© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Bulletin of the American Physical Society

Long range Rb{sub 2} excited state dispersion interactions and transition dipole moment from photoassociation spectra

M. Marinescu, A. Dalgarno, Chin‐Chun Tsai, Joseph D. Miller, Robert A. Cline, Daniel J. Heinzen

Published May 1, 1996• 0 citations

Abstract

Two identical alkali atoms, with one atom excited, interact at long range through the resonant dipole interaction - C{sub 3}/R{sup 3} and through the dispersion interaction - C{sub 6}/R{sup 6} - C{sub 8}/R{sup 8} - ... These interaction coefficients have been previously calculated, but not accurately measured. The authors have measured the bound levels of a unique, 0{sub g}{sup {minus}}{open_quotes} pure long range state{close_quotes} of {sub 87}Rb{sub 2} and {sup 85}Rb{sub 2} with photoassociation spectroscopy of ultracold Rb atoms. By fitting the levels predicted by the interaction Hamiltonian to the observed levels, they have derived accurate values of both C{sub 3} and of the dispersion interaction coefficients. They also obtain an accurate measurement of the Rb 5s-5p electric dipole matrix element, which is simply related to C{sub 3}. These results provide an excellent test of the theory. They are also important to cold collisions, which are very sensitive to long range interactions.

Related papers

Photoassociation spectroscopy of {sup 87}Rb{sub 2} (5s{sub 1/2}+5p{sub 1/2})0{sub g}{sup -} long-range molecular states: Analysis by Lu-Fano graph and improved LeRoy-Bernstein formula

Haikel Jelassi, B. Viaris de Lesegno, Laurence Pruvost

We report on cold atom photoassociation of {sup 87}Rb giving spectroscopy data of the (5s{sub 1/2}+5p{sub 1/2})0{sub g}{sup -} long-range molecular states in the asymptotic range of [-12.5 cm{sup -1}, -1.5 cm{sup -1}] below the dissociation limit. Using a Lu-Fano approach to analyze the data, we show that an improved LeRoy-Bernstein model has to be applied. This approach lets us determine the phase shift of the wave function at the dissociation limit of the 0{sub g}{sup -} series.

Physical Review A•Mar 15, 2006•0 citations

Photoassociation of85Rb atoms into 0u+states near the 5S+5P atomic limits

T. H. Bergeman, J Qi, Dajun Wang +8 more

New photoassociation data on the 0u+ levels of Rb2 below the 5S+5P1/2 limit are combined with older data (Cline et al 1994 Phys. Rev. Lett. 73 632) in a fit to potentials and spin–orbit functions. The P1/2 data exhibit oscillations in the B(v) values due to coupling between the two 0u+ series, as modelled accurately by a coupled potentials approach. The fitted value for the C3 dispersion parameter from the combined data agrees well with the value derived from the pure long-range 0g− state.

Journal of Physics B Atomic Molecular and Optical Physics•Sep 25, 2006•53 citations

Long-range interactions between excited helium and alkali-metal atoms

J. Y. Zhang, Li-Yan Tang, T.-Y. Shi +2 more

The dispersion coefficients for the long-range interaction of the first four excited states of He, i.e., He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$$S$) and He(2 ${}^{1,3}$$P$), with the low-lying states of the alkali-metal atoms Li, Na, K, and Rb are calculated by summing over the reduced matrix elements of the multipole transition operators. For the interaction between He and Li the uncertainty of the calculations is 0.1--0.5$%$. For interactions with other alkali-metal atoms the uncertainty is 1--3$%$ in the coefficient ${C}_{5}$, 1--5$%$ in the coefficient ${C}_{6}$, and 1--10$%$ in the coefficients ${C}_{8}$ and ${C}_{10}$. The dispersion coefficients ${C}_{n}$ for the interaction of He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$$S$) and He(2 ${}^{1,3}$$P$) with the ground-state alkali-metal atoms and for the interaction of He(2 ${}^{1,3}\phantom{\rule{-0.16em}{0ex}}$$S$) with the alkali-metal atoms in their first ${}^{2}$$P$ states are presented in this Brief Report. The coefficients for other pairs of atomic states are listed in the Supplemental Material.

Physical Review A•Dec 3, 2012•10 citations

Precision measurement of the 5s-5p-5d two-photon, two-color, polarization spectrum in atomic Rb

S. B. Bayram, Mark D. Havey, M. Roşu +1 more

Summary form only given. A number of sophisticated techniques have been applied to precise measurements of the strength of resonance transitions in heavier alkali atoms. These include refined lifetime measurements in atomic beams, photoassociative spectroscopy of cold atoms confined to atomic traps, and direct measurements of the natural width of an atomic transition. We have made a precise study of the 5s-5p-5d transition in atomic Rb. Measurements of the non-resonant two-photon, two-color linear depolarization spectrum show remarkable polarization-dependent interference structure. Using this novel approach, it was possible to extract the ratio of the transition matrix elements for the two contributing pathways.

