arXiv:1011.2563 · Physical Review A

Triplet-singlet conversion in ultracold Cs2 and production of ground-state molecules

Nadia Bouloufa-Maafa, Marin Pichler, M Aymar, Olivier Dulieu

Published Feb 8, 2011• 8 citations

Abstract

We propose a process to convert ultracold metastable ${\mathrm{Cs}}_{2}$ molecules in their lowest triplet state into (singlet) ground-state molecules in their lowest vibrational levels. Molecules are first pumped into an excited triplet state, and the triplet-singlet conversion is facilitated by a two-step spontaneous decay through the coupled $A {}^{1}{\ensuremath{\Sigma}}_{u}^{+}\ensuremath{-}b {}^{3}{\ensuremath{\Pi}}_{u}$ states. Using spectroscopic data and accurate quantum chemistry calculations for ${\mathrm{Cs}}_{2}$ potential curves and transition dipole moments, we show that this process competes favorably with the single-photon decay back to the lowest triplet state. In addition, we demonstrate that this conversion process represents a loss channel for vibrational cooling of metastable triplet molecules, preventing an efficient optical pumping cycle down to low vibrational levels.

DOI: 10.1103/physreva.83.022503

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arXiv:1011.2563 · Physical Review A

Triplet-singlet conversion in ultracold Cs2 and production of ground-state molecules

Nadia Bouloufa-Maafa, Marin Pichler, M Aymar, Olivier Dulieu

Published Feb 8, 2011• 8 citations

arXiv HTML PDF

Abstract

We propose a process to convert ultracold metastable

{\mathrm{Cs}}_{2}

molecules in their lowest triplet state into (singlet) ground-state molecules in their lowest vibrational levels. Molecules are first pumped into an excited triplet state, and the triplet-singlet conversion is facilitated by a two-step spontaneous decay through the coupled

A {}^{1}{\ensuremath{\Sigma}}_{u}^{+}\ensuremath{-}b {}^{3}{\ensuremath{\Pi}}_{u}

states. Using spectroscopic data and accurate quantum chemistry calculations for

{\mathrm{Cs}}_{2}

potential curves and transition dipole moments, we show that this process competes favorably with the single-photon decay back to the lowest triplet state. In addition, we demonstrate that this conversion process represents a loss channel for vibrational cooling of metastable triplet molecules, preventing an efficient optical pumping cycle down to low vibrational levels.

DOI: 10.1103/physreva.83.022503

Related papers

Triplet-singlet conversion in ultracold Cs $_2$ and production of ground state moleculesTriplet-singlet conversion in ultracold Cs$_2$ and production of ground state molecules

Nadia Bouloufa-Maafa, Marin Pichler, M Aymar +1 more

We propose a process to convert ultracold metastable Cs $_2$ molecules in their lowest triplet state into (singlet) ground state molecules in their lowest vibrational levels. Molecules are first pumped into an excited triplet state, and the triplet-singlet conversion is facilitated by a two-step spontaneous decay through the coupled $A^{1}\Sigma_{u}^{+} \sim b ^{3}\Pi_{u}$ states. Using spectroscopic data and accurate quantum chemistry calculations for Cs $_2$ potential curves and transition dipole moments, we show that this process has a high rate and competes favorably with the single-photon decay back to the lowest triplet state. In addition, we demonstrate that this conversion process represents a loss channel for vibrational cooling of metastable triplet molecules, preventing an efficient optical pumping cycle down to low vibrational levels.We propose a process to convert ultracold metastable Cs$_2$ molecules in their lowest triplet state into (singlet) ground state molecules in their lowest vibrational levels. Molecules are first pumped into an excited triplet state, and the triplet-singlet conversion is facilitated by a two-step spontaneous decay through the coupled $A^{1}\Sigma_{u}^{+} \sim b ^{3}\Pi_{u}$ states. Using spectroscopic data and accurate quantum chemistry calculations for Cs$_2$ potential curves and transition dipole moments, we show that this process has a high rate and competes favorably with the single-photon decay back to the lowest triplet state. In addition, we demonstrate that this conversion process represents a loss channel for vibrational cooling of metastable triplet molecules, preventing an efficient optical pumping cycle down to low vibrational levels.

