Physical Review A

Determination of dipole and quadrupole polarizabilities of Ba+ by measurement of the fine structure of high- L n=9 and 10 Rydberg states of barium

Erica L. Snow, M. A. Gearba, R. A. Komara, S. R. Lundeen, William G. Sturrus

Published Feb 25, 2005• 29 citations

Abstract

The fine structure of high-angular-momentum $n=9$ and 10 Rydberg states of barium has been measured precisely, using the resonant excitation Stark ionization spectroscopy method. Optical transitions corresponding to $(n,{n}^{\ensuremath{'}})=(10,30)$, (9,17), and (9,20) were induced with a Doppler-tuned ${\mathrm{CO}}_{2}$ laser, determining the fine-structure energies corresponding to all $n=9$ and 10 levels with $L\ensuremath{\geqslant}6$. The pattern of these fine-structure energies conforms closely with an effective potential model, by comparison with which the dipole and quadrupole polarizabilities of ${\mathrm{Ba}}^{+}$ can be determined. Combining our data with earlier measurements made it possible to deduce, in addition, the portion of ${\ensuremath{\alpha}}_{2}$ due to the lowest excited $D$ state of ${\mathrm{Ba}}^{+}$. Our best estimates of these three properties are ${\ensuremath{\alpha}}_{1}=124.30(16){a}_{0}^{3}$, ${\ensuremath{\alpha}}_{2}=2462(361){a}_{0}^{5}$, and ${\ensuremath{\alpha}}_{2}^{0}=1828(88){a}_{0}^{5}$.

DOI: 10.1103/physreva.71.022510

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Effective core polarizabilities in Ba high-l Nsnldouble Rydberg atoms

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Determination of the dipole and quadrupole polarizabilities of Ba+ by study of high-L, n=9 and 10 Rydberg states of Ba

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Physical Review A

Determination of dipole and quadrupole polarizabilities of Ba+ by measurement of the fine structure of high- L n=9 and 10 Rydberg states of barium

Erica L. Snow, M. A. Gearba, R. A. Komara, S. R. Lundeen, William G. Sturrus

Published Feb 25, 2005• 29 citations

Publisher

Abstract

The fine structure of high-angular-momentum

n=9

and 10 Rydberg states of barium has been measured precisely, using the resonant excitation Stark ionization spectroscopy method. Optical transitions corresponding to

(n,{n}^{\ensuremath{'}})=(10,30)

, (9,17), and (9,20) were induced with a Doppler-tuned

{\mathrm{CO}}_{2}

laser, determining the fine-structure energies corresponding to all

n=9

and 10 levels with

L\ensuremath{\geqslant}6

. The pattern of these fine-structure energies conforms closely with an effective potential model, by comparison with which the dipole and quadrupole polarizabilities of

{\mathrm{Ba}}^{+}

can be determined. Combining our data with earlier measurements made it possible to deduce, in addition, the portion of

