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Physical Review A

Rovibrational cooling of photoassociated Rb285 molecules at millikelvin temperature

Meng Wang, Bing-Kuan Lyu, Jing-Lun Li, Gao‐Ren Wang, Maodu Chen, Shu‐Lin Cong

Published May 30, 2019• 2 citations
Publisher

Abstract

We investigate theoretically the rovibrational cooling of the $^{85}\mathrm{Rb}_{2}$ molecule resulting from the photoassociation of $^{85}\mathrm{Rb}_{2}$ atoms at millikelvin temperature. At several millikelvin temperature, the populations of the initial state and the photoassociated $^{85}\mathrm{Rb}_{2}$ molecule are distributed on hundreds of rovibrational levels. In the laser rovibrational cooling process, the population of the photoassociated molecule is first transferred to the deep vibrational state $|{\ensuremath{\psi}}_{{v}^{\ensuremath{''}}=39}\ensuremath{\rangle}$ and then further to the rovibrational ground state $|{\ensuremath{\psi}}_{{v}^{\ensuremath{''}}=0,l=0}\ensuremath{\rangle}$ via the intermediate state $|{\ensuremath{\psi}}_{{v}^{\ensuremath{'}}=42,{l}_{e}=1}\ensuremath{\rangle}$. After the cooling process is over, the population transferred from the intermediate state $|{\ensuremath{\psi}}_{{v}^{\ensuremath{'}}=42,{l}_{e}=1}\ensuremath{\rangle}$ is fully distributed in the vibrational ground state $|{v}^{\ensuremath{''}}=0\ensuremath{\rangle}$. Of the population in the vibrational ground state, $51.59%$ is concentrated in the rotational ground state $|l=0\ensuremath{\rangle}$, and the rest of population is distributed in the low rotational states $|l=1\ensuremath{-}3\ensuremath{\rangle}$.

