Dissociation dynamics of a Bose-Einstein condensate of molecules

An unstable condensate of diatomic molecules will coherently disassociate into correlated pairs of atoms. This dissociation process exhibits very rich quantum dynamics depending on the quantum statistics of the constituent atoms. We show that in the case of bosonic atoms Bose enhancement can lead to stimulated dissociation, whereas, in the case of fermions Pauli blocking of the available states and a buildup of coherence between molecules and atom pairs can give rise to incomplete dissociation of the molecules and transient association-dissociation oscillations.

Figure 1

Example trajectories of ${\mathit{S}}_{\mathit{k}}\left(t\right)$ for fermions (a) and bosons (b).

Figure 2

Molecular population as a function of time for $\Gamma =4$ in the case where the decay products are pairs of bosons (dashed line) and pairs of fermions (solid line). For comparison the usual exponential decay at the rate $\gamma =\pi \rho \left(\nu \right)g^2$ is shown (dotted line). Inset: normalized population distribution of atoms over $\delta ={\omega }_{\mathit{k}}-\nu$ at the final time $tg=21.2$ for bosons (dashed line) and fermions (solid line). The dotted line is a Lorentzian of width $\gamma ∕4$. Only the $\delta ⩾0$ case is shown as the distribution is symmetric about $\delta =0$.

Figure 3

Same as Fig. 2 but with $\Gamma =100$. The horizontal dotted line shows the steady-state molecular population determined by a self-consistent solution using Eqs. (5, 6) (see text) which is a good fit in this case.