{\ensuremath{\alpha}}_{2}

due to the lowest excited

D

state of

{\mathrm{Ba}}^{+}

. Our best estimates of these three properties are

{\ensuremath{\alpha}}_{1}=124.30(16){a}_{0}^{3}

{\ensuremath{\alpha}}_{2}=2462(361){a}_{0}^{5}

, and

{\ensuremath{\alpha}}_{2}^{0}=1828(88){a}_{0}^{5}

DOI: 10.1103/physreva.71.022510

Related papers

Effective core polarizabilities in Ba high-l Nsnldouble Rydberg atoms

Pierre Camus, S. Cohen

We present experimental energy-level positions for Ba high-l Nsnl double Rydberg states with N=8 (n=13--15, l\ensuremath{\geqslant}7) and N=9 (n=13--15, l\ensuremath{\geqslant}7). These data as well as previously reported measurements for N=7 (n=12--15, l\ensuremath{\geqslant}5) and N=10 (n=13--15, l\ensuremath{\geqslant}10) are parametrized in order to yield values for the ${\mathrm{Ba}}^{+}$ Ns effective dipole ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{d}}^{\ensuremath{'}}$ and quadrupole ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{q}}^{\ensuremath{'}}$ polarizabilities. The obtained ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{d}}^{\ensuremath{'}}$ values are 1.25(5)\ifmmode\times\else\texttimes\fi{} ${10}^{3}$ , 7.05(4)\ifmmode\times\else\texttimes\fi{} ${10}^{3}$ , 2.95(4)\ifmmode\times\else\texttimes\fi{} ${10}^{4}$ , 9.39(15)\ifmmode\times\else\texttimes\fi{} ${10}^{4}$ in ${\mathrm{a}}_{0}^{3}$ units and the ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{q}}^{\ensuremath{'}}$ values are 1.7(8)\ifmmode\times\else\texttimes\fi{} ${10}^{4}$ , 1.8(2)\ifmmode\times\else\texttimes\fi{} ${10}^{5}$ , -1.0(2)\ifmmode\times\else\texttimes\fi{} ${10}^{6}$ , -1.0(2)\ifmmode\times\else\texttimes\fi{} ${10}^{7}$ in ${\mathrm{a}}_{0}^{5}$ units for N=7, 8, 9, and 10, respectively. The ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{d}}^{\ensuremath{'}}$ evolution with N is found to follow a ${\mathrm{N}}^{\mathrm{*}6.9(1)}$ power law, while calculated static polarizabilities present somewhat lower power dependence. From this small difference it is not possible to appreciate the importance of nonadiabatic effects between the two asymmetrically excited electrons. On the other hand, the larger discrepancies appearing between the calculated static and fitted quadrupole polarizabilities show clear evidence of nonadiabatic effects. Particularly the negative ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{q}}^{\ensuremath{'}}$ sign for N\ensuremath{\geqslant}9 is attributed to the increasing strength of dynamical effects on the Ns core electron caused by the motion of the outer high-l electron. It gives evidence of the increasing importance of nonadiabatic radial correlation between two planetary electrons when the Ns inner electron is sufficiently radially extended to be characterized as an inner Rydberg electron without, nevertheless, any appreciable overlapping with the outer electron.We present experimental energy-level positions for Ba high-l Nsnl double Rydberg states with N=8 (n=13--15, l\ensuremath{\geqslant}7) and N=9 (n=13--15, l\ensuremath{\geqslant}7). These data as well as previously reported measurements for N=7 (n=12--15, l\ensuremath{\geqslant}5) and N=10 (n=13--15, l\ensuremath{\geqslant}10) are parametrized in order to yield values for the ${\mathrm{Ba}}^{+}$ Ns effective dipole ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{d}}^{\ensuremath{'}}$ and quadrupole ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{q}}^{\ensuremath{'}}$ polarizabilities. The obtained ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{d}}^{\ensuremath{'}}$ values are 1.25(5)\ifmmode\times\else\texttimes\fi{}${10}^{3}$, 7.05(4)\ifmmode\times\else\texttimes\fi{}${10}^{3}$, 2.95(4)\ifmmode\times\else\texttimes\fi{}${10}^{4}$, 9.39(15)\ifmmode\times\else\texttimes\fi{}${10}^{4}$ in ${\mathrm{a}}_{0}^{3}$ units and the ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{q}}^{\ensuremath{'}}$ values are 1.7(8)\ifmmode\times\else\texttimes\fi{}${10}^{4}$, 1.8(2)\ifmmode\times\else\texttimes\fi{}${10}^{5}$, -1.0(2)\ifmmode\times\else\texttimes\fi{}${10}^{6}$, -1.0(2)\ifmmode\times\else\texttimes\fi{}${10}^{7}$ in ${\mathrm{a}}_{0}^{5}$ units for N=7, 8, 9, and 10, respectively. The ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{d}}^{\ensuremath{'}}$ evolution with N is found to follow a ${\mathrm{N}}^{\mathrm{*}6.9(1)}$ power law, while calculated static polarizabilities present somewhat lower power dependence. From this small difference it is not possible to appreciate the importance of nonadiabatic effects between the two asymmetrically excited electrons. On the other hand, the larger discrepancies appearing between the calculated static and fitted quadrupole polarizabilities show clear evidence of nonadiabatic effects. Particularly the negative ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{q}}^{\ensuremath{'}}$ sign for N\ensuremath{\geqslant}9 is attributed to the increasing strength of dynamical effects on the Ns core electron caused by the motion of the outer high-l electron. It gives evidence of the increasing importance of nonadiabatic radial correlation between two planetary electrons when the Ns inner electron is sufficiently radially extended to be characterized as an inner Rydberg electron without, nevertheless, any appreciable overlapping with the outer electron.

