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Physical Review A

Probing configuration interaction of the Ba 5d7dD21 state using radio-frequency spectroscopy and lifetime measurements

Thomas F. Gallagher, Wolfgang Sandner, Kambiz Ali Safinya

Published Jun 1, 1981• 52 citations
Publisher

Abstract

To probe the configuration mixing between the Ba $6snd^{1}D_{2}$ and $^{3}D_{2}$ Rydberg series and the $5d7d^{1}D_{2}$ perturber we have observed the radio-frequency transitions between the $5d7d^{1}D_{2}$ state and the $6s28s^{1}S_{0}$, $6s24f^{3}F_{2}$, and $6s24f^{1}F_{3}$ states using a delayed-field-ionization approach. The transitions are observed in the presence of small (\ensuremath{\sim}1 V/cm) electric fields, and from the Stark shifts of the transitions we are able to estimate the $^{1}D$ and $^{3}D$ Rydberg fractions of the $5d7d$ state. Our measured zero-field term separations tie together previous optical measurements of the various Rydberg series involved. In addition, we have measured the lifetimes of the $6snd$ states in the vicinity of the $5d7d$ perturber to estimate the fraction of $5d7d$ character in each of the Rydberg states. The values we find for the configuration mixing are in reasonable agreement with those determined by a multichannel-quantum-defect-theory analysis of the optical spectrum of the even-parity $J=2$ states of Ba.

DOI
10.1103/physreva.23.2969

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The hyperfine structure of $6snd^{1}D_{2}$ Rydberg states of $^{135,137}\mathrm{Ba}$ is reported for principal quantum numbers ranging between $n=10$ and $n=50$. From our data, singlet-triplet mixing coefficients have been deduced. A three-channel quantum-defect model has been used to analyze the resonance in singlet-triplet mixing of $6snd^{1}D_{2} \mathrm{and} ^{3}D_{2}$ Rydberg states in the vicinity of the $5d7d^{1}D_{2}$ perturber. For the determination of the scattering matrix, hyperfine-structure data were found to be essential. Good agreement has been achieved between calculated and experimental singlet-triplet mixing coefficients.

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Configuration interaction and singlet-triplet mixing probed by hyperfine structure of 6s14d1D2and3D1,2,3barium Rydberg states

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The hyperfine structure of the 6s14d configuration of barium has been measured by optical-optical double resonance. From the observed positions for the hyperfine components of the 1 D 2 and 3 D 1,2,3 Rydberg states, the singlet and triplet character as well as the amount of admixture of the 5d7d perturbing configuration was deduced. Although agreeing qualitatively, the authors' results differ quantitatively from predictions made by multichannel quantum defect theory (MQDT).

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Experimental studies of three-photon ionization of Ba: Evidence of channel interference and Raman coupling

James Floyd Kelly, Jan P. Hessler, G. Alber

Three-photon ionization spectra of Ba were studied which result from two-photon resonances between the 6${s}^{2}$ ${\mathrm{}}^{1}$${S}_{0}$ ground state and the 6snd J=2,6s(n+1)s ${\mathrm{}}^{1}$${S}_{0}$ (16\ensuremath{\le}n40) Rydberg states and 5d7d ${\mathrm{}}^{1}$${D}_{2}$,${\mathrm{}}^{3}$${P}_{0}$,2 perturber states. A tunable laser with field strength ${10}^{\mathrm{\ensuremath{-}}(4\mathrm{\ensuremath{-}}5)}$ a.u. was used to drive the excitation in a low-density atomic beam (n\ensuremath{\lesssim}3\ifmmode\times\else\texttimes\fi{}${10}^{8}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$). Resonant line shapes were systematically studied as a function of light polarization and intensity. Studies with linearly polarized light find all resonant line shapes manifest the same peak shift and asymmetry which is traced to the ac Stark shift of the ground state. The resonant peak height, shift, and linewidth scale linearly with light intensity which is accounted for with a rate-equation formulation.For the case of circular polarization, a distinct minimum of ionization occurs between each J=2 doublet of the 6snd series. One level (generally $^{3}\mathrm{D}_{2}$) is significantly broadened in comparison to the laser linewidth (0.1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) with increasing intensity while its sister level remains narrow (\ensuremath{\sim}0.2 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). Further, light shifts of the $^{3}\mathrm{D}_{2}$ states are generally \ensuremath{\gtrsim}1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ to the red while shifts of $^{1}\mathrm{D}_{2}$ states are negligible. This behavior switches for the n=27 doublet. Lastly, the dynamic shifts are not quadratic with the field strength. These effects are attributed in part to cancellation due to channel interference and a two-photon Raman process which mixes each J=2 doublet. These processes act in conjunction with the ac Stark effect to produce the observed profile behavior. The shifts and coupling of the excited states are attributed to the influence of the 6pnd ${J}^{\ensuremath{\pi}}$${=3}^{\mathrm{\ensuremath{-}}}$ autoionization series and are shown to be sensitive to the singlet-triplet mixing coefficient \ensuremath{\beta} of the J=2 doublets. A perturbation analysis is introduced which accounts for the salient features of the data, although it does not include bandwidth and saturation effects. Calculations of light shifts of the 6snd J=2 levels based on this analysis require \ensuremath{\beta} be modified from previous assignments based on hfs measurements for n in the vicinity of the 5d7d ${\mathrm{}}^{1}$${D}_{2}$ perturber.