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Triplet-singlet conversion by broadband optical pumping

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Photoassociation of two ultracold rubidium atoms and the subsequent formation of stable molecules in the singlet ground and lowest triplet states is investigated theoretically. The method employs laser pulses inducing transitions via excited states correlated to the $5S+5{P}_{1∕2}$ asymptote. Weakly bound molecules in the singlet ground or lowest triplet state can be created by a single pulse while the formation of more deeply bound molecules requires a two-color pump-dump scenario. More deeply bound molecules in the singlet ground or lowest triplet state can be produced only if efficient mechanisms for both pump and dump steps exist. While long-range $1∕{R}^{3}$ potentials allow for efficient photoassociation, stabilization is facilitated by the resonant spin-orbit coupling of the ${0}_{u}^{+}$ states. Molecules in the singlet ground state bound by a few wave numbers can thus be formed. This provides a promising first step toward ground-state molecules which are ultracold in both translational and vibrational degrees of freedom.Photoassociation of two ultracold rubidium atoms and the subsequent formation of stable molecules in the singlet ground and lowest triplet states is investigated theoretically. The method employs laser pulses inducing transitions via excited states correlated to the $5S+5{P}_{1∕2}$ asymptote. Weakly bound molecules in the singlet ground or lowest triplet state can be created by a single pulse while the formation of more deeply bound molecules requires a two-color pump-dump scenario. More deeply bound molecules in the singlet ground or lowest triplet state can be produced only if efficient mechanisms for both pump and dump steps exist. While long-range $1∕{R}^{3}$ potentials allow for efficient photoassociation, stabilization is facilitated by the resonant spin-orbit coupling of the ${0}_{u}^{+}$ states. Molecules in the singlet ground state bound by a few wave numbers can thus be formed. This provides a promising first step toward ground-state molecules which are ultracold in both translational and vibrational degrees of freedom.

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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 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. ^

Jan 1, 20071 citation

We propose a process to convert ultracold metastable

{\mathrm{Cs}}_{2}

A {}^{1}{\ensuremath{\Sigma}}_{u}^{+}\ensuremath{-}b {}^{3}{\ensuremath{\Pi}}_{u}

states. Using spectroscopic data and accurate quantum chemistry calculations for

{\mathrm{Cs}}_{2}

Triplet-singlet conversion in ultracold Cs

_2

and production of ground state molecules

We propose a process to convert ultracold metastable Cs

_2

molecules in their lowest triplet state into (singlet) ground state molecules in their lowest vibrational levels. Molecules are first pumped into an excited triplet state, and the triplet-singlet conversion is facilitated by a two-step spontaneous decay through the coupled

A^{1}\Sigma_{u}^{+} \sim b ^{3}\Pi_{u}

states. Using spectroscopic data and accurate quantum chemistry calculations for Cs

_2

potential curves and transition dipole moments, we show that this process has a high rate and competes favorably with the single-photon decay back to the lowest triplet state. In addition, we demonstrate that this conversion process represents a loss channel for vibrational cooling of metastable triplet molecules, preventing an efficient optical pumping cycle down to low vibrational levels.

We demonstrate the conversion of cold Cs

{}_{2}

molecules initially distributed over several vibrational levels of the lowest triplet state ${a}^{3}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\Sigma}}_{u}^{+}$ into the singlet ground state ${X}^{1}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\Sigma}}_{g}^{+}$. This conversion is realized by a broadband laser exciting the molecules to a well-chosen state from which they may decay to the singlet state through two sequential single-photon emission steps: The first photon populates levels with mixed triplet-singlet character, making possible a second spontaneous emission down to several vibrational levels of the ${X}^{1}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\Sigma}}_{g}^{+}$ states. By adding an optical scheme for vibrational cooling, a substantial fraction of molecules are transferred to the ground vibrational level of the singlet state. The efficiency of the conversion process, with and without vibrational cooling, is discussed at the end of the article. The presented conversion is general in scope and could be extended to other molecules.

^{85}\mathrm{Rb}

and

^{133}\mathrm{Cs}

atoms. We obtain extensive bound-bound excitation spectra of these molecules, which provide detailed information about their vibrational distribution, as well as spectroscopic data on several RbCs molecular states including $a\text{ }^{3}\ensuremath{\Sigma}^{+}$, $(2)\text{ }^{3}\ensuremath{\Sigma}^{+}$, and $(1)\text{ }^{1}\ensuremath{\Pi}$. Analysis of this data allows us to predict strong transitions from observed levels to the absolute vibronic ground state of RbCs, potentially allowing the production of stable, ultracold polar molecules at rates in excess of ${10}^{6}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$.

5S+5{P}_{1∕2}

asymptote. Weakly bound molecules in the singlet ground or lowest triplet state can be created by a single pulse while the formation of more deeply bound molecules requires a two-color pump-dump scenario. More deeply bound molecules in the singlet ground or lowest triplet state can be produced only if efficient mechanisms for both pump and dump steps exist. While long-range

1∕{R}^{3}

potentials allow for efficient photoassociation, stabilization is facilitated by the resonant spin-orbit coupling of the

{0}_{u}^{+}

states. Molecules in the singlet ground state bound by a few wave numbers can thus be formed. This provides a promising first step toward ground-state molecules which are ultracold in both translational and vibrational degrees of freedom.