Physical Review A

Resonance measurements of d−f and d−g intervals in lithium Rydberg states

William E. Cooke, Thomas F. Gallagher, R. M. Hill, S. A. Edelstein

Published Sep 1, 1977• 43 citations

Abstract

Using a laser-excitation, optical-detection scheme, we have observed microwave transitions from the $\mathrm{nd}$ to the $\mathrm{nf}$ and $\mathrm{ng}$ orbital levels in lithium states with principal quantum number $n$ from 7 to 11. These measurements yield precise values for the $d$, $f$, and $g$ state fine-structure intervals as well as $d\ensuremath{-}f$ and $d\ensuremath{-}g$ energy separations. Within the accuracy of these measurements, the fine structures are found to be hydrogenic. The dipole polarizability of the ${\mathrm{Li}}^{+}$ core is determined from the $d\ensuremath{-}f$ and $d\ensuremath{-}g$ energy splittings. The $d\ensuremath{-}f$ intervals are compared to pseudopotential calculations.

DOI: 10.1103/physreva.16.1141

Related papers

Measurement of the lithium 10p fine structure interval and absolute energy

Paul Oxley, Patrick Collins

Physical Review AFeb 16, 20105 citations

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 +2 more

Physical Review AFeb 25, 200529 citations

Laser diagnostics of the energy spectrum of Rydberg states of the lithium-7 atom

Boris B. Zelener, Sergey A. Saakyan, Vladimir A. Sautenkov +3 more

Journal of Experimental and Theoretical PhysicsDec 1, 201514 citations

Millimeter spectroscopy in sodium Rydberg states: Quantum-defect, fine-structure, and polarizability measurements

Claude Fabre, S. Haroche, P. Goy

Physical Review AJul 1, 197876 citations

Microwave Field Metrology Based on Rydberg States of Alkali-Metal Atoms

Vitaly D. Ovsiannikov, Vitaly G. Palchikov, Igor L. Glukhov

PhotonicsSep 3, 20227 citations

Magic wavelengths for optical cooling and trapping of lithium

Marianna S. Safronova, Marianna S. Safronova, Charles W. Clark

arXiv:1206.7115Physical Review AOct 10, 201254 citations

Physical Review A

Resonance measurements of d−f and d−g intervals in lithium Rydberg states

William E. Cooke, Thomas F. Gallagher, R. M. Hill, S. A. Edelstein

Published Sep 1, 1977• 43 citations

Publisher

Abstract

Using a laser-excitation, optical-detection scheme, we have observed microwave transitions from the

\mathrm{nd}

to the

\mathrm{nf}

and

\mathrm{ng}

orbital levels in lithium states with principal quantum number

n

from 7 to 11. These measurements yield precise values for the

d

f

, and

g

state fine-structure intervals as well as

d\ensuremath{-}f

and

d\ensuremath{-}g

energy separations. Within the accuracy of these measurements, the fine structures are found to be hydrogenic. The dipole polarizability of the

{\mathrm{Li}}^{+}

core is determined from the

d\ensuremath{-}f

and

d\ensuremath{-}g

energy splittings. The

d\ensuremath{-}f

intervals are compared to pseudopotential calculations.

DOI: 10.1103/physreva.16.1141

Related papers

Measurement of the lithium 10p fine structure interval and absolute energy

Paul Oxley, Patrick Collins

We report a measurement of the fine structure interval of the $^{7}\mathrm{Li}$ $10p$ atomic state with a precision significantly better than previous measurements of fine structure intervals of Rydberg $^{7}\mathrm{Li}$ $p$ states. Our result of $74.97(74)$ MHz provides an experimental value for the only $n=10$ fine structure interval which is yet to be calculated. We also report a measurement of the absolute energy of the $10p$ state and its quantum defect, which are, respectively, $42379.498(23){\mathrm{cm}}^{\ensuremath{-}1}$ and $0.04694(10)$ . These results are in good agreement with recent calculations.We report a measurement of the fine structure interval of the $^{7}\mathrm{Li}$ $10p$ atomic state with a precision significantly better than previous measurements of fine structure intervals of Rydberg $^{7}\mathrm{Li}$ $p$ states. Our result of $74.97(74)$ MHz provides an experimental value for the only $n=10$ fine structure interval which is yet to be calculated. We also report a measurement of the absolute energy of the $10p$ state and its quantum defect, which are, respectively, $42379.498(23){\mathrm{cm}}^{\ensuremath{-}1}$ and $0.04694(10)$. These results are in good agreement with recent calculations.

