Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Prospects for transferring 87Rb84Sr dimers to the rovibrational ground state based on calculated molecular structures

Tao Chen, Shaobing Zhu, Xiaolin Li, Jun Qian, Yuzhu Wang

Published Jun 4, 2014• 23 citations
Publisher

Abstract

Using fitted model potential curves of the ground and lowest three excited states yielded by the relativistic Kramers-restricted multireference configuration interaction method with 19 electrons correlated, we theoretically investigate the rovibrational properties including the number of vibrational state and diagonally distributed Franck-Condon factors for a ${}^{87}\text{Rb}{}^{84}\text{Sr}$ molecule. Benefiting from a turning point at about ${v}^{\ensuremath{'}}=20$ for the Franck-Condon factors between the ground state and spin-orbit $2(\ensuremath{\Omega}=1/2)$ excited state, we choose $|2(\ensuremath{\Omega}=1/2),{v}^{\ensuremath{'}}=21,{J}^{\ensuremath{'}}=1\ensuremath{\rangle}$ as the intermediate state in the three-level model to theoretically analyze the possibility of performing stimulated Raman adiabatic passage to transfer weakly bound RbSr molecules to the rovibrational ground state. With 1550 nm pump laser (2 W/${\text{cm}}^{2}$) and 1342 nm dump laser (10 mW/${\text{cm}}^{2}$) employed and appropriate settings of pulse time length (about 300 $\ensuremath{\mu}$s), we have formalistically achieved a round-trip transfer efficiency of 60%, namely 77% for one-way transfer. The results demonstrate the possibility of producing polar ${}^{87}\text{Rb}{}^{84}\text{Sr}$ molecules efficiently in a submicrokelvin regime, and further provide promising directions for future theoretical and experimental studies on alkali-alkaline(rare)-earth dimers.

DOI
10.1103/physreva.89.063402

Related papers

Ab-initio study of the ground and low-lying excited states including the spin-orbit effect of RbBa molecule and laser cooling feasibility

Hela Ladjimi, Wissem Zrafi, Abdul-Rahman Allouche +1 more

In this work, we present a thorough theoretical structure and spectroscopic study of the ground and low lying excited states of RbBa molecule. High-level ab-initio calculations are performed, using MCSCF/MRCI+Q level of method, based on the effective core potential (ECP) and core-polarization potential (CPP) approach. The potential energy curves, spectroscopic parameters, vibrationnel energy levels of the 16( 2,4 Σ + , 2,4 Π, 2,4 Δ) first electronic states, with respect to the lowest five dissociation limits were calculated. The comparison of the spectroscopic constants of the ground state X 2 Σ + with the available theoretical work, are in good agreement. The study of all the excited states is performed in this work for the first time. Afterwards, the spin-orbit operator is incorporated in valence MRCI calculation using optimized relativistic spin-orbit pseudo-potentials and 33 Ω states are generated and split into Λ-S states. In addition, both relativistic and non relativistic calculations of permanent and transition dipole moments are presented and discussed. Stimulated black body ( T = 300 K) and spontaneous transition rates of vibrational states of X 2 Σ + state were evaluated. The related vibrational lifetimes for RbBa are found to be in order of 10 3 s which is sufficiently large for ultracold experiments. Moreover, the vibrational life-time for the A 2 Σ + ( v’ ) and A 2 П ( v” ) states are measured and the possibility of Laser Cooling for the RbBa molecule is discussed based on Franck–Condon factors calculation of A 2 Σ + ( v’ )→ X 2 Σ + ( v ) and A 2 П( v” ) → X 2 Σ + ( v ) transition. This work represents a significant contribution for experimentalists as it provides efficient information in order to form cold alkali and alkaline-earth RbBa molecules.

