Photoassociation adiabatic passage of ultracold Rb atoms to form ultracold ${\mathrm{Rb}}_2$ molecules

We theoretically explore photoassociation by adiabatic passage of two colliding cold ${}^{85}\mathrm{Rb}$ atoms in an atomic trap to form an ultracold ${\mathrm{Rb}}_2$ molecule. We consider the incoherent thermal nature of the scattering process in a trap and show that coherent manipulations of the atomic ensemble, such as adiabatic passage, are feasible if performed within the coherence time window dictated by the temperature, which is relatively long for cold atoms. We show that a sequence of $\sim 2\times {10}^7$ pulses of moderate intensities, each lasting $\sim 750\mathrm{ns}$, can photoassociate a large fraction of the atomic ensemble at temperature of $100\mu \mathrm{K}$ and density of ${10}^{11}\text{atoms}∕{\mathrm{cm}}^3$. Use of multiple pulse sequences makes it possible to populate the ground vibrational state. Employing spontaneous decay from a selected excited state, one can accumulate the molecules in a narrow distribution of vibrational states in the ground electronic potential. Alternatively, by removing the created molecules from the beam path between pulse sets, one can create a low-density ensemble of molecules in their ground rovibrational state.

Figure 1

(Color online) The combination of photoassociation adiabatic passage (PAP) pairs discussed in the text.

Figure 2

Black lines: ${\mathrm{Rb}}_2$ Born-Oppenheimer potentials involved in the photoassociation calculations. Gray lines: ${\mathrm{Rb}}_2$ potentials not used in this paper. The data shown in the figure are adopted from Ref. 10.

Figure 3

(a) The Franck-Condon (FC) factors for the transition from a continuum state of $100\mu \mathrm{K}$ energy to the $A∕b\left(133\right)$ level, for different $X$-potential long-range/short-range interpolation radii. The full arrow indicates the fitting parameter that correctly yields the measured scattering resonance and scattering length, which is used in further calculations. (b) The continuum-bound FC factors for the transition to the $A∕b(v=133,J=1)$ level as a function of the scattering energy. The full (dashed) line corresponds to an interpolation radius marked by the full (dashed) arrow in (a). The inset shows the FC factor near the resonance at the $E=0-1\mu \mathrm{K}$ continuum energy range.

Figure 4

(Color online) (a) FC factors for the $X\text{−}A∕b$ continuum-bound transitions. (b) FC factors for the $A∕b\text{−}X$ bound-bound transitions, for the $v=0$ (green filled squares) and $v=4$ (red open squares) $X$-vibrational states.

Figure 5

Photoassociation of a coherent wave packet. (a) Initial continuum probability distribution ${\mid F_0\left(t\right)\mid }^2$, a.u.; (b) The population of the intermediate $A∕b$ state; (c) The population of the $X(v=4,J=0)$ target state.

Figure 6

(Color online) Photoassociation of the atomic ensemble in a trap. (a): Envelopes of the four laser pulses, unscaled. (b): Continuum population $F_0{\left(t\right)}^2$; (c)–(f): Bound state populations, weighted over the ensemble, for different bound states. (c): Intermediate state $\mid 2⟩\equiv A∕b(v=133,J=1)$, $E=0.042848\mathrm{a.u}$; (d): State $\mid 1⟩\equiv X(v=4,J=0)$, $E=-0.01823\mathrm{a.u.}$; (e): Intermediate state $\mid 3⟩\equiv A∕b(v=35,J=1)$, $E=0.03309\mathrm{a.u.}$; (f): State $\mid 4⟩\equiv X(v=0,J=0)$, $E=-0.0193\mathrm{a.u.}$

Figure 7

FC factors for the $A∕b-X$ bound-bound transitions from the states $A∕b(v=51)$ (a), and $A∕b(v=85)$ (b) in dependence on the vibrational quantum number of the $X$ potential.

Figure 8

Final population of the state $X(v=4,J=0)$ in photoassociation of a coherent wave packet in dependence on the pump pulse intensity.