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Physical Review A

One-photon-assisted formation of ultracold polar molecules

Elizabeth Juarros, Philippe Pellegrini, K. Kirby, Robin Côté

Published Apr 12, 2006• 28 citations
Publisher

Abstract

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 $v=0$. We show that photon emission in the cascade process does not contribute to trap loss and that a large population of molecules in $v=0$ can be achieved.

DOI
10.1103/physreva.73.041403

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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. ^

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Laser-assisted ultracold lithium-hydride molecule formation: stimulated versus spontaneous emission

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We investigate the feasibility of forming ultracold LiH from a mixture of the ultracold atomic gases, by using B 1 Π as an intermediate state in the photoassociation process. Using accurate molecular potential energy curves and dipole transition moments, we calculate and compare two possible schemes to populate vibrational levels of the ground electronic state, X 1 Σ + : (1) two-photon stimulated radiative association and (2) excitation to bound levels of the B 1 Π state, followed by spontaneous emission to the X 1 Σ + state. With laser intensities and atomic densities that are easily attainable experimentally, we find that significant quantities of molecules can be formed in various v , J levels of the electronic ground state. We examine the spontaneous emission cascade which takes place from the upper vibrational levels on a time scale of milliseconds. We discuss the issue of back-stimulation for the two-photon process and ways to mitigate it. Because photon emission in the cascade process does not contribute to trap loss, a sizable population of molecules in v = 0 can be achieved.

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Dimitri Borsalino, Romain Véxiau, M Aymar +3 more

Abstract Heteronuclear alkali-metal dimers represent the class of molecules of choice for creating samples of ultracold molecules exhibiting an intrinsic large permanent electric dipole moment. Among them, the KCs molecule, with a permanent dipole moment of 1.92 Debye still remains to be observed in ultracold conditions. Based on spectroscopic studies available in the literature completed by accurate quantum chemistry calculations, we propose several optical coherent schemes to create ultracold bosonic and fermionic KCs molecules in their absolute rovibrational ground level, starting from a weakly bound level of their electronic ground state manifold. The processes rely on the existence of convenient electronically excited states allowing an efficient stimulated Raman adiabatic transfer of the level population.

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Proposal for the formation of ultracold deeply bound RbSr dipolar molecules by all-optical methods

Adrien Devolder, Eliane Luc-Koenig, Osman Atabek +2 more

Ultracold paramagnetic and polar diatomic molecules are among the promising systems for quantum simulation of lattice-spin models. Unfortunately, their experimental observation is still challenging. Based on our recent ab initio calculations, we analyze the feasibility of all-optical schemes for the formation of ultracold $^{87}\mathrm{Rb}^{84}\mathrm{Sr}$ bosonic molecules. A first possibility is photoassociation followed by spontaneous emission. The photoassociation rate coefficients toward electronic states converging to the $^{87}\mathrm{Rb}(5s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2})+^{84}\mathrm{Sr}(5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0,1,2}$) asymptotes are particularly small for vibrational levels close to the asymptote. The creation of molecules would be more interesting by using deeply bound levels which preferentially relax to the ${v}^{\ensuremath{'}\ensuremath{'}}=0$ level of the ground state. On the other hand, the photoassociation rate coefficients toward electronic states correlated to the $\mathrm{Rb}(5p\phantom{\rule{0.16em}{0ex}}^{2}P_{1/2,3/2})+\mathrm{Sr}(5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$) are significant for levels close to the asymptote. The spontaneous emission thus creates weakly bound molecules in a single vibrational level. A second option relies on stimulated Raman adiabatic passage implemented in a tight optical trap. It efficiently creates weakly bound ground-state molecules in a well-defined level, thus providing a promising alternative to magnetic Feshbach resonances for further population transfer toward the absolute ground state of the RbSr molecule.

