Atom-atom correlations and relative number squeezing in dissociation of spatially inhomogeneous molecular condensates

We study atom-atom correlations and relative number squeezing in the dissociation of a Bose-Einstein condensate (BEC) of molecular dimers made of either bosonic or fermionic atom pairs. Our treatment addresses the role of the spatial inhomogeneity of the molecular BEC on the strength of correlations in the short time limit. We obtain explicit analytic results for the density-density correlation functions in momentum space, and show that the correlation widths and the degree of relative number squeezing are determined merely by the shape of the molecular condensate.

Figure 1

(Color online) Back-to-back (a) and collinear (b) correlation $g_{ij}^{\left(2\right)}(k,k_0,t)$ as a function of $k$ at $t∕t_0=0.5$. The dimensionless detuning is $\delta =\Delta t_0=-9$, where $t_0=1∕\chi \sqrt{{\rho }_0\left(0\right)}\simeq 5\mathrm{ms}$ is the time scale; the Thomas-Fermi radius of the molecular BEC is $R_{\mathrm{TF}}=250\mu \mathrm{m}$; for other parameters, see Ref. 24.

Figure 2

(Color online) (a) Width of the BB and CL correlations relative to the momentum width of the molecular BEC, $w_s\simeq 1.62∕R_{\mathrm{TF}}$, as a function of time, for the physical parameters of Fig. 1. (b) Relative number variance $V_{k_0,-k_0}\left(t\right)$ as a function of time, for $R_{\mathrm{TF}}^{\left(1\right)}=250\mu \mathrm{m}$ (1), $R_{\mathrm{TF}}^{\left(2\right)}=167\mu \mathrm{m}$ (2), and $R_{\mathrm{TF}}^{\left(3\right)}=83\mu \mathrm{m}$ (3). The counting length is $\Delta k=\pi ∕2R_{\mathrm{TF}}^{\left(1\right)}$ in all cases.