Journal of Quantitative Spectroscopy and Radiative Transfer•May 18, 2020•5 citations

VIBRONIC TRANSITIONS IN THE X-Sr SERIES (X=Li, Na, K, Rb): ON THE ACCURACY OF NUCLEAR WAVEFUNCTIONS DERIVED FROM QUANTUM CHEMISTRY

Andreas Hauser, Wolfgang Ernst, Johann Valentin Pototschnig +1 more

Research on ultracold molecules has seen a growing interest recently in the context of high-resolution spectroscopy and quantum computation. The preparation of molecules in low vibrational levels of the ground state is experimentally challenging, and typically achieved by population transfer using excited electronic states. On the theoretical side, highly accurate potential energy surfaces are needed for a correct description of processes such as the coherent de-excitation from the highest and therefore weakly bound vibrational levels in the electronic ground state via couplings to electronically excited states. Particularly problematic is the correct description of potential features at large intermolecular distances. Franck-Condon overlap integrals for nuclear wavefunctions in barely bound vibrational states are extremely sensitive to inaccuracies of the potential at long range. In this study, we compare the predictions of common, wavefunction-based ab initio techniques for a known de-excitation mechanism in alkali-alkaline earth dimers. It is the aim to analyze the predictive power of these methods for a preliminary evaluation of potential cooling mechanisms in heteronuclear open shell systems which offer the experimentalist an electric as well as a magnetic handle for manipulation. The series of $X$-Sr molecules, with $X$ = Li, Na, K and Rb, has been chosen for a direct comparison. Quantum degenerate mixtures of Rb and Sr have already been produced,\footnote{B. Pasquiou, A. Bayerle, S. M. Tzanova, S. Stellmer, J. Szczepkowski, M. Parigger, R. Grimm, and F. Schreck, Phys. Rev. A, 2013, 88, 023601} making this combination very promising for the production of ultracold molecules.

International Symposium on Molecular Spectroscopy (ISMS)•Jun 21, 2016•0 citations

Two-photon Raman transition channels of NaCs predicted from ab initio calculations

Jingbo Wei, Peng Li, Jizhou Wu +6 more

Obtaining effective spontaneous radiative transition channels is a fundamental topic in the preparation of ultracold rovibrational ground states of molecules. Herein, the ranges of prospective transition channels in the NaCs dimer are predicted via exploring the complex energy level structure and transition properties. The potential energy curves of \ensuremath{\Lambda}-$S$ states and \ensuremath{\Omega} states, spectroscopy constants, absolute energies of bound states, and transition information (Frank-Condon factors, lifetimes, transition dipole moments) have been researched. With this purpose, the results of our experiment on binding energies of the ${b}^{3}{\mathrm{\ensuremath{\Pi}}}_{0}{}^{+}$ rovibrational states are analyzed; the transition from the higher (photoassociated) ${}^{1}\mathrm{\ensuremath{\Pi}}$ state to the ground ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state is discussed. The wavelengths of the two lasers are predicted as 622.8-656.7 nm and 896.3-969.8 nm with the ${B}^{1}{\mathrm{\ensuremath{\Pi}}}_{1}$ and ${c}^{3}{\mathrm{\ensuremath{\Sigma}}}_{1}^{+}$ states, respectively, for the stimulated raman adiabatic passage method.

Physical Review A•Jun 22, 2022•3 citations

Four-Component Relativistic Coupled Cluster and Configuration Interaction Calculations on the Ground and Excited States of the RbYb Molecule

Lasse Kragh Sørensen, Stefan Knecht, Timo Fleig +1 more

We present high-level four-component coupled cluster and multireference configuration interaction calculations of potential energy curves, dipole moment, Franck-Condon factors and spectroscopic constants of the newly formed RbYb molecule. From finite-field calculations we obtain an electric dipole moment for RbYb of almost 1 D. In combination with its magnetic dipole moment this makes RbYb an excellent candidate for trapping and for studying dipolar interaction in the ultracold regime. Significant Franck-Condon factors are found between the rovibronic ground state and the lowest rovibrational levels of the first excited 2Sigma1/2+ state but also between a broad range of rovibrational levels of the 2Pi1/2 and 2Pi3/2 states. This allows for several two-step approaches to reach the rovibronic ground state after initial photoassociation.

