Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1311.7314

N-photon Correlation Functions in N-slit Diffraction Experiments with Thermal Light

Su-Heng Zhang, De-Zhong Cao

Published Nov 28, 2013• 0 citations
arXivHTMLPDF

Abstract

We discuss the analytic presentations of the high-order correlation functions in the N-slit diffraction with thermal light in a recent paper [Phys. Rev. Lett. 109, 233603 (2012)]. Our analysis shows that the superresolving fringes in the high-order correlation measurement have two classical counterparts.
DOI
10.48550/arxiv.1311.7314

Related papers

Super-resolving interference without intensity-correlation measurement

De-Zhong Cao, Baolong Xu, Su-Heng Zhang +1 more

The high-order intensity correlation function of $N$-photon interference with thermal light observed in a recent experiment [S. Oppel, T. B\"uttner, P. Kok, and J. von Zanthier, Phys. Rev. Lett. 109, 233603 (2012)] is analyzed. The terms in the expansion of the $N\mathrm{th}$-order correlation function are put into three groups. One group contributes a homogeneous background. Both of the other two contribute $(N\ensuremath{-}1)$-fold super-resolving fringes. In principle they correspond to coherent and incoherent superpositions of classical optical fields, respectively. Therefore similar super-resolving fringes can be obtained without intensity-correlation measurements. We report the experimental results of the coherent and incoherent super-resolving diffraction fringes, which are observed directly in the intensity distribution. The $N\ensuremath{-}1$ sources in both the coherent and incoherent cases are set in certain definite positions. In the coherent case, moreover, the phase difference between two adjacent source fields is $\ensuremath{\pi}$. The fringe visibility is unity in the incoherent case, while it decreases as $N$ increases in the incoherent case.

Physical Review A•May 28, 2015•3 citations

Direct measurement of sub-wavelength interference using thermal light and photon-number-resolved detection

Yanhua Zhai, F. E. Becerra, Jingyun Fan +1 more

We examine thermal light diffracted through a double slit using photon-number-resolved detection to directly measure high-order spatial correlations, and we see sinusoidal modulations of those correlations. The fringe width can, in principal, be made arbitrarily small, and we have experimentally obtained fringe widths as small as 30 nm with 800 nm wavelength light. This extreme sub-wavelength resolution, along with this direct detection technique, offers potential for high precision measurement applications.

Applied Physics Letters•Sep 8, 2014•12 citations

NOON-state generation and superresolved interference in a double-slit experiment

De-Zhong Cao, Xuezhi Zhang, Chong Wang +5 more

Maximally entangled NOON states are proposed to be generated with $N$ independent photons and a fixed double-slit in the Young's interference experiment. A strict condition is required that these photons have to be arranged in a straight line and separated from each other by certain equal distances. The initial product state turns into a NOON state of the photons at the double-slit, after $N$-photon postselected measurements. With a spatially random laser beam, we experimentally investigate the high-order correlation functions to imitate the behavior of the single-photon and $N$-photon wave packets of the NOON states. Since the $N$-photon wave packet is the product of $N$ single-photon wave packets, two methods are adopted to observe the superresolved fringes. The first method is to use the product of the second-order correlation functions. The second one is to measure the $2N\mathrm{th}$-order correlation functions. In the both cases, the superresolved fringes of up to fourth order are successfully observed.

Physical Review A•Feb 13, 2023•2 citations

Super sub-wavelength patterns in photon coincidence detection

Ruifeng Liu, Pei Zhang, Yu Zhou +2 more

High-precision measurements implemented with light are desired in all fields of science. However, light acts as a wave, and the Rayleigh criterion in classical optics yields a diffraction limit that prevents obtaining a resolution smaller than the wavelength. Sub-wavelength interference has potential application in lithography because it beats the classical Rayleigh resolution limit. Here, we carefully study second-order correlation theory to establish the physics behind sub-wavelength interference in photon coincidence detection. A Young's double slit experiment with pseudo-thermal light is performed to test the second-order correlation pattern. The results show that when two point detectors are scanned in different ways, super sub-wavelength interference patterns can be obtained. We then provide a theoretical explanation for this surprising result, and demonstrate that this explanation is also suitable for the results found for entangled light. Furthermore, we discuss the limitations of these types of super sub-wavelength interference patterns in quantum lithography.

