Spatial Pair Correlations of Atoms in Molecular Dissociation

We perform first-principles quantum simulations of dissociation of trapped, spatially inhomogeneous Bose-Einstein condensates of molecular dimers. Specifically, we study spatial pair correlations of atoms produced in dissociation after time of flight. We find that the observable correlations may significantly degrade in systems with spatial inhomogeneity compared to the predictions of idealized uniform models. We show how binning of the signal can enhance the detectable correlations and lead to the violation of the classical Cauchy-Schwartz inequality and relative number squeezing.

Figure 1

Dissociation of a molecular condensate in free space, for dissociation time of $t=0.2\mathrm{ms}$ with $\chi =7\times {10}^{-7}{\mathrm{m}}^{3/2}{\mathrm{s}}^{-1}$ and a further expansion of $t_e=2.5\mathrm{ms}$ with $\chi =0$ [26]. Each dimension is $55\mu \mathrm{m}$ long and contains 256 lattice points. 10 000 stochastic paths were averaged. (a) Slice through $z=0$ of the 3D atomic density $n(\mathbf{x})=⟨\widehat{n}(\mathbf{x})⟩$ after expansion. (b) 2D column density $n_{\perp }(\mathbf{r})=⟨{\widehat{n}}_{\perp }(\mathbf{r})⟩$ after integration along the $z$ axis. (c) local pair-correlation, $g^{(2)}(\mathbf{r},\mathbf{r})$. The $g^{(2)}$ data are too noisy outside the dissociation sphere where the signal is negligible and should be discarded at radii $r\gtrsim 15\mu \mathrm{m}$. (d) Pair-correlation at opposite locations, $g^{(2)}(\mathbf{r},-\mathbf{r})$. (e) Pair-correlation $g^{(2)}(\mathbf{r},{\mathbf{r}}_{90})$ at orthogonal locations. (f) Number-difference variance $V_{\mathbf{r},-\mathbf{r}}$ at opposite locations. (g) Binned atomic signal on the detection plane, for bins of size $32\times 32$ pixels, and (h) number-difference variance between the opposite bins.

Figure 2

The effect of binning on the angle averaged number-difference variance between the opposite bins, ${\overline{V}}_{{\mathbf{r}}_{\mathbf{0}},-{\mathbf{r}}_{\mathbf{0}}}$, as a function of the expansion time $t_e$ following 0.2 ms of dissociation. Graphs (a),(b) and (c) correspond, respectively, to the initial molecular BEC size of 1.4, 3, and $6.4\mu \mathrm{m}$ [26]. The different curves are for different bin sizes. The largest bins into just four quadrants on the detection plane.