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Physical Review A

Fluctuations of Beams of Quantum Particles

Christine Bénard

Published Nov 1, 1970• 14 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.2.2140

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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.
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.
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.
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.
For a number of noninteracting identical particles entering a multichannel scatterer in various wave-packet states, we construct a generating function for the probabilities of various scattering outcomes. This is used to evaluate the mean numbers of particles, n‾m{\overline{n}}_{m}nm​, scattered into a given (mth)(m\mathrm{th})(mth) channel, single-channel statistics, and interchannel correlations. We show that for initially uncorrelated particles, indistinguishability changes single-channel statistics without altering the value of n‾m{\overline{n}}_{m}nm​. For uncorrelated bosons and fermions, bunching and antibunching behavior can be detected in the extreme-case probabilities, to have all particles scattered into the same channel, or none of particles scattered into a channel, or channels. As an example, we consider a cavity with a single long-lived resonance accessible to the particles, which allows them to ``pile up'' inside the scatterer.
In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This is, for electrons, the Pauli Exclusion Principle, or in general, the Symmetrization Postulate. Then, we introduce fermions and bosons and the distributions respectively describing their statistical behaviour in indistinguishable situations. Following that, we discuss the spin-statistics connection, as well as alternative statistics and experimental evidence for all these results, including the use of bunching and antibunching of particles emerging from a beam splitter as a signature for some bosonic or fermionic states.
In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This is, for electrons, the Pauli Exclusion Principle, or in general, the Symmetrization Postulate. Then, we introduce fermions and bosons and the distributions respectively describing their statistical behaviour in indistinguishable situations. Following that, we discuss the spin-statistics connection, as well as alternative statistics and experimental evidence for all these results, including the use of bunching and antibunching of particles emerging from a beam splitter as a signature for some bosonic or fermionic states.