arXiv:1306.0276•Scientific Reports•Feb 17, 2014•11 citations

Nonlocal Double-Slit Interference with Pseudothermal Light

Lu Gao, Jun Xiong, Lu-Fang Lin +3 more

We perform a nonlocal double-slit interference experiment with pseudothermal light. The experimental result exhibits a typical double-slit interference fringe in the intensity correlation measurement, in agreement with the theoretical analysis by means of the property of the second-order spatial correlation of field.

arXiv:0705.1745•May 12, 2007•0 citations

Theoretical Research of Fourier-Transform Multi-Photon Correlated Imaging

Chuang Wu

The research for the three-photon correlated imaging with incoherent light(classical thermal light) of lensless Fourier-transform is reported.The analytical formula of imaging three-order correlation function of high-order coherent light is presented.That multi-photon correlated can be realized with classical incoherent thermal light by Fourier-transform is shown.

Journal of Liaoning University•Jan 1, 2007•0 citations
The high-order intensity correlation function of NNN-photon interference with thermal light observed in a recent experiment [S. Oppel, T. B\"uttner, P. Kok, and J. von Zanthier, Phys. Rev. Lett. 109, 233603 (2012)] is analyzed. The terms in the expansion of the NthN\mathrm{th}Nth-order correlation function are put into three groups. One group contributes a homogeneous background. Both of the other two contribute $(N\ensuremath{-}1)$-fold super-resolving fringes. In principle they correspond to coherent and incoherent superpositions of classical optical fields, respectively. Therefore similar super-resolving fringes can be obtained without intensity-correlation measurements. We report the experimental results of the coherent and incoherent super-resolving diffraction fringes, which are observed directly in the intensity distribution. The $N\ensuremath{-}1$ sources in both the coherent and incoherent cases are set in certain definite positions. In the coherent case, moreover, the phase difference between two adjacent source fields is $\ensuremath{\pi}$. The fringe visibility is unity in the incoherent case, while it decreases as NNN increases in the incoherent case.
We examine thermal light diffracted through a double slit using photon-number-resolved detection to directly measure high-order spatial correlations, and we see sinusoidal modulations of those correlations. The fringe width can, in principal, be made arbitrarily small, and we have experimentally obtained fringe widths as small as 30 nm with 800 nm wavelength light. This extreme sub-wavelength resolution, along with this direct detection technique, offers potential for high precision measurement applications.
Maximally entangled NOON states are proposed to be generated with NNN independent photons and a fixed double-slit in the Young's interference experiment. A strict condition is required that these photons have to be arranged in a straight line and separated from each other by certain equal distances. The initial product state turns into a NOON state of the photons at the double-slit, after NNN-photon postselected measurements. With a spatially random laser beam, we experimentally investigate the high-order correlation functions to imitate the behavior of the single-photon and NNN-photon wave packets of the NOON states. Since the NNN-photon wave packet is the product of NNN single-photon wave packets, two methods are adopted to observe the superresolved fringes. The first method is to use the product of the second-order correlation functions. The second one is to measure the 2Nth2N\mathrm{th}2Nth-order correlation functions. In the both cases, the superresolved fringes of up to fourth order are successfully observed.
High-precision measurements implemented with light are desired in all fields of science. However, light acts as a wave, and the Rayleigh criterion in classical optics yields a diffraction limit that prevents obtaining a resolution smaller than the wavelength. Sub-wavelength interference has potential application in lithography because it beats the classical Rayleigh resolution limit. Here, we carefully study second-order correlation theory to establish the physics behind sub-wavelength interference in photon coincidence detection. A Young's double slit experiment with pseudo-thermal light is performed to test the second-order correlation pattern. The results show that when two point detectors are scanned in different ways, super sub-wavelength interference patterns can be obtained. We then provide a theoretical explanation for this surprising result, and demonstrate that this explanation is also suitable for the results found for entangled light. Furthermore, we discuss the limitations of these types of super sub-wavelength interference patterns in quantum lithography.