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Annual Meeting Optical Society of America

Two-particle correlation experiments with massive particles

David W. Keith, Herbert Joseph Bernstein

Published Jan 1, 1990• 0 citations
Publisher

Abstract

Since the first observation of two-point correlation effects in optical fields (Hanbury, Brown, and Twiss, 1957) there has been continuous theoretical and experimental interest in photon correlation. In this paper we examine the possibility of measuring similar effects involving massive particles. We first discuss the theory of correlations between noninteracting massive particles by using the formalism of second quantization. This theory is considerably simpler than that for light because we can treat particles in the strictly nonrelativistic limit. However, the theory provides a particularly interesting contrast with the photon case because we may choose particles that are either fermions or bosons. We then apply the theory to the case of beams of atoms and neutrons and consider the experimental parameters of existing beams. In particular, we consider the case of experiments with laser-cooled metastable helium.

DOI
10.1364/oam.1990.fh2

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Since the first observation of two-point correlation effects in optical fields (Hanbury, Brown, and Twiss, 1957) there has been continuous theoretical and experimental interest in photon correlation. In this paper we examine the possibility of measuring similar effects involving massive particles. We first discuss the theory of correlations between noninteracting massive particles by using the formalism of second quantization. This theory is considerably simpler than that for light because we can treat particles in the strictly nonrelativistic limit. However, the theory provides a particularly interesting contrast with the photon case because we may choose particles that are either fermions or bosons. We then apply the theory to the case of beams of atoms and neutrons and consider the experimental parameters of existing beams. In particular, we consider the case of experiments with laser-cooled metastable helium.
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This thesis presents two experiments on ultracold gases of metastable Helium that constitute the extension, to matter waves, of experiments that have been fundamental for the development of quantum optics. Both experiments have been realized by using a single atom detector, that allows one to reconstruct the position of the atoms in three dimensions. In the first experiment we directly compared the two-body correlation function for a cold cloud of identical fermions and for a cold cloud of identical bosons at the same temperature issued from the same experimental apparatus. Since bosons and fermions obey different quantum statistics, the two-body correlation functions are different: identical bosons tend to be detected bunched in pairs, while identical fermions tend to antibunch because of the Pauli exclusion principle. In the second experiment we studied the correlation between pairs of bosonic atoms generated in the collision of two Bose-Einstein condensates. The measurement of the correlation function allows us to demonstrate that atoms flying back to back in the centre of mass frame are correlated in pairs. Furthermore the observation of a Hanbury Brown Twiss correlation between atoms with collinear velocity demonstrates that our system cannot be interpreted in terms of classical mechanics, but that the bosonic statistics plays a crucial role. A new version of the experiment will allow us to measure the angular dependence of the population of the scattering modes and the number difference squeezing between two correlated modes.
The experimental study of second-order interference with fermions is much more difficult than that with bosons. Inspired by the conclusion that the behavior of two identical classical particles has exactly half fermionic and half bosonic characteristics [Phys. Rev. A88, 012130 (2013)PLRAAN1050-294710.1103/PhysRevA.88.012130], we have studied the second-order interference of fermions via the second-order interference of photons in Hanbury Brown–Twiss and Hong–Ou–Mandel interferometers, respectively. The experimental results are consistent with the theoretical predictions, which may serve as guidance for future interference experiments with fermions. The employed method offers an interesting and convenient way to study the coherence of fermions.
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