Molecular vortex generated from an atom-molecule dark state

We consider a Raman photoassociation model in a field configuration in which a Gaussian and a first-order Laguerre Gaussian laser field are applied between the bound-bound and free-bound transitions, respectively. We show that such a configuration can lead to a coherent population trapping superposition of an atomic condensate and a ground molecular vortex of unit winding number. We develop stimulated Raman adiabatic passages that minimize the effect of mean-field shifts due to collisions, for optimal conversion of an atomic condensate into a ground molecular vortex.

Figure 1

The energy diagram of a two-color Raman photoassociation model.

Figure 2

(a) Populations $N_a^0$ and $N_g^0$, and (b) the required laser detuning ${\delta }_0$ of a quasi-CPT state in a system with ${\Omega }_d^0∕\sqrt{N}{\Omega }_p^0=1$, $t_d=2T,t_p=4.5T$, $T=5\mathrm{ms}$, $n{\lambda }_{aa}=n{\lambda }_{gg}=2\pi \times 0.3948\mathrm{MHz}$, and other ${\lambda }_{ij}=0$.

Figure 3

A comparison of populations in different STIRAPs with (a) $\gamma =0$ and $\sqrt{N}{\Omega }_p^0={\Omega }_d^0=2\pi \times 0.2650\mathrm{MHz}$ and (b) $\gamma =$2 $\pi \times 1.18\mathrm{MHz}$ and $\sqrt{N}{\Omega }_p^0={\Omega }_d^0=2\pi \times 5.3\mathrm{MHz}$. (c) Initial atomic condensate density profile $\mid {\psi }_a(\rho ,t=0){\mid }^2$ for both (a) and (b), and the final stable molecular condensate density profile $\mid {\psi }_g(\rho ,t=\infty ){\mid }^2$ for the chirped STIRAP in (b). $\Delta =-2\pi \times 0.11844\mathrm{MHz}$ and other parameters are the same as in Fig. 2.