Physical Review AMar 1, 199510 citations

Unusually large polarizabilities and previously unidentified atomic states in Ba

C.-H. Li, Simon Rochester, M. G. Kozlov +1 more

Electric polarizabilities of four even-parity states of atomic barium in the range $35 600--36 000\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$, excited via two successive $E1$ transitions, are measured using direct spectroscopy. Several states have polarizabilities more than two orders of magnitude larger than might be expected from the known energy levels of Ba, implying the existence of two previously unobserved odd-parity states nearby. These two states are located using Stark-induced excitation, and tentatively identified as $(\text{Xe})6s8p\phantom{\rule{0.3em}{0ex}}^{3}P_{0,2}$ . The (also unusually high) polarizabilities of these states, as well as that of a third odd-parity state, are reported.Electric polarizabilities of four even-parity states of atomic barium in the range $35 600--36 000\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$, excited via two successive $E1$ transitions, are measured using direct spectroscopy. Several states have polarizabilities more than two orders of magnitude larger than might be expected from the known energy levels of Ba, implying the existence of two previously unobserved odd-parity states nearby. These two states are located using Stark-induced excitation, and tentatively identified as $(\text{Xe})6s8p\phantom{\rule{0.3em}{0ex}}^{3}P_{0,2}$. The (also unusually high) polarizabilities of these states, as well as that of a third odd-parity state, are reported.

arXiv:physics/0307060Physical Review AApr 7, 200410 citations

Field-ionization Stark spectra of Ba Rydberg atoms at high density of states

Andreas Sebastian Konig, Jörg Neukammer, H. Hieronymus +1 more

Stark spectra of barium Rydberg states above the classical field-ionization limit have been recorded at high density of states employing high-resolution laser spectroscopy. The spectra, taken at a binding energy of about \ensuremath{\varepsilon}\ensuremath{\approxeq}-55 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ with respect to zero-field threshold and at electric-field strengths F\ensuremath{\approxeq}100 V/cm exhibit dramatic variations in line profiles with increasing external field strength. The WKB quantum-defect theory of the Stark effect of nonhydrogenic atoms was used to analyze the recorded spectra, and excellent agreement between measured and calculated line profiles was achieved. Core-induced coupling of closed and open hydrogenic Stark channels was found to contribute dominantly to the linewidth of the recorded Stark resonances. In addition, a reformulation of this theory by McNicholl, Ivri, and Bergeman (unpublished) in terms of a configuration-interaction model was employed to analyze a particular avoided crossing of several Stark components. In this way recorded line profiles were parametrized within a limited model to obtain resonance energies, linewidths, and Fano q parameters.Stark spectra of barium Rydberg states above the classical field-ionization limit have been recorded at high density of states employing high-resolution laser spectroscopy. The spectra, taken at a binding energy of about \ensuremath{\varepsilon}\ensuremath{\approxeq}-55 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ with respect to zero-field threshold and at electric-field strengths F\ensuremath{\approxeq}100 V/cm exhibit dramatic variations in line profiles with increasing external field strength. The WKB quantum-defect theory of the Stark effect of nonhydrogenic atoms was used to analyze the recorded spectra, and excellent agreement between measured and calculated line profiles was achieved. Core-induced coupling of closed and open hydrogenic Stark channels was found to contribute dominantly to the linewidth of the recorded Stark resonances. In addition, a reformulation of this theory by McNicholl, Ivri, and Bergeman (unpublished) in terms of a configuration-interaction model was employed to analyze a particular avoided crossing of several Stark components. In this way recorded line profiles were parametrized within a limited model to obtain resonance energies, linewidths, and Fano q parameters.

