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

arXiv:quant-ph/0008075 · The Journal of Chemical Physics

Tuning the scattering length on the ground triplet state of Cs2

Viatcheslav Kokoouline, J. Vala, Ronnie Kosloff

Published Feb 15, 2001• 16 citations
arXivHTMLPDF

Abstract

Two schemes for tuning the scattering length on the ground triplet state of Cs2 are developed. The absolute value of the triplet scattering length of 133Cs2 is determined from the experimental data [A. Fioretti, D. Comparat, C. Drag, C. Amiot, O. Dulieu, F. Masnou-Seeuws, and P. Pillet, Eur. Phys. J. D 5, 389 (1999)], we demonstrate that the large scattering length can be made small and positive by coupling the 3Σu+(6S+6S) potential to the 3Πg state by strong off-resonant radiation. A weaker laser field coupling the 3Σu+(6S+6S) continuum to the lowest bound level of the excited 3Σg+(6S+6P) state also leads to a small positive scattering length. The scattering length of the 135Cs isotope is found to be positive. The method used solves the Schrödinger equation for two electronic states coupled by an electromagnetic field with no approximations employed. The scattering length is determined from the calculated continuum wave functions at low energies.

DOI
10.1063/1.1343080

Related papers

Tuning the scattering length on the ground triplet state of $Cs_{2}$

Viatcheslav Kokoouline, J. Vala, R. Kosloff

We develop two schemes for tuning the scattering length on the ground triplet state of Cs2. First, an absolute value of the triplet scattering length of 133Cs2 is determined using the experimental data (Fioretti et al, Eur.Phys.J. 5, 389 (1999)). We demonstrate that the large scattering length can be made small and positive by coupling of the 3Σ + u (6S +6S) potential to the 3Πg state by strong off-resonant radiation. A weaker laser field coupling the 3Σ + u (6S + 6S) continuum to the lowest bound level of the excited 3Σ + g (6S + 6P) also leads to a small positive scattering length. In addition, the scattering length of the 135Cs isotope is found to be positive. The method used solves the Schrödinger equation for two electronic states coupled by an electromagnetic field with approximations employed. The scattering length is determined from calculated continuum wavefunctions of low energy. 1 A positive scattering length is a crucial ingredient in obtaining Bose-Einstein condensation from a gas of ultra-cold atoms. This parameter controls the long range repulsion

•Jan 1, 2000•18 citations

Improved Models for the Potential Energy Functions of the Ground Singlet and Lowest-Lying Triplet States of the Cesium Dimer

Jesse Baldwin

The Morse/Long Range (MLR) potential has become one of the most reliable and highly \nused potential energy functions for diatomic molecules. It includes the theoretical long range \nbehaviour that diatomic molecules are known to exhibit as they approach the dissociation \nlimit. Heavy alkali metals with adjacent electronic states often exhibit strong coupling \nbetween the spin and orbital angular momentum. The ground state X¹Σg⁺ and the lowest \nlying triplet state aᶟΣᵤ⁺ of Cs₂ exhibit such coupling effects and as a result, modeling the \nhighest vibrational states of these states is a non-trivial problem. Utilizing scattering length \nvalues obtained from published analysis of 60 Feshbach resonances, the correct form of the \npotential energy function was determined. Moreover, the scattering length values were used \nto determine the correct leading dispersion coefficient that describes the true form of the \nlong-range potential energy functions. All previous attempts to determine global potential \nenergy functions for these states have considered only the optical spectroscopic data. This is \nthe first ever effort attempting to use scattering lengths determined from cold atom collision \nexperiments in a combined analysis with conventional spectroscopic data.