The Journal of Physical Chemistry A•Aug 18, 2009•48 citations

Vibronic transitions in the alkali-metal (Li, Na, K, Rb) – alkaline-earth-metal (Ca, Sr) series: A systematic analysis of de-excitation mechanisms based on the graphical mapping of Frank-Condon integrals

Johann Valentin Pototschnig, Ralf Meyer, Andreas W. Hauser +1 more

Research on ultracold molecules has seen a growing interest recently in the context of high-resolution spectroscopy and quantum computation. After forming weakly bound molecules from atoms in cold collisions, the preparation of molecules in low vibrational levels of the ground state is experimentally challenging, and typically achieved by population transfer using excited electronic states. Accurate potential energy surfaces are needed for a correct description of processes such as the coherent de-excitation from the highest and therefore weakly bound vibrational levels in the electronic ground state via couplings to electronically excited states. This paper is dedicated to the vibrational analysis of potentially relevant electronically excited states in the alkali-metal (Li, Na, K, Rb)-- alkaline-earth metal (Ca,Sr) diatomic series. Graphical maps of Frank-Condon overlap integrals are presented for all molecules of the group. By comparison to overlap graphics produced for idealized potential surfaces, we judge the usability of the selected states for future experiments on laser-enhanced molecular formation from mixtures of quantum degenerate gases.

Physical Review A•Feb 2, 2017•19 citations

All-optical quantum control of angular momentum orientation and high-resolution spectroscopy of alkali dimers

J. T. Stahovich

In this dissertation, three distinct but related experimental works are reported. The first is a study of the highly excited 3^1 Δ_g and 4^1 Δ_g electronic states of 85Rb2. Rovibrational levels of the two electronic states were probed using the high-resolution optical-optical double resonance (OODR) technique by exciting 85Rb2 molecules from thermally populated levels of the X(_ ^1)Σ_g^+ ground state through intermediate levels of the B^1 Π_u electronic state. The (_ ^1)Δ_g resonances induced by the probe laser were observed by detecting laser induced fluorescence (LIF) from nearby, collisionally populated triplet levels to the a^3 Σ_u^+ triplet ground state. The (_ ^1)Δ_g character of the two electronic states was confirmed by showing that the probe transitions to these states abide by (_ ^1)Δ←(_ ^1)Π dipole selection rules and by observing that their lowest rotational level is J = 2. A set of molecular constants and a Rydberg-Klein-Rees (RKR) potential energy curve (PEC) were calculated from the observed term values for each electronic state and compared with ab initio predictions. This is the first observation of (_ ^1)Δ_g states in Rb2.The next results are on the highly excited 6(_ ^3)Π_0g electronic state of the 133Cs2 molecule in an energetic region where very little is known. Rovibrational levels of the excited triplet state were experimentally observed by the perturbation-facilitated-OODR (PFOODR) using a level of the A(_ ^1)Σ_u^+ ~b(_ ^3)Π_u mixed manifold as an intermediate. A progression of P and R branch probe laser resonances were detected by measuring (LIF) to the a(_ ^3)Σ_u^+ state as a function of the probe laser frequency. For select rovibrational levels of the 6(_ ^3)Π_0g state, dispersed fluorescence to the a(_ ^3)Σ_u^+ state and the A(_ ^1)Σ_u^+ ~b(_ ^3)Π_u manifold were also recorded and compared with Frank-Condon factor (FCF) calculations to determine spin multiplicity and vibrational numbering. Term values of the 284 observed rovibrational levels and their quantum numbers were fit to a Dunham expansion to obtain molecular constants, which were in turn used to generate a corresponding RKR-PEC. Comparison to ab initio results led to the assignment of 6(_ ^3)Π_0g . Accurate and high-resolution potential energy curves for the excited states of alkali dimers are crucial for quantum control and cooling experiments relying on techniques such as Stimulated Raman adiabatic passage (STIRAP) and resonantly enhanced multiphoton ionization (REMPI).Lastly, the results of producing state selective molecular angular momentum orientation using dressed states created by a cw optical field are reported. The experiment was carried out with 7Li2 molecules and a combination of left- and right-hand circularly polarized lasers. Our approach exploits the dependence of the Rabi frequency on the quantum number M, which makes it possible to achieve complete M-state selectivity and thus molecular angular momentum orientation relative to laboratory frame space-fixed axes. Using molecules in a (_ ^1)Σ state, orientation of the rotational angular momentum, R ⃑, can be achieved by spectrally resolving the Autler-Townes split M components of the total angular momentum, J ⃑. Results of orienting J ⃑ in (_ ^1)Π state molecules are also discussed. This is the first time complete angular momentum orientation has been achieved in nonpolar molecules and should aid the efforts of stereochemistry, molecular imaging, photodissociation and photoassociation, to name a few.

