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

Journal of Mathematical Physics

Detection and ``emission'' processes of quantum particles in a ``chaotic state''

Christine Bénard, Odile Macchi

Published Feb 1, 1973• 22 citations
Publisher

Abstract

We study the statistical properties of a chaotic beam of quantum particles (bosons or fermions) by using wavepacket formalism, which allows us to deal with bosons and fermions in a very symmetrical way. Our study is based on the definition and analysis of two different stochastic point processes consisting, respectively, of the ``emission'' time instants and detection time instants (or positions in a space) of the particles of the beam. The two processes are shown to be identical in the chaotic boson case and in the chaotic fermion case, respectively. The symmetry between the well-known results concerning the photon detection process and the new results concerning the fermion detection process is pointed out. And finally it is noted that in the chaotic case the bunching (or antibunching) effect is present already in the ``emission'' of the particles.

DOI
10.1063/1.1666287

Related papers

Second-order statistical properties of quantum chaotic beams

C. Bendjaballah, M. Pourmir

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.

Physical Review A•May 15, 2009•1 citation

Fluctuations of Beams of Quantum Particles

Christine Bénard

A beam of noninteracting particles, bosons or fermions, is described by the superposition of stochastic wave packets. This description allows in each case (bosons or fermions) the determination of the detection process of the particles. This process is defined by the set of the $p$-order coincidence probability densities, a general formulation of which is given. In the case of a stationary and weak incoherent beam, these coincidence probability densities are studied thoroughly and several results are obtained. The well-known bunching effect for bosons and the "antibunching effect" for fermions are shown to come from the detection of indistinguishable particles. In the boson case, all the well-known results for thermal light are found. In the fermion case, the detection process is, under certain conditions, identical to a renewal process.

Physical Review A•Nov 1, 1970•14 citations

The role of self‐coherence in correlations of bosons and fermions in linear counting experiments. Notes on the wave‐particle duality

S. Varró

Abstract Correlations of detection events in two detectors are studied in case of linear excitations of the measuring apparatus. On the basis of classical probability theory and fundamental conservation laws, a general formula is derived for the two‐point correlation functions for both bosons and fermions. The results obtained coincide with that derivable from quantum theory which uses quantized field amplitudes. By applying both the particle and the wave picture at the same time, the phenomena of photon bunching and antibunching, photon anticorrelation and fermion antibunching measured in beam experiments are interpreted in the frame of an intuitively clear description.

arXiv:1004.2975•Fortschritte der Physik•Dec 9, 2010•4 citations

Some properties of point processes in statistical optics

B. Picinbono, C. Bendjaballah

The analysis of the statistical properties of the point process (PP) of photon detection times can be used to determine whether or not an optical field is classical, in the sense that its statistical description does not require the methods of quantum optics. This determination is, however, more difficult than ordinarily admitted and the first aim of this paper is to illustrate this point by using some results of the PP theory. For example, it is well known that the analysis of the photodetection of classical fields exhibits the so-called bunching effect. But this property alone cannot be used to decide the nature of a given optical field. Indeed, we have presented examples of point processes for which a bunching effect appears and yet they cannot be obtained from a classical field. These examples are illustrated by computer simulations. Similarly, it is often admitted that for fields with very low light intensity the bunching or antibunching can be described by using the statistical properties of the distance between successive events of the point process, which simplifies the experimental procedure. We have shown that, while this property is valid for classical PPs, it has no reason to be true for nonclassical PPs, and we have presented some examples of this situation also illustrated by computer simulations.

Physical Review A•Dec 8, 2010•7 citations

A definition of quantum detection point processes

Christine Bénard

A definition of quantum particle detection point processes is given for normal and locally normal systems. This is realized by building coincidence measurement operators, describing in a thoroughly quantum formalism the coincidence experiments that have been actually performed (photon) or that might be performed (electron, neutron). The quantum mean values of these coincidence operators are shown to be the coincidence probabilities of a mathematically well−defined regular process. Some applications of the latter result are given, in particular in the case of fermion point processes.

Journal of Mathematical Physics•Mar 1, 1975•2 citations

Coherence and photon statistics for optical fields generated by Poisson random emissions

Bahaa E. A. Saleh, David Stoler, Malvin Carl Teich

We examine the coherence properties and photon statistics of stationary light obtained by the superposition of nonstationary emissions occurring at random times, in accordance with a homogeneous Poisson point process. The individual emissions are assumed to be in a coherent, chaotic, or $n$ state. The statistical nature of the emission times results in fluctuations of the relative contributions of different emissions at a given time. This is manifested by an additional positive term, exhibiting particlelike properties, in the normalized second-order correlation function. Thus, the photon-counting variance is increased. For coherent emissions, interference between the randomly delayed emissions produces additional wavelike noise. In the limit when the emissions overlap strongly, the field exhibits the correlation properties of chaotic light, regardless of the statistics of the individual emissions. In the opposite limit, when emissions seldom overlap, the light intensity is describable by a shot-noise stochastic process, and the detected photocounts show an enhanced particlelike noise, which has its largest value when the counting time is long. In that limit, the photocounts obey the Neyman type-$A$ and generalized Polya-Aeppli distributions, when the individual emissions are coherent and chaotic, respectively. When the individual emissions correspond to the $n$ state, the Poisson emission times result in bunching which reduces or eliminates the inherent antibunching associated with the $n$ state.

