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Physical Review A

High-order correlation of chaotic bosons and fermions

Hongchao Liu

Published Aug 15, 2016• 9 citations
Publisher

Abstract

We theoretically study the high-order correlation functions of chaotic bosons and fermions. Based on the different parity of the Stirling number, the products of the first-order correlation functions are well classified and employed to represent the high-order correlation function. The correlation of bosons conduces a bunching effect, which will be enhanced as order $N$ increases. Different from bosons, the anticommutation relation of fermions leads to the parity of the Stirling number, which thereby results in a mixture of bunching and antibunching behaviors in high-order correlation. By further investigating third-order ghost diffraction and ghost imaging, the differences between the high-order correlations of bosons and fermions are discussed in detail. A larger $N$ will dramatically improve the ghost image quality for bosons, but a good strategy should be carefully chosen for the fermionic ghost imaging process due to its complex correlation components.

DOI
10.1103/physreva.94.023827

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We theoretically study the high-order correlation functions of chaotic bosons and fermions. Based on the different parity of the Stirling number, the products of the first-order correlation functions are well classified and employed to represent the high-order correlation function. The correlation of bosons conduces a bunching effect, which will be enhanced as order NNN increases. Different from bosons, the anticommutation relation of fermions leads to the parity of the Stirling number, which thereby results in a mixture of bunching and antibunching behaviors in high-order correlation. By further investigating third-order ghost diffraction and ghost imaging, the differences between the high-order correlations of bosons and fermions are discussed in detail. A larger NNN will dramatically improve the ghost image quality for bosons, but a good strategy should be carefully chosen for the fermionic ghost imaging process due to its complex correlation components.
We consider the situation in which the field of quantum particles such as photons (bosons) or electrons (fermions) undergoes a significant attenuation during the detection process. We characterize the second-order statistical properties of the field by the bunching for bosons and the antibunching for fermions. Bunching and antibunching effects are derived from the time intervals distributions of the random point process of detection instead of the moments of the number of particles registered in a given time interval. Fields of both beams are supposed to be in chaotic states and have second-order time correlation functions of exponential profile and of arbitrary correlation time. A test is proposed for nonclassical states: the behavior of the antibunching function is a nondecreasing function near the origin of the time axis.
Quantum imaging with a thermal source of fermions is analyzed and compared with that of bosons. Due to the Pauli exclusive principle and Fermi-Dirac statistics, fermions can manifest antibunching effects in the second-order correlation function. Our analysis finds that quantum imaging with free fermions can construct dark patterns against a bright intensity background. This distinguishing feature highlights the quantum nature of fermions without any classical analog. A scheme of magnifying ghost imaging of an electron microscope is also proposed.
Abstract We present an experimental technique that can accurately measure the high-order photon correlations of various light fields based on double Hanbury Brown–Twiss scheme. The system consists of four conventional binary response single-photon counting modules which are non-photon-number-resolving detectors. We theoretically analyze the effects of the experimental conditions on the high-order photon correlations of coherent, chaotic thermal, Fock and squeezed vacuum states with considering the overall efficiency and background noise. In experiment, we determine the proper resolution time from 2 9 = 512 ns to 2 11 = 2048 ns and counting rate from 10 kc s −1 to 100 kc s −1 for characterizing the exact second-, third- and fourth-order photon correlations of chaotic thermal state. At complete time delays, we also observe the third- and fourth-order photon correlations of chaotic thermal state, with the maximum high-order correlation values of 5.99 ± 0.02 and 23.9 ± 0.2 respectively, which are in good agreement with the theoretical values of 6 and 24. The demonstrated experimental technique with high accuracy is a promising tool for investigating quantum optical coherence and ghost imaging.
Ghost imaging is a quantum optics technique that uses correlations between two beams to reconstruct an image from photons that do not interact with the object being imaged. While pairwise (second-order) correlations are usually used to create the ghost image, higher-order correlations can be utilized to improve the performance. In this Letter, we demonstrate higher-order atomic ghost imaging, using entangled ultracold metastable helium atoms from an s-wave collision halo. We construct higher-order ghost images up to fifth order and show that using higher-order correlations can improve the visibility of the images without impacting the resolution. This is the first demonstration of higher-order ghost imaging with massive particles and the first higher-order ghost imaging protocol of any type using a quantum source.
Abstract Classical correlation of Rayleigh speckle fields E ( x ) can only mimic second-order correlation in quantum imaging. Here, we propose a method to explore the high-order correlation of non-Rayleigh speckle fields E N ( x ) which shows a totally different property from the Rayleigh speckle fields. As a specific example, we illustrate and analyze in detail the third-order speckle scanning imaging which overcomes the diffraction barrier by a factor of 3 . The influences of diffractions in the illumination path and the detection path are also discussed. This investigation may pave the way for applications in super-resolution imaging.
In a near-field three-photon correlation measurement, we observed the third-order temporal and spatial correlation functions of chaotic thermal light in the single-photon counting regime. In the study, we found that the probability of jointly detecting three randomly radiated photons from a chaotic thermal source by three individual detectors is 666 times greater if the photodetection events fall in the coherence time and coherence area of the radiation field than if they do not. From the viewpoint of quantum mechanics, the observed phenomenon is the result of three-photon interference. By making use of this property, we measured the three-photon thermal light lensless ghost image of a double spot and achieved higher visibility compared with the two-photon thermal light ghost image.