Physical Review AMar 1, 19918 citations

Resonance spectra of Ba Rydberg atom in electric field above the ionization limit

Jiakun Xu, Wenjie Yu, Qing Ye

International Photonics and Optoelectronics MeetingsJan 1, 20170 citations

Determination of the dipole and quadrupole polarizabilities of Ba+ by study of high-L, n=9 and 10 Rydberg states of Ba

Erica L. Snow, R. A. Komara, M. A. Gearba +2 more

APSMay 1, 20041 citation

Measurement of the reduced dipole matrix element in Ba $^+$ Measurement of the reduced dipole matrix element in Ba$^+$

N. Jayjong, M. D. K. Lee, K. J. Arnold +1 more

We present a high-precision measurement of the reduced electric-dipole matrix element $\langle P_{1/2}\|r\|S_{1/2}\rangle$ in $^{138}\mathrm{Ba}^+$ . By comparing off-resonant scattering rates with dispersive Stark-shift measurements, we determine the matrix element to be $3.322\,7(12)$ , corresponding to a $P_{1/2}$ excited-state radiative lifetime of $7.866\,3(56)$ ~ns. Combining our experimental results with a prior model for the differential scalar polarizability $Δα_0(ω)$ , we extract the static value $Δα_0(0) = -73.09(12)$ a.u. This determination directly improves the evaluation of the blackbody radiation (BBR) shift, minimizing a prominent systematic limitation in room-temperature $\mathrm{Ba}^+$ optical clock error budgets. These results provide a stringent benchmark for atomic-structure calculations and advance high-precision applications in quantum metrology and tests of fundamental physics.We present a high-precision measurement of the reduced electric-dipole matrix element $\langle P_{1/2}\|r\|S_{1/2}\rangle$ in $^{138}\mathrm{Ba}^+$. By comparing off-resonant scattering rates with dispersive Stark-shift measurements, we determine the matrix element to be $3.322\,7(12)$, corresponding to a $P_{1/2}$ excited-state radiative lifetime of $7.866\,3(56)$~ns. Combining our experimental results with a prior model for the differential scalar polarizability $Δα_0(ω)$, we extract the static value $Δα_0(0) = -73.09(12)$a.u. This determination directly improves the evaluation of the blackbody radiation (BBR) shift, minimizing a prominent systematic limitation in room-temperature $\mathrm{Ba}^+$ optical clock error budgets. These results provide a stringent benchmark for atomic-structure calculations and advance high-precision applications in quantum metrology and tests of fundamental physics.

physics.atom-phCross-listedarXiv:2607.20920Jul 24, 2026

The fine structure of high-angular-momentum

n=9

and 10 Rydberg states of barium has been measured precisely, using the resonant excitation Stark ionization spectroscopy method. Optical transitions corresponding to

(n,{n}^{\ensuremath{'}})=(10,30)

, (9,17), and (9,20) were induced with a Doppler-tuned

{\mathrm{CO}}_{2}

laser, determining the fine-structure energies corresponding to all

n=9

and 10 levels with

L\ensuremath{\geqslant}6

. The pattern of these fine-structure energies conforms closely with an effective potential model, by comparison with which the dipole and quadrupole polarizabilities of

{\mathrm{Ba}}^{+}

can be determined. Combining our data with earlier measurements made it possible to deduce, in addition, the portion of