•Oct 19, 2026•0 citations
Using fitted model potential curves of the ground and lowest three excited states yielded by the relativistic Kramers-restricted multireference configuration interaction method with 19 electrons correlated, we theoretically investigate the rovibrational properties including the number of vibrational state and diagonally distributed Franck-Condon factors for a 87Rb84Sr{}^{87}\text{Rb}{}^{84}\text{Sr}87Rb84Sr molecule. Benefiting from a turning point at about v\ensuremath′=20{v}^{\ensuremath{'}}=20v\ensuremath′=20 for the Franck-Condon factors between the ground state and spin-orbit 2(\ensuremathΩ=1/2)2(\ensuremath{\Omega}=1/2)2(\ensuremathΩ=1/2) excited state, we choose ∣2(\ensuremathΩ=1/2),v\ensuremath′=21,J\ensuremath′=1\ensuremath⟩|2(\ensuremath{\Omega}=1/2),{v}^{\ensuremath{'}}=21,{J}^{\ensuremath{'}}=1\ensuremath{\rangle}∣2(\ensuremathΩ=1/2),v\ensuremath′=21,J\ensuremath′=1\ensuremath⟩ as the intermediate state in the three-level model to theoretically analyze the possibility of performing stimulated Raman adiabatic passage to transfer weakly bound RbSr molecules to the rovibrational ground state. With 1550 nm pump laser (2 W/cm2{\text{cm}}^{2}cm2) and 1342 nm dump laser (10 mW/cm2{\text{cm}}^{2}cm2) employed and appropriate settings of pulse time length (about 300 \ensuremathμ\ensuremath{\mu}\ensuremathμs), we have formalistically achieved a round-trip transfer efficiency of 60%, namely 77% for one-way transfer. The results demonstrate the possibility of producing polar 87Rb84Sr{}^{87}\text{Rb}{}^{84}\text{Sr}87Rb84Sr molecules efficiently in a submicrokelvin regime, and further provide promising directions for future theoretical and experimental studies on alkali-alkaline(rare)-earth dimers.
In this work, we present a thorough theoretical structure and spectroscopic study of the ground and low lying excited states of RbBa molecule. High-level ab-initio calculations are performed, using MCSCF/MRCI+Q level of method, based on the effective core potential (ECP) and core-polarization potential (CPP) approach. The potential energy curves, spectroscopic parameters, vibrationnel energy levels of the 16( 2,4 Σ + , 2,4 Π, 2,4 Δ) first electronic states, with respect to the lowest five dissociation limits were calculated. The comparison of the spectroscopic constants of the ground state X 2 Σ + with the available theoretical work, are in good agreement. The study of all the excited states is performed in this work for the first time. Afterwards, the spin-orbit operator is incorporated in valence MRCI calculation using optimized relativistic spin-orbit pseudo-potentials and 33 Ω states are generated and split into Λ-S states. In addition, both relativistic and non relativistic calculations of permanent and transition dipole moments are presented and discussed. Stimulated black body ( T = 300 K) and spontaneous transition rates of vibrational states of X 2 Σ + state were evaluated. The related vibrational lifetimes for RbBa are found to be in order of 10 3 s which is sufficiently large for ultracold experiments. Moreover, the vibrational life-time for the A 2 Σ + ( v’ ) and A 2 П ( v” ) states are measured and the possibility of Laser Cooling for the RbBa molecule is discussed based on Franck–Condon factors calculation of A 2 Σ + ( v’ )→ X 2 Σ + ( v ) and A 2 П( v” ) → X 2 Σ + ( v ) transition. This work represents a significant contribution for experimentalists as it provides efficient information in order to form cold alkali and alkaline-earth RbBa molecules.