•Aug 23, 2012•1 citation

Observation of Cesium (nD 5/2 +6S 1/2 ) Ultralong-Range Rydberg-Ground Molecules

Suying Bai, Jingxu Bai, Xiaoxuan Han +3 more

Ultralong-range Cs 2 Rydberg-ground molecules ( nD 5/2 + 6 S 1/2 F ) (33 ≤ n ≤ 39, F = 3 or 4) are investigated by a two-photon photo-association spectroscopy of an ultracold Cs gas. Two vibrational ground molecular spectra of triplet 3 Σ and hyperfine mixed singlet-triplet 1,3 Σ molecular states and their corresponding binding energies are attained. The experimental observations are simulated by an effective Hamiltonian including low energy electron scattering pseudopotentials, the spin-orbit interaction of the Rydberg atom, and the hyperfine interaction of the ground-state atom. The zero-energy singlet and triplet s-wave scattering lengths are extracted by comparing the experimental observations and calculations. Dependences of the measured binding energies on the effective principal quantum number, n eff = n − δ D ( δ D is the quantum defect of Rydberg D state), yield the scaling of n eff − 5.60 ± 0.16 ( 3 ​ Σ , F = 3 ) , n eff − 5.62 ± 0.16 ( 3 ​ Σ , F = 4 ) for deep triplet potential and n eff − 5.65 ± 0.38 ( 1 , 3 ​ Σ , F = 3 ) , n eff − 6.19 ± 0.14 ( 1 , 3 ​ Σ , F = 4 ) for shallow mixed singlet-triplet potential well. The simulations of low-energy Rydberg electron scattering show agreement well with the experimental measurements.

Chinese Physics Letters•Dec 1, 2020•6 citations

Scattering properties of the ultracold 133 Cs 2 triplet state

Sun Jin-Feng, Du Bing-Ge, Zhang Ji-Cai +2 more

The elastic scattering properties of ultracold 133Cs2 triplet state are investigated in detail. We construct a potential curve of the 133Cs2 triplet state, based on the latest ab initio molecular potential data and show how the scattering parameters are obtained by using three methods: the Numerov method, the semiclassical method and the variable phase method, where the scattering lengths of the 133Cs2 triplet state, i.e. 301.79a0, 300.67a0 and 310.81a0 are obtained respectively, with a0 being the Bohr radius. We also calculate the effective range and the number of bound states for the 133Cs2 triplet state. Our results are in agreement with the recent experimental data and the theoretical calculations. This confirms that the results of the scattering properties of the ultracold 133Cs2 triplet state, calculated by using these three methods, are reliable.

Chinese Physics B•Mar 1, 2009•0 citations

Observation of photoassociation spectroscopy of ultralong 37 D 5/2 + 6 S 1/2 Cs 2 Rydberg molecules

Suying Bai, Xiaoxuan Han, Jingxu Bai +4 more

We present an experimental observation of 37D5/2 + 6S1/2 Cs2 Rydberg-ground molecules by employing a two-photon photoassociation method. Two distinct Rydberg-ground molecular signals, deep and shallow bound molecules, are observed at the red detuning of atomic line. In theory, the model of scattering interaction between the Rydberg electron and ground-state atom is used to simulate the experiments. Two potential energy curves with energy minimum, deep pure triplet 3Σ and shallow hyperfine-mixed singlet–triplet 1,3Σ potentials, refer to the attained Rydberg-ground molecular signals, respectively. Calculations of the binding energy of triplet 3Σ and mixed 1,3Σv = 0 states are compared with the measurements. The agreement between the calculated and measured values of the binding energy yields zero-energy scattering lengths asT(0) = −19.2a0 and asS(0) = −1.3a0, respectively.

