Correlations in Amplified Four-Wave Mixing of Matter Waves

The coherence properties of amplified matter waves generated by four-wave mixing (FWM) are studied using the Hanbury-Brown–Twiss method. We examine two limits. In the first case stimulated processes lead to the selective excitation of a pair of spatially separated modes, which we show to be second order coherent, while the second occurs when the FWM process is multimode, due to spontaneous scattering events which leads to incoherent matter waves. Amplified FWM is a promising candidate for fundamental tests of quantum mechanics where correlated modes with large occupations are required.

Figure 1

Experimental schematic showing the BEC, the atom laser, and the cones that result from the FWM process (not to scale). The resulting image on our multichannel plate (MCP) and delay line detector shows peaks due to the FWM cones.

Figure 2

Typical intensity plots (arb. units) for (a) $s$-wave scattering shell and (b) the amplified FWM waves as seen on the detector. The tight trapping direction is along the $y$ axis, while the $x$ axis corresponds to the weak trapping direction. Each image is $3\mathrm{cm}\times 3\mathrm{cm}$.

Figure 3

Normalized second order correlation functions for (a) spontaneous FWM events, which form an $s$-wave scattering shell, and (b) the amplified FWM cones. Error bars indicate the contribution due to shot noise. The spontaneous case shows clear bunching, whereas the amplified modes show a correlation function of unity.