Quantum Electronics and Laser Science Conference•May 12, 2000•0 citations

Long-range interactions between the alkali-metal atoms and alkaline earth ions

Jasmeet Kaur, D. K. Nandy, Bindiya Arora +1 more

Accurate knowledge of interaction potentials among the alkali atoms and alkaline earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali atoms with the Ca$^+$, Ba$^+$, Sr$^+$, and Ra$^+$ alkaline earth ions systematically which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation $R$. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above mentioned systems which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representation of the interaction potentials versus $R$ are given among all the considered atoms and ions.

arXiv:1409.7154•Sep 25, 2014•0 citations

Long-range interactions between alkali and alkaline-earth atoms

Jun Jiang, Yongjun Cheng, Jim Mitroy

Dispersion coefficients between the alkali metal atoms (Li-Rb) and alkaline-earth metal atoms (Be-Sr) are evaluated using matrix elements computed from frozen core configuration interaction calculations. Besides dispersion coefficients with both atoms in their respective ground states, dispersion coefficients are also given for the case where one atom is in its ground state and the other atom is in a low lying excited state.

arXiv:1303.1234•Journal of Physics B Atomic Molecular and Optical Physics•Jun 10, 2013•11 citations

Two identical alkali atoms, with one atom excited, interact at long range through the resonant dipole interaction - C{sub 3}/R{sup 3} and through the dispersion interaction - C{sub 6}/R{sup 6} - C{sub 8}/R{sup 8} - ... These interaction coefficients have been previously calculated, but not accurately measured. The authors have measured the bound levels of a unique, 0{sub g}{sup {minus}}{open_quotes} pure long range state{close_quotes} of {sub 87}Rb{sub 2} and {sup 85}Rb{sub 2} with photoassociation spectroscopy of ultracold Rb atoms. By fitting the levels predicted by the interaction Hamiltonian to the observed levels, they have derived accurate values of both C{sub 3} and of the dispersion interaction coefficients. They also obtain an accurate measurement of the Rb 5s-5p electric dipole matrix element, which is simply related to C{sub 3}. These results provide an excellent test of the theory. They are also important to cold collisions, which are very sensitive to long range interactions.

The dispersion coefficients for the long-range interaction of the first four excited states of He, i.e., He(2

{}^{1,3}\phantom{\rule{-0.16em}{0ex}}

S

) and He(2

{}^{1,3}

P

), with the low-lying states of the alkali-metal atoms Li, Na, K, and Rb are calculated by summing over the reduced matrix elements of the multipole transition operators. For the interaction between He and Li the uncertainty of the calculations is 0.1--0.5

%

. For interactions with other alkali-metal atoms the uncertainty is 1--3

%

in the coefficient

{C}_{5}

, 1--5

%

in the coefficient

{C}_{6}

, and 1--10

%

in the coefficients

{C}_{8}

and

{C}_{10}

. The dispersion coefficients

{C}_{n}

for the interaction of He(2

{}^{1,3}\phantom{\rule{-0.16em}{0ex}}

S

) and He(2

{}^{1,3}

P

) with the ground-state alkali-metal atoms and for the interaction of He(2

{}^{1,3}\phantom{\rule{-0.16em}{0ex}}

S

) with the alkali-metal atoms in their first

{}^{2}

P

states are presented in this Brief Report. The coefficients for other pairs of atomic states are listed in the Supplemental Material.

Summary form only given. A number of sophisticated techniques have been applied to precise measurements of the strength of resonance transitions in heavier alkali atoms. These include refined lifetime measurements in atomic beams, photoassociative spectroscopy of cold atoms confined to atomic traps, and direct measurements of the natural width of an atomic transition. We have made a precise study of the 5s-5p-5d transition in atomic Rb. Measurements of the non-resonant two-photon, two-color linear depolarization spectrum show remarkable polarization-dependent interference structure. Using this novel approach, it was possible to extract the ratio of the transition matrix elements for the two contributing pathways.

Accurate knowledge of interaction potentials among the alkali atoms and alkaline earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali atoms with the Ca

^+

, Ba

^+

, Sr

^+

, and Ra

^+

alkaline earth ions systematically which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation

R

. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above mentioned systems which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representation of the interaction potentials versus

R

are given among all the considered atoms and ions.