Directional effects due to quantum statistics in dissociation of elongated molecular condensates

Ultracold clouds of dimeric molecules can dissociate into quantum mechanically correlated constituent atoms that are either both bosons or both fermions. We theoretically model the dissociation of two-dimensional anisotropic molecular condensates for which this difference manifests as complementary geometric structures of the dissociated atoms. Atomic bosons are preferentially emitted along the long axis of the molecular condensate, while atomic fermions are preferentially emitted along the short axis. This anisotropy potentially simplifies the measurement of correlations between the atoms through relative number squeezing.

Figure 1

(Color online) Upper panel: Density in position space for the initial molecular condensate showing the geometry of the system. It corresponds to the ground state of a harmonic trap with TF radii: $R_{\text{TF},x}\simeq 60\mu \text{m}$ and $R_{\text{TF},y}\simeq 6\mu \text{m}$ [27]. (a)–(f) 2D atomic density in momentum space (in units of ${\text{m}}^2$) at different times $t$ after the start of dissociation. The left and right columns are for bosonic and fermionic atoms, respectively. We have chosen the times $t_1/t_0=1.1$ for (a) and (b), $t_2/t_0=2.2$ for (c) and (d), and $t_3/t_0=3.3$ for (e) and (f), with $t_0=1/\left(\chi \sqrt{{\rho }_{M,0}}\right)=2.5\text{ms}$ being the time scale.

Figure 2

(Color online) Atomic density in momentum space at the position of resonance $\left(\left|\mathbf{k}\right|=k_0\right)$ along the two different Cartesian directions, in units of ${10}^{-11}{\text{m}}^2$. The two upper (red) curves are for bosons, which grow exponentially due to Bose stimulation. The two lower (blue) curves are for fermions. Solid lines are along the $k_x$ direction $\left(k_x=k_0,k_y=0\right)$ and dashed lines are along the $k_y$ direction $\left(k_x=0,k_y=k_0\right)$. Inset shows the fractional atom number (relative to the total initial number of molecules), in units of tenths of a percent, for fermions (solid blue) and bosons (dashed red).

Figure 3

(Color online) Atomic density distribution in momentum space (in units of ${\text{m}}^2$) at $t_3/t_0=3.3$ calculated using the positive-$P$ representation. The distribution can be compared to that of Fig. 1e.

Figure 4

(Color online) Relative number variance according to Eqs. (5, 12), raw (unbinned) and binned, for fermions (solid blue) and bosons (dashed red). The dotted (black) line in the inset is the $t⪡t_0$ asymptote, Eq. (11). It is almost on top of the dashed line.