{\ensuremath{\alpha}}_{2}

due to the lowest excited

D

state of

{\mathrm{Ba}}^{+}

. Our best estimates of these three properties are

{\ensuremath{\alpha}}_{1}=124.30(16){a}_{0}^{3}

{\ensuremath{\alpha}}_{2}=2462(361){a}_{0}^{5}

, and

{\ensuremath{\alpha}}_{2}^{0}=1828(88){a}_{0}^{5}

{\mathrm{Ba}}^{+}

Ns effective dipole ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{d}}^{\ensuremath{'}}$ and quadrupole ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{q}}^{\ensuremath{'}}$ polarizabilities. The obtained ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{d}}^{\ensuremath{'}}$ values are 1.25(5)\ifmmode\times\else\texttimes\fi{}

{10}^{3}

, 7.05(4)\ifmmode\times\else\texttimes\fi{}

{10}^{3}

, 2.95(4)\ifmmode\times\else\texttimes\fi{}

{10}^{4}

, 9.39(15)\ifmmode\times\else\texttimes\fi{}

{10}^{4}

{\mathrm{a}}_{0}^{3}

units and the ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{q}}^{\ensuremath{'}}$ values are 1.7(8)\ifmmode\times\else\texttimes\fi{}

{10}^{4}

, 1.8(2)\ifmmode\times\else\texttimes\fi{}

{10}^{5}

, -1.0(2)\ifmmode\times\else\texttimes\fi{}

{10}^{6}

, -1.0(2)\ifmmode\times\else\texttimes\fi{}

{10}^{7}

{\mathrm{a}}_{0}^{5}

units for N=7, 8, 9, and 10, respectively. The ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{d}}^{\ensuremath{'}}$ evolution with N is found to follow a

{\mathrm{N}}^{\mathrm{*}6.9(1)}

power law, while calculated static polarizabilities present somewhat lower power dependence. From this small difference it is not possible to appreciate the importance of nonadiabatic effects between the two asymmetrically excited electrons. On the other hand, the larger discrepancies appearing between the calculated static and fitted quadrupole polarizabilities show clear evidence of nonadiabatic effects. Particularly the negative ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{q}}^{\ensuremath{'}}$ sign for N\ensuremath{\geqslant}9 is attributed to the increasing strength of dynamical effects on the Ns core electron caused by the motion of the outer high-l electron. It gives evidence of the increasing importance of nonadiabatic radial correlation between two planetary electrons when the Ns inner electron is sufficiently radially extended to be characterized as an inner Rydberg electron without, nevertheless, any appreciable overlapping with the outer electron.

Electric polarizabilities of four even-parity states of atomic barium in the range $35 600--36 000\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$, excited via two successive

E1

transitions, are measured using direct spectroscopy. Several states have polarizabilities more than two orders of magnitude larger than might be expected from the known energy levels of Ba, implying the existence of two previously unobserved odd-parity states nearby. These two states are located using Stark-induced excitation, and tentatively identified as

(\text{Xe})6s8p\phantom{\rule{0.3em}{0ex}}^{3}P_{0,2}

. The (also unusually high) polarizabilities of these states, as well as that of a third odd-parity state, are reported.

Measurement of the reduced dipole matrix element in Ba

^+

We present a high-precision measurement of the reduced electric-dipole matrix element

\langle P_{1/2}\|r\|S_{1/2}\rangle

^{138}\mathrm{Ba}^+

. By comparing off-resonant scattering rates with dispersive Stark-shift measurements, we determine the matrix element to be

3.322\,7(12)

, corresponding to a

P_{1/2}

excited-state radiative lifetime of

7.866\,3(56)

~ns. Combining our experimental results with a prior model for the differential scalar polarizability

Δα_0(ω)

, we extract the static value

Δα_0(0) = -73.09(12)

a.u. This determination directly improves the evaluation of the blackbody radiation (BBR) shift, minimizing a prominent systematic limitation in room-temperature

\mathrm{Ba}^+

optical clock error budgets. These results provide a stringent benchmark for atomic-structure calculations and advance high-precision applications in quantum metrology and tests of fundamental physics.