DOI
10.1103/physreva.99.053428

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We investigate theoretically the rovibrational cooling of the 85Rb2^{85}\mathrm{Rb}_{2}85Rb2​ molecule resulting from the photoassociation of 85Rb2^{85}\mathrm{Rb}_{2}85Rb2​ atoms at millikelvin temperature. At several millikelvin temperature, the populations of the initial state and the photoassociated 85Rb2^{85}\mathrm{Rb}_{2}85Rb2​ molecule are distributed on hundreds of rovibrational levels. In the laser rovibrational cooling process, the population of the photoassociated molecule is first transferred to the deep vibrational state ∣\ensuremathψv\ensuremath′′=39\ensuremath⟩|{\ensuremath{\psi}}_{{v}^{\ensuremath{''}}=39}\ensuremath{\rangle}∣\ensuremathψv\ensuremath′′=39​\ensuremath⟩ and then further to the rovibrational ground state ∣\ensuremathψv\ensuremath′′=0,l=0\ensuremath⟩|{\ensuremath{\psi}}_{{v}^{\ensuremath{''}}=0,l=0}\ensuremath{\rangle}∣\ensuremathψv\ensuremath′′=0,l=0​\ensuremath⟩ via the intermediate state ∣\ensuremathψv\ensuremath′=42,le=1\ensuremath⟩|{\ensuremath{\psi}}_{{v}^{\ensuremath{'}}=42,{l}_{e}=1}\ensuremath{\rangle}∣\ensuremathψv\ensuremath′=42,le​=1​\ensuremath⟩. After the cooling process is over, the population transferred from the intermediate state ∣\ensuremathψv\ensuremath′=42,le=1\ensuremath⟩|{\ensuremath{\psi}}_{{v}^{\ensuremath{'}}=42,{l}_{e}=1}\ensuremath{\rangle}∣\ensuremathψv\ensuremath′=42,le​=1​\ensuremath⟩ is fully distributed in the vibrational ground state ∣v\ensuremath′′=0\ensuremath⟩|{v}^{\ensuremath{''}}=0\ensuremath{\rangle}∣v\ensuremath′′=0\ensuremath⟩. Of the population in the vibrational ground state, 51.5951.59%51.59 is concentrated in the rotational ground state ∣l=0\ensuremath⟩|l=0\ensuremath{\rangle}∣l=0\ensuremath⟩, and the rest of population is distributed in the low rotational states ∣l=1\ensuremath−3\ensuremath⟩|l=1\ensuremath{-}3\ensuremath{\rangle}∣l=1\ensuremath−3\ensuremath⟩.
We theoretically investigate the vibrational cooling of RbCs molecules formed via the photoassociation of Rb and Cs atoms.A sample of cold molecules, initially distributed across multiple vibrational levels, can be transferred into a specific vibrational level of the singlet ground electronic state, X 1 ∑ + .This is achieved by repeated optical pumping with a laser light spectrum broad enough to excite all populated vibrational levels except the target one.The results show that this cooling method achieves an efficiency of nearly 90 %.
We have produced ultracold, polar RbCs∗{\mathrm{R}\mathrm{b}\mathrm{C}\mathrm{s}}^{*}RbCs∗ molecules via photoassociation in a laser-cooled mixture of Rb and Cs atoms. Using a model of the RbCs∗{\mathrm{R}\mathrm{b}\mathrm{C}\mathrm{s}}^{*}RbCs∗ molecular interaction which reproduces the observed rovibrational structure, we infer decay rates in our experiments into deeply bound $X\text{ }^{1}\ensuremath{\Sigma}^{+}$ ground-state RbCs vibrational levels as high as $5\ifmmode\times\else\texttimes\fi{}{10}^{5}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ per level. Population in such deeply bound levels could be efficiently transferred to the vibrational ground state using a single stimulated Raman transition, opening the possibility to create large samples of stable, ultracold polar molecules.
We investigate theoretically the photoassociation process of 85Rb^{85}\mathrm{Rb}85Rb atoms driven by a short laser pulse at several millikelvins. At this temperature, the actions of the rotational barrier, weights of initial scattering states, and shape resonance emerge and have an influence on the thermally averaged photoassociation probability. The calculated thermal weighted population distribution of rotational states agrees well with photoassociation spectrum experiment. The thermally averaged photoassociation probability decreases with an increase in temperature.
We demonstrate rotational and vibrational cooling of cesium dimers by optical pumping techniques. We use two laser sources exciting all the populated rovibrational states, except a target state that thus behaves like a dark state where molecules pile up thanks to absorption-spontaneous emission cycles. We are able to accumulate photoassociated cold Cs(2) molecules in their absolute ground state (v = 0, J = 0) with up to 40% efficiency. Given its simplicity, the method could be extended to other molecules and molecular beams. It also opens up general perspectives in laser cooling the external degrees of freedom of molecules.
We have studied the effect of resonant electronic-state coupling on the formation of ultracold ground-state 85Rb2^{85}\mathrm{Rb}_{2}85Rb2​. Ultracold Rb2{\mathrm{Rb}}_{2}Rb2​ molecules are formed by photoassociation (PA) to a coupled pair of 0u+{0}_{u}^{+}0u+​ states, 0u+(P1∕2){0}_{u}^{+}({P}_{1∕2})0u+​(P1∕2​) and 0u+(P3∕2){0}_{u}^{+}({P}_{3∕2})0u+​(P3∕2​), in the region below the 5S+5P1∕25S+5{P}_{1∕2}5S+5P1∕2​ limit. Subsequent radiative decay produces high vibrational levels of the ground state, $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$. The population distribution of these XXX-state vibrational levels is monitored by resonance-enhanced two-photon ionization through the $2\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}$ state. We find that the populations of vibrational levels ${v}^{\ensuremath{''}}=112--116$ are far larger than can be accounted for by the Franck-Condon factors for ${0}_{u}^{+}({P}_{1∕2})\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ transitions with the 0u+(P1∕2){0}_{u}^{+}({P}_{1∕2})0u+​(P1∕2​) state treated as a single channel. Further, the ground-state molecule population exhibits oscillatory behavior as the PA laser is tuned through a succession of 0u+{0}_{u}^{+}0u+​ state vibrational levels. Both of these effects are explained by a calculation of transition amplitudes that includes the resonant character of the spin-orbit coupling of the two 0u+{0}_{u}^{+}0u+​ states. The resulting enhancement of more deeply bound ground-state molecule formation will be useful for future experiments on ultracold molecules.
We theoretically explore photoassociation by adiabatic passage of two colliding cold 85Rb^{85}\mathrm{Rb}85Rb atoms in an atomic trap to form an ultracold Rb2{\mathrm{Rb}}_{2}Rb2​ 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 $\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{7}$ pulses of moderate intensities, each lasting $\ensuremath{\sim}750\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$, can photoassociate a large fraction of the atomic ensemble at temperature of $100\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{K}$ and density of 1011atoms∕cm3{10}^{11}\phantom{\rule{0.3em}{0ex}}\text{atoms}∕{\mathrm{cm}}^{3}1011atoms∕cm3. 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.