Physical Review AFeb 16, 20105 citations

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 +2 more

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

Physical Review AFeb 25, 200529 citations

Laser diagnostics of the energy spectrum of Rydberg states of the lithium-7 atom

Boris B. Zelener, Sergey A. Saakyan, Vladimir A. Sautenkov +3 more

The spectra of excited lithium-7 atoms prepared in a magneto-optical trap are studied using a UV laser. The laser diagnostics of the energy of Rydberg atoms is developed based on measurements of the change in resonance fluorescence intensity of ultracold atoms as the exciting UV radiation frequency passes through the Rydberg transition frequency. The energies of various nS configurations are obtained in a broad range of the principal quantum number n from 38 to 165. The values of the quantum defect and ionization energy obtained in experiments and predicted theoretically are discussed.The spectra of excited lithium-7 atoms prepared in a magneto-optical trap are studied using a UV laser. The laser diagnostics of the energy of Rydberg atoms is developed based on measurements of the change in resonance fluorescence intensity of ultracold atoms as the exciting UV radiation frequency passes through the Rydberg transition frequency. The energies of various nS configurations are obtained in a broad range of the principal quantum number n from 38 to 165. The values of the quantum defect and ionization energy obtained in experiments and predicted theoretically are discussed.

Journal of Experimental and Theoretical PhysicsDec 1, 201514 citations

Millimeter spectroscopy in sodium Rydberg states: Quantum-defect, fine-structure, and polarizability measurements

Claude Fabre, S. Haroche, P. Goy

Millimeter resonances corresponding to single- and double-photon transitions have been observed between Rydberg levels of sodium with principal quantum number $n$ ranging from 23 to 41. The levels are prepared by laser excitation; transitions are induced by microwaves produced by a backwave oscillator working around 300 GHz; detection is performed through the selective field-ionization technique. Experimental values for quantum defects, fine-structure intervals, and polarizabilities are reported.Millimeter resonances corresponding to single- and double-photon transitions have been observed between Rydberg levels of sodium with principal quantum number $n$ ranging from 23 to 41. The levels are prepared by laser excitation; transitions are induced by microwaves produced by a backwave oscillator working around 300 GHz; detection is performed through the selective field-ionization technique. Experimental values for quantum defects, fine-structure intervals, and polarizabilities are reported.

Physical Review AJul 1, 197876 citations

Microwave Field Metrology Based on Rydberg States of Alkali-Metal Atoms

Vitaly D. Ovsiannikov, Vitaly G. Palchikov, Igor L. Glukhov

The high-precision determination of microwave radiation parameters may be based on measurements of the spectral characteristics of radiation transitions between the Rydberg states of atoms. Frequencies and matrix elements are calculated for dipole transitions from even-parity nS1/2 and nD5/2 to odd-parity n′P3/2 and n′F7/2 (where n′ = n, n ± 1, n ± 2) for the Rydberg states of alkali-metal atoms. The matrix elements determine the splitting of Rydberg-state energy levels in the field of a resonance microwave (μw) radiation, which results in the splitting of the resonance in electromagnetic induced transparency (EIT). Numerical computations based on the single-electron quantum defect method (QDM) and the Fues’ model potential (FMP) approach with the use of the most reliable data of the current literature on quantum defect values were performed for the 2S, 2P, 2D and 2F series of the Rydberg states of Li, Na, K, Rb and Cs atoms. The calculated data were approximated by quadratic polynomials of the principal quantum number. The polynomial coefficients were determined with the use of a standard curve-fitting interpolation polynomial procedure for numerically presented functions. The approximation equations may be used for the accurate evaluation of the frequencies and matrix elements of μw transitions in wide ranges of the Rydberg-state quantum numbers n >> 1.The high-precision determination of microwave radiation parameters may be based on measurements of the spectral characteristics of radiation transitions between the Rydberg states of atoms. Frequencies and matrix elements are calculated for dipole transitions from even-parity nS1/2 and nD5/2 to odd-parity n′P3/2 and n′F7/2 (where n′ = n, n ± 1, n ± 2) for the Rydberg states of alkali-metal atoms. The matrix elements determine the splitting of Rydberg-state energy levels in the field of a resonance microwave (μw) radiation, which results in the splitting of the resonance in electromagnetic induced transparency (EIT). Numerical computations based on the single-electron quantum defect method (QDM) and the Fues’ model potential (FMP) approach with the use of the most reliable data of the current literature on quantum defect values were performed for the 2S, 2P, 2D and 2F series of the Rydberg states of Li, Na, K, Rb and Cs atoms. The calculated data were approximated by quadratic polynomials of the principal quantum number. The polynomial coefficients were determined with the use of a standard curve-fitting interpolation polynomial procedure for numerically presented functions. The approximation equations may be used for the accurate evaluation of the frequencies and matrix elements of μw transitions in wide ranges of the Rydberg-state quantum numbers n >> 1.

