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arXiv:0807.5062 · Physical Review A

Atom-atom correlations in colliding Bose-Einstein condensates

Magnus Ögren, Karen V. Kheruntsyan

Published Feb 17, 2009• 37 citations
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Abstract

We analyze atom-atom correlations in the $s$-wave scattering halo of two colliding condensates. By developing a simple perturbative approach, we obtain explicit analytic results for the collinear (CL) and back-to-back (BB) correlations corresponding to realistic density profiles of the colliding condensates with interactions. The results in the short-time limit are in agreement with the first-principles simulations using the positive-$P$ representation and provide analytic insights into the experimental observations of Perrin et al. [Phys. Rev. Lett. 99, 150405 (2007)]. For long collision durations, we predict that the BB correlation becomes broader than the CL correlation.

DOI
10.1103/physreva.79.021606

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We perform a theoretical analysis of atomic four-wave mixing via a collision of two Bose–Einstein condensates of metastable helium atoms, and compare the results to a recent experiment. We calculate atom–atom pair correlations within the scattering halo produced spontaneously during the collision. We also examine the expected relative number squeezing of atoms on the sphere. The analysis includes first-principles quantum simulations using the positive P -representation method. We develop a unified description of the experimental and simulation results.
The quantum dynamics of colliding Bose-Einstein condensates with 150,000 atoms are simulated directly from the Hamiltonian using the stochastic positive-P method. Two-body correlations between the scattered atoms and their velocity distribution are found for experimentally accessible parameters. Hanbury Brown-Twiss or thermal-like correlations are seen for copropagating atoms, while number correlations for counterpropagating atoms are even stronger than thermal correlations at short times. The coherent phase grains grow in size as the collision progresses with the onset of growth coinciding with the beginning of stimulated scattering. The method is versatile and usable for a range of cold atom systems.
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