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arXiv:0807.3435 · Physical Review A

Pair correlations of scattered atoms from two colliding Bose-Einstein condensates: Perturbative approach

Jan Chwedeńczuk, Paweł Zin, Marek Trippenbach, A. Perrin, Vanessa Y. F. Leung, Denis Boiron, Christoph Ira Westbrook

Published Nov 4, 2008• 25 citations
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Abstract

We apply an analytical model for anisotropic, colliding Bose-Einstein condensates in a spontaneous four-wave-mixing geometry to evaluate the second-order correlation function of the field of scattered atoms. Our approach uses quantized scattering modes and the equivalent of a classical, undepleted pump approximation. Results to lowest order in perturbation theory are compared with a recent experiment and with other theoretical approaches.

DOI
10.1103/physreva.78.053605

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We apply an analytical model for anisotropic, colliding Bose-Einstein condensates in a spontaneous four-wave-mixing geometry to evaluate the second-order correlation function of the field of scattered atoms. Our approach uses quantized scattering modes and the equivalent of a classical, undepleted pump approximation. Results to lowest order in perturbation theory are compared with a recent experiment and with other theoretical approaches.
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We study atom scattering from two colliding Bose-Einstein condensates using a position sensitive, time resolved, single atom detector. In analogy to quantum optics, the process can also be thought of as spontaneous, degenerate four wave mixing of de Broglie waves. We find a clear correlation between atoms with opposite momenta, demonstrating pair production in the scattering process. We also observe a Hanbury Brown and Twiss correlation for collinear momenta, which permits an independent measurement of the size of the pair production source and thus the size of the spatial mode. The back to back pairs occupy very nearly two oppositely directed spatial modes, a promising feature for future quantum optics experiments.
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.
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Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently, Zi\ifmmode \acute{n}\else \'{n}\fi{} et al. [Phys. Rev. Lett. 94, 200401 (2005)] introduced a model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first-order approximation, we derive analytical expressions for the density matrix and anomalous density that provide excellent insight into correlation properties of scattered atoms.
We analyze atom-atom correlations in the sss-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-PPP 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.