PhotonicsSep 3, 20227 citations

Magic wavelengths for optical cooling and trapping of lithium

Marianna S. Safronova, Marianna S. Safronova, Charles W. Clark

Using first-principles calculations, we identify magic wavelengths ${\ensuremath{\lambda}}_{\mathrm{magic}}$ for the $2s$ - $2p$ and $2s$ - $3p$ transitions in lithium. The $ns$ and $np$ atomic levels have the same ac Stark shifts at the corresponding magic wavelength, which facilitates state-insensitive optical cooling and trapping. Tune-out wavelengths for which the ground-state frequency-dependent polarizability vanishes are also calculated. Differences of these wavelengths between ${}^{6}$ Li and ${}^{7}$ Li are reported. Our approach uses high-precision, relativistic all-order methods in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of Li electric-dipole matrix elements. Static polarizabilities for the $2s$ , $2p$ , $3s$ , $3p$ , and $3d$ levels are compared with other theory and experiment where available. Uncertainties of all recommended values are estimated. The magic wavelengths for the uv $2s$ - $3p$ transition are of particular interest for the production of a quantum gas of lithium [Duarte et al., Phys. Rev. A 84, 061406R (2011)].Using first-principles calculations, we identify magic wavelengths ${\ensuremath{\lambda}}_{\mathrm{magic}}$ for the $2s$-$2p$ and $2s$-$3p$ transitions in lithium. The $ns$ and $np$ atomic levels have the same ac Stark shifts at the corresponding magic wavelength, which facilitates state-insensitive optical cooling and trapping. Tune-out wavelengths for which the ground-state frequency-dependent polarizability vanishes are also calculated. Differences of these wavelengths between ${}^{6}$Li and ${}^{7}$Li are reported. Our approach uses high-precision, relativistic all-order methods in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of Li electric-dipole matrix elements. Static polarizabilities for the $2s$, $2p$, $3s$, $3p$, and $3d$ levels are compared with other theory and experiment where available. Uncertainties of all recommended values are estimated. The magic wavelengths for the uv $2s$-$3p$ transition are of particular interest for the production of a quantum gas of lithium [Duarte et al., Phys. Rev. A 84, 061406R (2011)].

arXiv:1206.7115Physical Review AOct 10, 201254 citations

Using a laser-excitation, optical-detection scheme, we have observed microwave transitions from the

\mathrm{nd}

to the

\mathrm{nf}

and

\mathrm{ng}

orbital levels in lithium states with principal quantum number

n

from 7 to 11. These measurements yield precise values for the

d

f

, and

g

state fine-structure intervals as well as

d\ensuremath{-}f

and

d\ensuremath{-}g

energy separations. Within the accuracy of these measurements, the fine structures are found to be hydrogenic. The dipole polarizability of the

{\mathrm{Li}}^{+}

core is determined from the

d\ensuremath{-}f

and

d\ensuremath{-}g

energy splittings. The

d\ensuremath{-}f

intervals are compared to pseudopotential calculations.

We report a measurement of the fine structure interval of the

^{7}\mathrm{Li}

10p

atomic state with a precision significantly better than previous measurements of fine structure intervals of Rydberg

^{7}\mathrm{Li}

p

states. Our result of

74.97(74)

MHz provides an experimental value for the only

n=10

fine structure interval which is yet to be calculated. We also report a measurement of the absolute energy of the

10p

state and its quantum defect, which are, respectively, $42379.498(23){\mathrm{cm}}^{\ensuremath{-}1}$ and

0.04694(10)

. These results are in good agreement with recent calculations.

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

Millimeter resonances corresponding to single- and double-photon transitions have been observed between Rydberg levels of sodium with principal quantum number

n

ranging from 23 to 41. The levels are prepared by laser excitation; transitions are induced by microwaves produced by a backwave oscillator working around 300 GHz; detection is performed through the selective field-ionization technique. Experimental values for quantum defects, fine-structure intervals, and polarizabilities are reported.

Using first-principles calculations, we identify magic wavelengths ${\ensuremath{\lambda}}_{\mathrm{magic}}$ for the

2s

2p

and

2s

3p

transitions in lithium. The

ns

and

np

atomic levels have the same ac Stark shifts at the corresponding magic wavelength, which facilitates state-insensitive optical cooling and trapping. Tune-out wavelengths for which the ground-state frequency-dependent polarizability vanishes are also calculated. Differences of these wavelengths between

{}^{6}

Li and

{}^{7}

Li are reported. Our approach uses high-precision, relativistic all-order methods in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of Li electric-dipole matrix elements. Static polarizabilities for the

2s

2p

3s

3p

, and

3d

levels are compared with other theory and experiment where available. Uncertainties of all recommended values are estimated. The magic wavelengths for the uv

2s

3p

transition are of particular interest for the production of a quantum gas of lithium [Duarte et al., Phys. Rev. A 84, 061406R (2011)].