arXiv:1806.10346•Physical Review A•Nov 9, 2018•14 citations
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 X1\ensuremathΣ+X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}X1\ensuremathΣ+ 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.
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. ^
We investigate the feasibility of forming ultracold LiH from a mixture of the ultracold atomic gases, by using B 1 Π as an intermediate state in the photoassociation process. Using accurate molecular potential energy curves and dipole transition moments, we calculate and compare two possible schemes to populate vibrational levels of the ground electronic state, X 1 Σ + : (1) two-photon stimulated radiative association and (2) excitation to bound levels of the B 1 Π state, followed by spontaneous emission to the X 1 Σ + state. With laser intensities and atomic densities that are easily attainable experimentally, we find that significant quantities of molecules can be formed in various v , J levels of the electronic ground state. We examine the spontaneous emission cascade which takes place from the upper vibrational levels on a time scale of milliseconds. We discuss the issue of back-stimulation for the two-photon process and ways to mitigate it. Because photon emission in the cascade process does not contribute to trap loss, a sizable population of molecules in v = 0 can be achieved.
Photoassociation is a process by which two cold, trapped atoms can be optically excited during a collision to make a vibrational level of an excited electronic state of a molecular dimer. High-resolution photoassociation spectra are now well-known for most alkali dimers. The upper level normally decays by spontaneous emission to a number of final molecular levels, bound and unbound. A laser of a second color can be used to stimulate a transition from the upper level to a particular ground state vibrational level. Such a Raman photoassociation process can be used to form translationally cold molecules in a cold atomic gas or a Bose-Einstein condensate. Coupled channels scattering calculations show that the collisional rate coefficient for coherent production of molecules in specific target states, >10−10cm3/s,> 10^{-10} cm^{3}/s,>10−10cm3/s, can greatly exceed the rate coefficient for forming products due to excited state spontaneous decay. This implies the feasibility of rapid coherent conversion of atom pairs in a condensate to molecules on a time scale short compared to the trap oscillation time. The untrapped molecules can form a coherent molecular beam. We will examine the prospects for the experimental realization of photoassociative molecule formation in cold alkali gases or condensates.
Ultracold quantum gases are versatile model systems for exploring quantum physics or for the simulation of solid state materials. Meanwhile, they have been created from various atomic species - from alkali metals over alkaline earths to rare earth elements. The latest addition are quantum gases of different kinds of polar molecules. Expectations for quantum gases of heteronuclear molecules are high: Due to their large electric dipole moments, these molecules can interact with each other via long-range interactions - not just via contact interactions as is the case for most atoms. Additionally, they have vibrational and rotational degrees of freedom, with open up new possibilities for quantum simulation. But the same degrees of freedom also pose some challenges. For example, they make the preparation of the quantum gas more difficult, which is typically produced with a combination of laser cooling and evaporative cooling in the atomic case. Molecules mostly lack closed transitions in their spectra, which are required for laser cooling. Therefore, we create our molecular quantum gas from a mixture of two atomic quantum gases. In this work, such an experimental method was developed for fermionic NaK molecules, which is based on the two-photon process Stimulated Raman Adiabatic Passage (STIRAP). Within STIRAP, the hyperfine structure of the chosen intermediate state plays an important role. Experimentally, and with the help of a theoretical model describing the whole process, we find that we produce the most molecules when we use a large one-photon detuning, if the hyperfine structure of the intermediate state is unresolved. In another project, we explored the rotational level structure of the molecular ground state populated by STIRAP. Rotation is closely linked to the electric dipole moment. The superposition of the ground state with the first excited rotational state, for example, has a transition dipole moment of almost 60% of the permanent electric dipole moment. Unfortunately, coherence times of such superpositions are typically short, as the different polarizabilities of the rotational states lead to dephasing in optical traps. However, using a special polarization angle and a small, dc electric field, we can compensate these differences and realize a spin-decoupled magic trap. With this new technique we obtain record coherence times, at least for small molecular densities. For larger densities we observe first indications for dipolar interactions in a bulk gas of polar molecules, which we also model using the moving-average cluster expansion (MACE).
Abstract Heteronuclear alkali-metal dimers represent the class of molecules of choice for creating samples of ultracold molecules exhibiting an intrinsic large permanent electric dipole moment. Among them, the KCs molecule, with a permanent dipole moment of 1.92 Debye still remains to be observed in ultracold conditions. Based on spectroscopic studies available in the literature completed by accurate quantum chemistry calculations, we propose several optical coherent schemes to create ultracold bosonic and fermionic KCs molecules in their absolute rovibrational ground level, starting from a weakly bound level of their electronic ground state manifold. The processes rely on the existence of convenient electronically excited states allowing an efficient stimulated Raman adiabatic transfer of the level population.
Ultracold paramagnetic and polar diatomic molecules are among the promising systems for quantum simulation of lattice-spin models. Unfortunately, their experimental observation is still challenging. Based on our recent ab initio calculations, we analyze the feasibility of all-optical schemes for the formation of ultracold 87Rb84Sr^{87}\mathrm{Rb}^{84}\mathrm{Sr}87Rb84Sr bosonic molecules. A first possibility is photoassociation followed by spontaneous emission. The photoassociation rate coefficients toward electronic states converging to the 87Rb(5s2S1/2)+84Sr(5s5p3P0,1,2^{87}\mathrm{Rb}(5s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2})+^{84}\mathrm{Sr}(5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0,1,2}87Rb(5s2S1/2​)+84Sr(5s5p3P0,1,2​) asymptotes are particularly small for vibrational levels close to the asymptote. The creation of molecules would be more interesting by using deeply bound levels which preferentially relax to the ${v}^{\ensuremath{'}\ensuremath{'}}=0$ level of the ground state. On the other hand, the photoassociation rate coefficients toward electronic states correlated to the Rb(5p2P1/2,3/2)+Sr(5s21S0\mathrm{Rb}(5p\phantom{\rule{0.16em}{0ex}}^{2}P_{1/2,3/2})+\mathrm{Sr}(5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}Rb(5p2P1/2,3/2​)+Sr(5s21S0​) are significant for levels close to the asymptote. The spontaneous emission thus creates weakly bound molecules in a single vibrational level. A second option relies on stimulated Raman adiabatic passage implemented in a tight optical trap. It efficiently creates weakly bound ground-state molecules in a well-defined level, thus providing a promising alternative to magnetic Feshbach resonances for further population transfer toward the absolute ground state of the RbSr molecule.