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Quantum-Atom Optics Downunder (QAO)

Atomic four-wave mixing via condensates collisions

A. Perrin, C. M. Savage, Valentina Krachmalnicoff, Denis Boiron, Alain Aspect, Christoph Ira Westbrook, Karen V. Kheruntsyan

Published Jan 1, 2007• 1 citation
Publisher

Abstract

We perform first principles quantum simulations of atomic four-wave mixing via a collision of two Bose-Einstein condensates of metastable helium atoms. We analyse the collinear and back-to-back pair correlations of atoms on the s-wave scattering halo. The results provide qualitative and quantitative understanding of the recent experiments at Orsay [A. Perrin et al., arXiv: 0704.3047].

DOI
10.1364/qao.2007.qwb3

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We perform first principles quantum simulations of atomic four-wave mixing via a collision of two Bose-Einstein condensates of metastable helium atoms. We analyse the collinear and back-to-back pair correlations of atoms on the s-wave scattering halo. The results provide qualitative and quantitative understanding of the recent experiments at Orsay [A. Perrin et al., arXiv: 0704.3047].
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.
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.
We investigate the atom-optical analog of degenerate four-wave mixing by colliding two Bose-Einstein condensates of metastable helium. The momentum distribution of the scattered atoms is measured in three dimensions. A simple analogy with photon phase matching conditions suggests a spherical final distribution. We find, however, that it is an ellipsoid with radii smaller than the initial collision momenta. Numerical and analytical calculations agree with this and reveal the interplay between many-body effects, mean-field interaction, and the anisotropy of the source condensate.
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 propose a method for simulating a single realization of a collision of two Bose-Einstein condensates. Recently [Phys. Rev. Lett. 94, 200401 (2005)], we introduced a quantum model of incoherent elastic scattering in a collision of two counterpropagating atomic Gaussian wave packets. Here we show that this model is capable of generating data that can be interpreted as results of a single collisional event. We find a range of parameters, including relative velocity, population, and the size of colliding condensates, where the structure of the halo of scattered atoms in a single realization strongly differs from that averaged over many realizations.