Research on ultracold molecules has seen a growing interest recently in the context of high-resolution spectroscopy and quantum computation. The preparation of molecules in low vibrational levels of the ground state is experimentally challenging, and typically achieved by population transfer using excited electronic states. On the theoretical side, highly accurate potential energy surfaces are needed for a correct description of processes such as the coherent de-excitation from the highest and therefore weakly bound vibrational levels in the electronic ground state via couplings to electronically excited states. Particularly problematic is the correct description of potential features at large intermolecular distances. Franck-Condon overlap integrals for nuclear wavefunctions in barely bound vibrational states are extremely sensitive to inaccuracies of the potential at long range. In this study, we compare the predictions of common, wavefunction-based ab initio techniques for a known de-excitation mechanism in alkali-alkaline earth dimers. It is the aim to analyze the predictive power of these methods for a preliminary evaluation of potential cooling mechanisms in heteronuclear open shell systems which offer the experimentalist an electric as well as a magnetic handle for manipulation. The series of XXX-Sr molecules, with XXX = Li, Na, K and Rb, has been chosen for a direct comparison. Quantum degenerate mixtures of Rb and Sr have already been produced,\footnote{B. Pasquiou, A. Bayerle, S. M. Tzanova, S. Stellmer, J. Szczepkowski, M. Parigger, R. Grimm, and F. Schreck, Phys. Rev. A, 2013, 88, 023601} making this combination very promising for the production of ultracold molecules.
Obtaining effective spontaneous radiative transition channels is a fundamental topic in the preparation of ultracold rovibrational ground states of molecules. Herein, the ranges of prospective transition channels in the NaCs dimer are predicted via exploring the complex energy level structure and transition properties. The potential energy curves of \ensuremath{\Lambda}-SSS states and \ensuremath{\Omega} states, spectroscopy constants, absolute energies of bound states, and transition information (Frank-Condon factors, lifetimes, transition dipole moments) have been researched. With this purpose, the results of our experiment on binding energies of the ${b}^{3}{\mathrm{\ensuremath{\Pi}}}_{0}{}^{+}$ rovibrational states are analyzed; the transition from the higher (photoassociated) ${}^{1}\mathrm{\ensuremath{\Pi}}$ state to the ground ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ state is discussed. The wavelengths of the two lasers are predicted as 622.8-656.7 nm and 896.3-969.8 nm with the ${B}^{1}{\mathrm{\ensuremath{\Pi}}}_{1}$ and ${c}^{3}{\mathrm{\ensuremath{\Sigma}}}_{1}^{+}$ states, respectively, for the stimulated raman adiabatic passage method.
We present high-level four-component coupled cluster and multireference configuration interaction calculations of potential energy curves, dipole moment, Franck-Condon factors and spectroscopic constants of the newly formed RbYb molecule. From finite-field calculations we obtain an electric dipole moment for RbYb of almost 1 D. In combination with its magnetic dipole moment this makes RbYb an excellent candidate for trapping and for studying dipolar interaction in the ultracold regime. Significant Franck-Condon factors are found between the rovibronic ground state and the lowest rovibrational levels of the first excited 2Sigma1/2+ state but also between a broad range of rovibrational levels of the 2Pi1/2 and 2Pi3/2 states. This allows for several two-step approaches to reach the rovibronic ground state after initial photoassociation.
Research on ultracold molecules has seen a growing interest recently in the context of high-resolution spectroscopy and quantum computation. After forming weakly bound molecules from atoms in cold collisions, the preparation of molecules in low vibrational levels of the ground state is experimentally challenging, and typically achieved by population transfer using excited electronic states. Accurate potential energy surfaces are needed for a correct description of processes such as the coherent de-excitation from the highest and therefore weakly bound vibrational levels in the electronic ground state via couplings to electronically excited states. This paper is dedicated to the vibrational analysis of potentially relevant electronically excited states in the alkali-metal (Li, Na, K, Rb)-- alkaline-earth metal (Ca,Sr) diatomic series. Graphical maps of Frank-Condon overlap integrals are presented for all molecules of the group. By comparison to overlap graphics produced for idealized potential surfaces, we judge the usability of the selected states for future experiments on laser-enhanced molecular formation from mixtures of quantum degenerate gases.