The Journal of Chemical Physics•Feb 24, 2020•8 citations

Experimental Characterization of Singlet Scattering Channels in Long-Range Rydberg Molecules

Heiner Saßmannshausen, Frédéric Merkt, Johannes Deiglmayr

We observe the formation of long-range Cs2 Rydberg molecules consisting of a Rydberg and a ground-state atom by photoassociation spectroscopy in an ultracold Cs gas near 6s1/2(F=3,4)→np3/2 resonances (n=26-34). The spectra reveal two types of molecular states recently predicted by D. A. Anderson, S. A. Miller, and G. Raithel [Phys. Rev. A 90, 062518 (2014)]: states bound purely by triplet s-wave scattering with binding energies ranging from 400 MHz at n=26 to 80 MHz at n=34, and states bound by mixed singlet-triplet s-wave scattering with smaller and F-dependent binding energies. The experimental observations are accounted for by an effective Hamiltonian including s-wave scattering pseudopotentials, the hyperfine interaction of the ground-state atom, and the spin-orbit interaction of the Rydberg atom. The analysis enables the characterization of the role of singlet scattering in the formation of long-range Rydberg molecules and the determination of an effective singlet s-wave scattering length for low-energy-electron-Cs collisions.

arXiv:1412.0846•Physical Review Letters•Mar 31, 2015•94 citations
Two schemes for tuning the scattering length on the ground triplet state of Cs2 are developed. The absolute value of the triplet scattering length of 133Cs2 is determined from the experimental data [A. Fioretti, D. Comparat, C. Drag, C. Amiot, O. Dulieu, F. Masnou-Seeuws, and P. Pillet, Eur. Phys. J. D 5, 389 (1999)], we demonstrate that the large scattering length can be made small and positive by coupling the 3Σu+(6S+6S) potential to the 3Πg state by strong off-resonant radiation. A weaker laser field coupling the 3Σu+(6S+6S) continuum to the lowest bound level of the excited 3Σg+(6S+6P) state also leads to a small positive scattering length. The scattering length of the 135Cs isotope is found to be positive. The method used solves the Schrödinger equation for two electronic states coupled by an electromagnetic field with no approximations employed. The scattering length is determined from the calculated continuum wave functions at low energies.
Tuning the scattering length on the ground triplet state of Cs2Cs_{2}Cs2​
We develop two schemes for tuning the scattering length on the ground triplet state of Cs2. First, an absolute value of the triplet scattering length of 133Cs2 is determined using the experimental data (Fioretti et al, Eur.Phys.J. 5, 389 (1999)). We demonstrate that the large scattering length can be made small and positive by coupling of the 3Σ + u (6S +6S) potential to the 3Πg state by strong off-resonant radiation. A weaker laser field coupling the 3Σ + u (6S + 6S) continuum to the lowest bound level of the excited 3Σ + g (6S + 6P) also leads to a small positive scattering length. In addition, the scattering length of the 135Cs isotope is found to be positive. The method used solves the Schrödinger equation for two electronic states coupled by an electromagnetic field with approximations employed. The scattering length is determined from calculated continuum wavefunctions of low energy. 1 A positive scattering length is a crucial ingredient in obtaining Bose-Einstein condensation from a gas of ultra-cold atoms. This parameter controls the long range repulsion
The Morse/Long Range (MLR) potential has become one of the most reliable and highly \nused potential energy functions for diatomic molecules. It includes the theoretical long range \nbehaviour that diatomic molecules are known to exhibit as they approach the dissociation \nlimit. Heavy alkali metals with adjacent electronic states often exhibit strong coupling \nbetween the spin and orbital angular momentum. The ground state X¹Σg⁺ and the lowest \nlying triplet state aᶟΣᵤ⁺ of Cs₂ exhibit such coupling effects and as a result, modeling the \nhighest vibrational states of these states is a non-trivial problem. Utilizing scattering length \nvalues obtained from published analysis of 60 Feshbach resonances, the correct form of the \npotential energy function was determined. Moreover, the scattering length values were used \nto determine the correct leading dispersion coefficient that describes the true form of the \nlong-range potential energy functions. All previous attempts to determine global potential \nenergy functions for these states have considered only the optical spectroscopic data. This is \nthe first ever effort attempting to use scattering lengths determined from cold atom collision \nexperiments in a combined analysis with conventional spectroscopic data.
