Efficient optical schemes to create ultracold KRb molecules in their rovibronic ground state

In ongoing experiments ultracold molecules are first created in a weakly bound level of their electronic ground-state manifold, requiring further manipulation with optical fields to transfer them in their absolute ground state. We performed a detailed theoretical analysis of the spectroscopic properties of potassium rubidium diatomic to determine efficient routes for this purpose via stimulated Raman adiabatic passage. We used state-of-the-art molecular potentials, spin-orbit coupling and transition dipole moment to perform our calculations. The dependence of spin-orbit couplings with internuclear distance are of crucial importance as the relevant transitions mainly occur in the chemical bond domain. Two main mechanisms involving a different pair of excited electronic states are modeled and compared for the various isotopologues ${}^{39}\mathrm{K}{}^{85}\mathrm{Rb}$, ${}^{39}\mathrm{K}{}^{87}\mathrm{Rb}$, ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$, and ${}^{41}\mathrm{K}{}^{87}\mathrm{Rb}$, starting from the uppermost levels of their lowest triplet state $a^3{\Sigma }^{+}$ towards the lowest vibrational level of their ground state $X^1{\Sigma }^{+}$. The present model confirms the experimental findings. In addition, it predicts a transfer scheme which involves more efficient transitions.

Figure 1

Optimal STIRAP schemes for ${}^{39}\mathrm{K}{}^{87}\mathrm{Rb}$ and relevant molecular data. (Left panels) The $[b-A]$ scheme; (right panels) the $[B-c]$ scheme. (a),(d) $R$-dependent diagonal and off-diagonal spin-orbit matrix elements coupling the $b^3\Pi$ and $A^1{\Sigma }^{+}$ states of panel (b) and the $B^1\Pi$, $c^3{\Sigma }^{+}$, and $b^3\Pi$ states of panel (e). (c),(f) Relevant TEDMs for the considered STIRAP schemes. The bibliography for these data is indicated in the text. The optimal intermediate levels for each scheme are reported and connected with upward and downward arrows to the initial $v_a=29$ level of the $a^3{\Sigma }^{+}$ state and to the $v=0$ level of the $X^1{\Sigma }^{+}$ state. The current range of spectroscopic knowledge is indicated with indexed vertical colored bars drawn close to the related PEC: (i) [97]; (ii) [86]; (iii) [31]; (iv) [73]; (v) [75]; (vi) [87]; (vii) [88]; (viii) [37] (see Table 1).

Figure 2

Computed squared matrix elements $|d_{ba}^{v_{0^{+}}^{\prime }{v}_a}{|}^2$ as a function of pump transition energy (bottom horizontal axis) and $|d_{XA}^{v{v}_{0^{+}}^{\prime }}{|}^2$ as a function of dump transition energy (top horizontal axis) of the ${}^{39}\mathrm{K}{}^{87}\mathrm{Rb}$ TEDM relevant for the $[b-A]$ STIRAP scheme through $\Omega =0^{+}$ intermediate levels $v_{0^{+}}^{\prime }$. The pump transition starts from the $v_a=29$ (solid red circles) and $v_a=31$ (open black circles) levels of $a^3{\Sigma }^{+}$, towards vibrational levels $v_{0^{+}}^{\prime }$ of the $A^1{\Sigma }^{+}$ and $b^3\Pi$ coupled states located well below the $\text{K}\left(4^2{S}_{1/2}\right)+\text{Rb}\left(5^2{P}_{1/2}\right)$ limit. The dump transition (blue triangles) starts from those levels to end into the $v=0$ level of the $X^1{\Sigma }^{+}$ ground state. The inset enlarges the most favorable region where both matrix elements are nearly equal. The intermediate levels $v_{0^{+}}^{\prime }=88$ and $v_{0^{+}}^{\prime }=103$ (reached from $v_a=31$) and $v_{0^{+}}^{\prime }=90$ and $v_{0^{+}}^{\prime }=105$ (reached from $v_a=29$) correspond to optimal efficiency. The pump transition frequency toward $v_{0^{+}}^{\prime }=103$ and $v_{0^{+}}^{\prime }=105$ are close to the one of a 1064-nm laser.

Figure 3

(a) Computed squared matrix elements $|d_{j_{t}a}^{v_1^{\prime }{v}_a}{|}^2$ as a function of pump transition energy (bottom horizontal axis) and $|d_{XB}^{v{v}_1^{\prime }}{|}^2$ as a function of dump transition energy (top horizontal axis) of the ${}^{41}\mathrm{K}{}^{87}\mathrm{Rb}$ TEDM relevant for the $[B-c]$ STIRAP scheme through $\Omega =1$ excited states. The pump transition starts from the $v_a=29$ level of $a^3{\Sigma }^{+}$, towards vibrational levels $v_1^{\prime }$ of the $B^1\Pi$, $c^3{\Sigma }^{+}$, and $b^3\Pi$ coupled states located well below the $\text{K}\left(4^2{S}_{1/2}\right)+\text{Rb}\left(5^2{P}_{1/2}\right)$ limit. The curves for $j_t=c$ (red solid circles) and $j_t=b$ (open black circles) are displayed. The dump transition (blue triangles) starts from those levels to end at the $v=0$ level of the $X^1{\Sigma }^{+}$ ground state. (b) Magnification of the region of the most favorable intermediate coupled levels. The $v_1^{\prime }=101$ and $v_1^{\prime }=165$ are the optimal intermediate levels predicted by our calculations. The level $v_1^{\prime }=96$ (assigned to $v_1^{\prime c}=23$) is analogous to the one used in the experiment of Ref. [61] with Feshbach ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$ molecules. The $v_1^{\prime }=146$ and $v_1^{\prime }=152$ levels exhibit a strong mixture of $v_1^{\prime B}=\sim 7–8$ and $v_1^{\prime c}=\sim 48–50$ and could result in optimal STIRAP transfer in ${}^{39}\mathrm{K}{}^{85}\mathrm{Rb}$ [84].