In this dissertation, three distinct but related experimental works are reported. The first is a study of the highly excited 3^1 Δ_g and 4^1 Δ_g electronic states of 85Rb2. Rovibrational levels of the two electronic states were probed using the high-resolution optical-optical double resonance (OODR) technique by exciting 85Rb2 molecules from thermally populated levels of the X(_ ^1)Σ_g^+ ground state through intermediate levels of the B^1 Π_u electronic state. The (_ ^1)Δ_g resonances induced by the probe laser were observed by detecting laser induced fluorescence (LIF) from nearby, collisionally populated triplet levels to the a^3 Σ_u^+ triplet ground state. The (_ ^1)Δ_g character of the two electronic states was confirmed by showing that the probe transitions to these states abide by (_ ^1)Δ←(_ ^1)Π dipole selection rules and by observing that their lowest rotational level is J = 2. A set of molecular constants and a Rydberg-Klein-Rees (RKR) potential energy curve (PEC) were calculated from the observed term values for each electronic state and compared with ab initio predictions. This is the first observation of (_ ^1)Δ_g states in Rb2.The next results are on the highly excited 6(_ ^3)Π_0g electronic state of the 133Cs2 molecule in an energetic region where very little is known. Rovibrational levels of the excited triplet state were experimentally observed by the perturbation-facilitated-OODR (PFOODR) using a level of the A(_ ^1)Σ_u^+ ~b(_ ^3)Π_u mixed manifold as an intermediate. A progression of P and R branch probe laser resonances were detected by measuring (LIF) to the a(_ ^3)Σ_u^+ state as a function of the probe laser frequency. For select rovibrational levels of the 6(_ ^3)Π_0g state, dispersed fluorescence to the a(_ ^3)Σ_u^+ state and the A(_ ^1)Σ_u^+ ~b(_ ^3)Π_u manifold were also recorded and compared with Frank-Condon factor (FCF) calculations to determine spin multiplicity and vibrational numbering. Term values of the 284 observed rovibrational levels and their quantum numbers were fit to a Dunham expansion to obtain molecular constants, which were in turn used to generate a corresponding RKR-PEC. Comparison to ab initio results led to the assignment of 6(_ ^3)Π_0g . Accurate and high-resolution potential energy curves for the excited states of alkali dimers are crucial for quantum control and cooling experiments relying on techniques such as Stimulated Raman adiabatic passage (STIRAP) and resonantly enhanced multiphoton ionization (REMPI).Lastly, the results of producing state selective molecular angular momentum orientation using dressed states created by a cw optical field are reported. The experiment was carried out with 7Li2 molecules and a combination of left- and right-hand circularly polarized lasers. Our approach exploits the dependence of the Rabi frequency on the quantum number M, which makes it possible to achieve complete M-state selectivity and thus molecular angular momentum orientation relative to laboratory frame space-fixed axes. Using molecules in a (_ ^1)Σ state, orientation of the rotational angular momentum, R ⃑, can be achieved by spectrally resolving the Autler-Townes split M components of the total angular momentum, J ⃑. Results of orienting J ⃑ in (_ ^1)Π state molecules are also discussed. This is the first time complete angular momentum orientation has been achieved in nonpolar molecules and should aid the efforts of stereochemistry, molecular imaging, photodissociation and photoassociation, to name a few.