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Physical Review A

Formation of ultracold polar molecules in a single quantum state

Robin Côté, Elizabeth Juarros, K. Kirby

Published Jun 16, 2010• 7 citations
Publisher

Abstract

We compute the formation rate of a polar molecule, LiH, into the lowest triplet electronic state, $a {}^{3}{\ensuremath{\Sigma}}^{+}$, via population of the intermediate excited electronic state, $b {}^{3}\ensuremath{\Pi}$, followed by radiative decay. We find large formation rates into the single rovibrational bound state ($v=0,J=0$) of the $a {}^{3}{\ensuremath{\Sigma}}^{+}$, which can be explained by the unusually large overlap of its wave function with those of the two upper-most bound levels of the $b {}^{3}\ensuremath{\Pi}$. With conservative parameters, we estimate that over $10$${}^{4}$ molecules/s could be produced in the single rovibrational level of the $a {}^{3}{\ensuremath{\Sigma}}^{+}$ state. We also discuss scattering properties of LiH triplet molecules and their relevance to ultracold chemical reactions.

DOI
10.1103/physreva.81.060704

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We compute the formation rate of a polar molecule, LiH, into the lowest triplet electronic state, a3\ensuremathΣ+a {}^{3}{\ensuremath{\Sigma}}^{+}a3\ensuremathΣ+, via population of the intermediate excited electronic state, b3\ensuremathΠb {}^{3}\ensuremath{\Pi}b3\ensuremathΠ, followed by radiative decay. We find large formation rates into the single rovibrational bound state (v=0,J=0v=0,J=0v=0,J=0) of the a3\ensuremathΣ+a {}^{3}{\ensuremath{\Sigma}}^{+}a3\ensuremathΣ+, which can be explained by the unusually large overlap of its wave function with those of the two upper-most bound levels of the b3\ensuremathΠb {}^{3}\ensuremath{\Pi}b3\ensuremathΠ. With conservative parameters, we estimate that over 10$${}^{4} molecules/s could be produced in the single rovibrational level of the a3\ensuremathΣ+a {}^{3}{\ensuremath{\Sigma}}^{+}a3\ensuremathΣ+ state. We also discuss scattering properties of LiH triplet molecules and their relevance to ultracold chemical reactions.
Alkali hydride molecules are polar, exhibiting large ground-state dipole moments. As ultracold sources of alkali atoms, as well as hydrogen, have been created in the laboratory, we explore theoretically the feasibility of forming such molecules from a mixture of the ultracold atomic gases, employing various photoassociation schemes. In this work we use lithium and sodium hydride as benchmark systems to calculate molecule formation rates through stimulated one-photon radiative association directly from the continuum as well as two-photon stimulated radiative association (Raman transfer) and excitation to bound levels of an excited state followed by spontaneous emission to the ground state. Using accurate molecular potential energy curves and dipole transition moments and with laser intensities and MOT densities that are easily attainable experimentally, we have found that substantial molecule formation rates can be realized even after the effect of back-stimulation has been accounted for. We examine the spontaneous emission cascade which takes place from the upper vibrational levels of the singlet ground state on a time scale of milliseconds. Because photon emission in the cascade process does not contribute to trap loss, a sizable population of molecules in the lowest vibrational level can be achieved. The triplet ground electronic state is of particular interest for experimental efforts since, although it has never been observed experimentally, molecular structure calculations of the a3Σ+ state for LiH and NaH predict a small van der Waals attraction, with a potential energy well so shallow that it can support only one bound rotational-vibrational level. Any molecule formed in the triplet ground state would then be immediately in the lowest and most stable level of that state and would be quite long-lived, unlike molecules in high vibrational levels which have significantly shorter lifetimes. As an analysis of our method of calculating molecule formation rates, we investigate more thoroughly the two-photon stimulated photoassociation process by employing the exact treatment of Dalgarno & Lewis to solve the Raman scattering problem. ^
Alkali-metal hydride molecules have large dipole moments in their ground electronic states. We explore the possibility of forming such molecules from a mixture of the ultracold atomic gases, employing a one-photon stimulated radiative association process. Using accurate molecular potential-energy curves and dipole moments, we have calculated the rate coefficients for populating each of the vibrational levels of the $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ states of LiH and NaH. We have found that significant molecule formation rates into the upper vibrational levels can be realized with laser intensities and atomic densities that are easily attainable experimentally. We examine the spontaneous emission cascade which takes place from these upper vibrational levels on a time scale of milliseconds, and calculate the resulting rotational populations in v=0v=0v=0. We show that photon emission in the cascade process does not contribute to trap loss and that a large population of molecules in v=0v=0v=0 can be achieved.
Starting from an ultracold ensemble of 6Li2{}^{6}{\mathrm{Li}}_{2}6Li2​ Feshbach molecules, we produce deeply bound triplet $a(1{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}{}^{+})$ molecules in a single quantum state by stimulated Raman adiabatic passage. The ensemble lifetime is found to be limited by two-body molecule-molecule collisions that depend on both the vibrational and rotational states. The loss rate observed is near the universal rate for the $|v=0,5,8;N=0,2\ensuremath{\rangle}$ states and, remarkably, below universality for the $|v=9,N=0\ensuremath{\rangle}$ state. We also observe a strong rotational state dependence of the v=9v=9v=9 reaction rate. Consistent with theoretical predictions, we observe that molecules in the absolute lowest triplet level are unstable and likely decay due to trimer formation.
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.
Translationally cold molecules can be produced during photoassociation experiments on ultracold atoms. We explore the photodissociation of these ultracold molecules in given rovibrational levels of their lowest electronic state into the excited electronic states. More precisely, we study the dissociation of 7Li2{^{7}}Li_{2}7Li2​ molecules in specific rovibrational level of the triplet electronic state alpha3Sigmau+\\alpha^{3}\\Sigma^{+}_{u}alpha3Sigmau+​ to the 2s+2p2s+2p2s+2p limit. We observe structures at extremely low energies. We also explore the dissociation of the vibrational levels of the excited electronic states formed during photoassociation experiments on ultracold atoms. They are produced in specific rovibrational levels, and due to the presence of shape resonances, it is found that for certain energy regimes, the cross sections are strongly enhanced. Precise calculations will be presented for lithium.
Ultracold polar and magnetic 23Na6Li^{23}\mathrm{Na}^{6}\mathrm{Li}23Na6Li molecules in the rovibrational ground state of the lowest triplet ${a}^{3}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic state have been recently produced. Here, we calculate the electronic and rovibrational structure of these 14-electron molecules with spectroscopic accuracy ($<0.5\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$) using state-of-the-art ab initio methods of quantum chemistry. We employ the hierarchy of the coupled-cluster wave functions and Gaussian basis sets extrapolated to the complete basis set limit. We show that the inclusion of higher-level excitations, core-electron correlation, relativistic, QED, and adiabatic corrections is necessary to accurately reproduce scattering and spectroscopic properties of alkali-metal systems. We obtain the well depth, ${D}_{e}=229.9(5)\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, the dissociation energy, ${D}_{0}=208.2(5)\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, and the scattering length, ${a}_{s}=\ensuremath{-}{84}_{\ensuremath{-}41}^{+25}\phantom{\rule{4pt}{0ex}}\mathrm{bohr}$, in good agreement with recent experimental measurements. We predict the permanent electric dipole moment in the rovibrational ground state, d0=0.167{d}_{0}=0.167d0​=0.167(1) D. These values are obtained without any adjustment to experimental data, showing that quantum chemistry methods are capable of predicting scattering properties of many-electron systems, provided relatively weak interaction and small reduced mass of the system.