixia Chen, Xun Zhang, Dayu Zhu, Chang Yang, Tao Jiang, Huaibin Zheng, Yanpeng Zhang

Published Oct 21, 2014• 32 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.90.043846

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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.
\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
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 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.
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.
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.
We investigate theoretically the spontaneous four-wave mixing (FWM) process that occurs in optical waveguides, as a source of quantum correlated photon-pairs. We consider that the waveguide used to implement the spontaneous FWM process presents a high value of nonlinear parameter, γ = 93.4 W-1m-1, and a non-negligible value of loss coefficient, α = 133.3 dB/m. Moreover, the theoretical model also consider the Raman scattering that inevitably accompanies the FWM process, and generates time-uncorrelated (noise) photon pairs. We use the coincident-to-accidental ratio (CAR) as a figure of merit of the photon pair source, and we were able to observe a CAR of the order of 65 in a high loss regime. After, we use the time-correlated photon pairs generated by the spontaneous FWM process to implement a heralded single photon source at waveguide output. In this scenario, the detection of one photon of the pair heralds the presence of the other photon. The quality of the source was studied by the evaluation of the second order coherence function for one photon of the pair conditioned by the detection of its twin photon. We observe that the presence of a high loss coefficient tends to improve the quality of the photon source, when compared with the lossless regime, even considering the Raman noise photons. We obtain a value for the conditional second order coherence function of the order of 0.11 in absence of loss, and a value of 0.03 for a loss coefficient of 133.3 dB/m.