Photoassociation to the $2{}^1{\Sigma }_g^{+}$ state in ultracold ${}^{85}$Rb${}_2$ in the presence of a shape resonance

We report the observation of photoassociation to the $2{}^1{\Sigma }_g^{+}$ state of ${}^{85}$Rb${}_2$. We have observed two vibrational levels ($v^{\prime }=98,99$) below the $5s_{1/2}+5p_{1/2}$ atomic limit and 11 vibrational levels ($v^{\prime }=102$–112) above it. The photoassociation—and subsequent spontaneous emission—occur predominantly between 15 and 20 bohrs in a region of internuclear distance best described as a transition between Hund's case (a) and Hund's case (c) coupling. The presence of a $g$-wave shape resonance in the collision of two ground-state atoms affects the photoassociation rate and line shape of the $J^{\prime }=3$ and 5 rotational levels.

Figure 1

Potential energy curves with molecule formation and detection pathways. Arrows indicate photoassociation (PA) to $2{}^1{\Sigma }_g^{+}$, spontaneous emission (SE) to $a{}^3{\Sigma }_u^{+}$, and REMPI to ${{\text{Rb}}_2}^{+}$. Note that the $2{}^1{\Sigma }_g^{+}$ state has a barrier of 250 cm${}^{-1}$ at $R=19$ $a_0$. Potential energy curves are from Refs. [20, 21].

Figure 2

Some spontaneous emission pathways in Hund's case (a) and Hund's case (c) basis sets. Solid arrows denote allowed transitions and dashed arrows denote forbidden transitions according to one-photon E1 selection rules. Some transitions that are forbidden in Hund's case (a) are allowed in Hund's case (c).

Figure 3

Potential energy curves [24, 25] showing photoassociation (PA) to 2($0_g^{+}$) and spontaneous emission (SE) to 1($1_u$). (b) Transition dipole moment between the 2($0_g^{+}$) and 1($1_u$) states, from Ref. [20].

Figure 4

PA spectrum of the $2{}^1{\Sigma }_g^{+}$ $v^{\prime }=109$ level showing the rotational assignment ($J^{\prime }$) and the possible partial-wave ($l$) content of each rotational line. The line intensities reveal the presence of partial waves $l=0,1,2,4$ and exclude the presence of partial waves $l=3,5,6$. Lines marked with an asterisk (*) are hyperfine ghost lines of the $J^{\prime }=3$ and 5 transitions as described in the text.

Figure 5

(a) Closeup of the $a{}^3{\Sigma }_u^{+}$ effective potential curves of ${}^{85}$Rb${}_2$ around the region of the centrifugal barriers for $s$, $p$, $d$, $f$, and $g$ partial waves. The $g$-wave quasibound level responsible for the shape resonance is also shown. (b) The Maxwell-Boltzmann energy distribution of a MOT at 120 $\mu$K showing the high-energy tail extending to, and past, the quasibound level.

Figure 6

Experimental ($•$) and fitted (—) line shapes for $J^{\prime }=1$ (a) and $J^{\prime }=3$ (b) at different PA powers. Lines are offset vertically for clarity and horizontally to match the peak position. The small deviation between experimental and fitted line shapes in (b) is not physical and is due to the PA laser scan rate.