Ultralong-range Cs 2 Rydberg-ground molecules ( nD 5/2 + 6 S 1/2 F ) (33 ≤ n ≤ 39, F = 3 or 4) are investigated by a two-photon photo-association spectroscopy of an ultracold Cs gas. Two vibrational ground molecular spectra of triplet 3 Σ and hyperfine mixed singlet-triplet 1,3 Σ molecular states and their corresponding binding energies are attained. The experimental observations are simulated by an effective Hamiltonian including low energy electron scattering pseudopotentials, the spin-orbit interaction of the Rydberg atom, and the hyperfine interaction of the ground-state atom. The zero-energy singlet and triplet s-wave scattering lengths are extracted by comparing the experimental observations and calculations. Dependences of the measured binding energies on the effective principal quantum number, n eff = n − δ D ( δ D is the quantum defect of Rydberg D state), yield the scaling of n eff − 5.60 ± 0.16 ( 3 ​ Σ , F = 3 ) , n eff − 5.62 ± 0.16 ( 3 ​ Σ , F = 4 ) for deep triplet potential and n eff − 5.65 ± 0.38 ( 1 , 3 ​ Σ , F = 3 ) , n eff − 6.19 ± 0.14 ( 1 , 3 ​ Σ , F = 4 ) for shallow mixed singlet-triplet potential well. The simulations of low-energy Rydberg electron scattering show agreement well with the experimental measurements.
The elastic scattering properties of ultracold 133Cs2 triplet state are investigated in detail. We construct a potential curve of the 133Cs2 triplet state, based on the latest ab initio molecular potential data and show how the scattering parameters are obtained by using three methods: the Numerov method, the semiclassical method and the variable phase method, where the scattering lengths of the 133Cs2 triplet state, i.e. 301.79a0, 300.67a0 and 310.81a0 are obtained respectively, with a0 being the Bohr radius. We also calculate the effective range and the number of bound states for the 133Cs2 triplet state. Our results are in agreement with the recent experimental data and the theoretical calculations. This confirms that the results of the scattering properties of the ultracold 133Cs2 triplet state, calculated by using these three methods, are reliable.
We present an experimental observation of 37D5/2 + 6S1/2 Cs2 Rydberg-ground molecules by employing a two-photon photoassociation method. Two distinct Rydberg-ground molecular signals, deep and shallow bound molecules, are observed at the red detuning of atomic line. In theory, the model of scattering interaction between the Rydberg electron and ground-state atom is used to simulate the experiments. Two potential energy curves with energy minimum, deep pure triplet 3Σ and shallow hyperfine-mixed singlet–triplet 1,3Σ potentials, refer to the attained Rydberg-ground molecular signals, respectively. Calculations of the binding energy of triplet 3Σ and mixed 1,3Σv = 0 states are compared with the measurements. The agreement between the calculated and measured values of the binding energy yields zero-energy scattering lengths asT(0) = −19.2a0 and asS(0) = −1.3a0, respectively.
We observe the formation of long-range Cs2 Rydberg molecules consisting of a Rydberg and a ground-state atom by photoassociation spectroscopy in an ultracold Cs gas near 6s1/2(F=3,4)→np3/2 resonances (n=26-34). The spectra reveal two types of molecular states recently predicted by D. A. Anderson, S. A. Miller, and G. Raithel [Phys. Rev. A 90, 062518 (2014)]: states bound purely by triplet s-wave scattering with binding energies ranging from 400 MHz at n=26 to 80 MHz at n=34, and states bound by mixed singlet-triplet s-wave scattering with smaller and F-dependent binding energies. The experimental observations are accounted for by an effective Hamiltonian including s-wave scattering pseudopotentials, the hyperfine interaction of the ground-state atom, and the spin-orbit interaction of the Rydberg atom. The analysis enables the characterization of the role of singlet scattering in the formation of long-range Rydberg molecules and the determination of an effective singlet s-wave scattering length for low-energy-electron-Cs collisions.