Correlated directional atomic clouds via four-heterowave mixing

We investigate the coherence properties of pairs of counterpropagating atomic clouds, produced in superradiant Rayleigh scattering off atomic condensates. It is shown that these clouds exhibit long-range spatial coherence and strong nonclassical density cross-correlations, which make this scheme a promising candidate for the production of highly directional nonclassically correlated atomic pulses.

Figure 1

Degree of first-order coherence for the $j$th side mode at various times, in the (a) WP and (b) SP regimes. The function is symmetric with respect to $\Delta \xi =0$.

Figure 2

Normalized density cross-correlation function at two different times. (a) WP regime: $\tau =1.025$ $(+)$, $\tau =4.025$ $(\square )$; (b) SP regime: $\tau =0.03025$ $(+)$, $\tau =0.12075$ $(\square )$.

Figure 3

Density plots of $\mathcal{V}$ at $\Gamma N\tau \simeq 3$ for the (a) SP and the (b) WP regimes. (c) Time evolution of $\mathcal{S}$ (upper) and $\mathcal{E}$ (lower) for the SP (solid, dotted) and the WP (dashed, dot-dashed) regimes. The isolines in (a) and (b) separate regions of positive and negative $\mathcal{V}$, with its absolute value (normalized to its maximum or minimum) shown in the inset of (c).