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Measuring two particle correlation functions

Christoph Ira Westbrook

Published Jun 16, 2008• 0 citations
OpenAlex

Abstract

This talk discusses two types of measurements on two particle correlations in a Bose-Einstein condensate. In one apparatus we perform the analog of the famous Hanbury-Brown Twiss experiment to investigate correlations in momentum space. In a second experiments we use insitu measurements of atom clouds on a chip to obtain measuremnents of density fluctuations.

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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.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations
This talk discusses two types of measurements on two particle correlations in a Bose-Einstein condensate. In one apparatus we perform the analog of the famous Hanbury-Brown Twiss experiment to investigate correlations in momentum space. In a second experiments we use insitu measurements of atom clouds on a chip to obtain measuremnents of density fluctuations.
In our laboratory, we have been developing measurement methods to extract at two-particle correlations functions in degenerate gases. Simple examples include the observation of correlated atom pairs in a four wave mixing geometry, and Hanbury Brown-Twiss type interferometry. In these experiments we observe the correlations in momentum space. We have also been able to observe density fluctuations in position space by using in situ imaging on an atom chip. I will attempt to review some of the possibilities open to us and discuss some of our plans for the immediate future.
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.
Bose–Einstein condensates of particles behave in many ways like coherent radiation fields, and the realization of Bose–Einstein condensation in dilute gases has opened up the experimental study of interactions between coherent matter waves. In addition, the existence of these dilute trapped quantum gases has prompted a re-examination of a number of theoretical issues. In Sec. 13.1 we discuss Josephson tunnelling of a condensate between two wells and the role of fluctuations in particle number and phase. The number and phase variables play a key role in the description of the classic interference experiment, in which two clouds of atoms are allowed to expand and overlap (Sec. 13.2). Rather surprisingly, an interference pattern is produced even though initially the two clouds are completely isolated. Density fluctuations in a Bose gas are studied in Sec. 13.3, where we relate atomic clock shifts to the two-particle correlation function. The ability to manipulate gaseous Bose–Einstein condensates by lasers has made possible the study of coherent matter wave optics and in Sec. 13.4 we describe applications of these techniques to observe solitons, Bragg scattering, and non-linear mixing of matter waves. How to characterize Bose–Einstein condensation in terms of the density matrix is the subject of Sec. 13.5, where we also consider fragmented condensates.
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.