Physical Review A•Jan 1, 1983•36 citations
We study the statistical properties of a chaotic beam of quantum particles (bosons or fermions) by using wavepacket formalism, which allows us to deal with bosons and fermions in a very symmetrical way. Our study is based on the definition and analysis of two different stochastic point processes consisting, respectively, of the emission'' time instants and detection time instants (or positions in a space) of the particles of the beam. The two processes are shown to be identical in the chaotic boson case and in the chaotic fermion case, respectively. The symmetry between the well-known results concerning the photon detection process and the new results concerning the fermion detection process is pointed out. And finally it is noted that in the chaotic case the bunching (or antibunching) effect is present already in the emission'' of the particles.
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.
A beam of noninteracting particles, bosons or fermions, is described by the superposition of stochastic wave packets. This description allows in each case (bosons or fermions) the determination of the detection process of the particles. This process is defined by the set of the ppp-order coincidence probability densities, a general formulation of which is given. In the case of a stationary and weak incoherent beam, these coincidence probability densities are studied thoroughly and several results are obtained. The well-known bunching effect for bosons and the "antibunching effect" for fermions are shown to come from the detection of indistinguishable particles. In the boson case, all the well-known results for thermal light are found. In the fermion case, the detection process is, under certain conditions, identical to a renewal process.
Abstract Correlations of detection events in two detectors are studied in case of linear excitations of the measuring apparatus. On the basis of classical probability theory and fundamental conservation laws, a general formula is derived for the two‐point correlation functions for both bosons and fermions. The results obtained coincide with that derivable from quantum theory which uses quantized field amplitudes. By applying both the particle and the wave picture at the same time, the phenomena of photon bunching and antibunching, photon anticorrelation and fermion antibunching measured in beam experiments are interpreted in the frame of an intuitively clear description.
The analysis of the statistical properties of the point process (PP) of photon detection times can be used to determine whether or not an optical field is classical, in the sense that its statistical description does not require the methods of quantum optics. This determination is, however, more difficult than ordinarily admitted and the first aim of this paper is to illustrate this point by using some results of the PP theory. For example, it is well known that the analysis of the photodetection of classical fields exhibits the so-called bunching effect. But this property alone cannot be used to decide the nature of a given optical field. Indeed, we have presented examples of point processes for which a bunching effect appears and yet they cannot be obtained from a classical field. These examples are illustrated by computer simulations. Similarly, it is often admitted that for fields with very low light intensity the bunching or antibunching can be described by using the statistical properties of the distance between successive events of the point process, which simplifies the experimental procedure. We have shown that, while this property is valid for classical PPs, it has no reason to be true for nonclassical PPs, and we have presented some examples of this situation also illustrated by computer simulations.
A definition of quantum particle detection point processes is given for normal and locally normal systems. This is realized by building coincidence measurement operators, describing in a thoroughly quantum formalism the coincidence experiments that have been actually performed (photon) or that might be performed (electron, neutron). The quantum mean values of these coincidence operators are shown to be the coincidence probabilities of a mathematically well−defined regular process. Some applications of the latter result are given, in particular in the case of fermion point processes.
We examine the coherence properties and photon statistics of stationary light obtained by the superposition of nonstationary emissions occurring at random times, in accordance with a homogeneous Poisson point process. The individual emissions are assumed to be in a coherent, chaotic, or nnn state. The statistical nature of the emission times results in fluctuations of the relative contributions of different emissions at a given time. This is manifested by an additional positive term, exhibiting particlelike properties, in the normalized second-order correlation function. Thus, the photon-counting variance is increased. For coherent emissions, interference between the randomly delayed emissions produces additional wavelike noise. In the limit when the emissions overlap strongly, the field exhibits the correlation properties of chaotic light, regardless of the statistics of the individual emissions. In the opposite limit, when emissions seldom overlap, the light intensity is describable by a shot-noise stochastic process, and the detected photocounts show an enhanced particlelike noise, which has its largest value when the counting time is long. In that limit, the photocounts obey the Neyman type-AAA and generalized Polya-Aeppli distributions, when the individual emissions are coherent and chaotic, respectively. When the individual emissions correspond to the nnn state, the Poisson emission times result in bunching which reduces or eliminates the inherent antibunching associated with the nnn state.