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Multichannel quantum-defect theory of perturbed Rydberg atoms in external fields

K. T. Lu, A. R. P. Rau

The diamagnetic and Stark shifts of strongly perturbed Rydberg spectra such as those of the alkaline earths are expressed in terms of multichannel---quantum-defect parameters. The theory is applicable when the shifts produced by the external fields are smaller than the neighboring Rydberg separations. It is applied to evaluate the diamagnetic shifts in Ba, an atom in which Rydberg and doubly excited channels are strongly mixed. In such complex spectra, the diamagnetic effect can serve a useful purpose as a tool to disentangle the interacting series. The radial sizes and, therefore, the diamagnetic shifts are quite different for singly and doubly excited states even when they are at the same energy. In fact, for the field strengths considered ($\ensuremath{\simeq}40$ kG), the diamagnetic contribution of the doubly excited configuration is quite negligible. As a result, the observed shift is a direct measure of the amount of singly excited configuration in the state of interest. Exactly similar conclusions apply to Stark shifts. The last part of this paper considers states of very high excitation further up in the spectrum which are no longer in a perturbative regime. Spectra of atoms in a magnetic field have shown equally spaced resonances near the ionization threshold with characteristic spacings. By the consideration of the effects of electric fields which are also often simultaneously present, a criterion is established for the nature of these spacings depending on the relative strengths of the crossed electric and magnetic fields. The spacing seen in any particular experiment is shown to depend on the mass and quantum defect of the atom, the strengths of the external fields, and experimental conditions such as the temperature of the atomic vapor whose absorption spectrum is being studied.

Physical Review A•Nov 1, 1983•11 citations

Stark-enhanced decay of the 1 D2 state in Ba

Jerzy Kwela, Adriaan J. van Wijngaarden

The 877.5-nm electric-field-induced quench radiation on a thermal beam of Ba atoms in the metastable 6s5d $^{1}$${\mathit{D}}_{2}$ state for transition to the 5${\mathit{s}}^{2}$ $^{1}$${\mathit{S}}_{0}$ ground state has been measured at the 3% precision level. The Stark-enhanced dipole radiation yields a simple relationship between the field-free-decay rates for transitions between the metastable $^{1}$${\mathit{D}}_{2}$ state and the nearby states that are mixed in by the field. Using the known decay rates, we obtain a decay rate of A(6s6p $^{3}$${\mathit{P}}_{1}$--6s5d $^{1}$${\mathit{D}}_{2}$)\ensuremath{\sim}7\ifmmode\times\else\texttimes\fi{}${10}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$.

Physical Review A•Dec 1, 1990•5 citations
To probe the configuration mixing between the Ba 6snd1D26snd^{1}D_{2}6snd1D2​ and 3D2^{3}D_{2}3D2​ Rydberg series and the 5d7d1D25d7d^{1}D_{2}5d7d1D2​ perturber we have observed the radio-frequency transitions between the 5d7d1D25d7d^{1}D_{2}5d7d1D2​ state and the 6s28s1S06s28s^{1}S_{0}6s28s1S0​, 6s24f3F26s24f^{3}F_{2}6s24f3F2​, and 6s24f1F36s24f^{1}F_{3}6s24f1F3​ states using a delayed-field-ionization approach. The transitions are observed in the presence of small (\ensuremath{\sim}1 V/cm) electric fields, and from the Stark shifts of the transitions we are able to estimate the 1D^{1}D1D and 3D^{3}D3D Rydberg fractions of the 5d7d5d7d5d7d state. Our measured zero-field term separations tie together previous optical measurements of the various Rydberg series involved. In addition, we have measured the lifetimes of the 6snd6snd6snd states in the vicinity of the 5d7d5d7d5d7d perturber to estimate the fraction of 5d7d5d7d5d7d character in each of the Rydberg states. The values we find for the configuration mixing are in reasonable agreement with those determined by a multichannel-quantum-defect-theory analysis of the optical spectrum of the even-parity J=2J=2J=2 states of Ba.
The hyperfine structure of 6snd1D26snd^{1}D_{2}6snd1D2​ Rydberg states of 135,137Ba^{135,137}\mathrm{Ba}135,137Ba is reported for principal quantum numbers ranging between n=10n=10n=10 and n=50n=50n=50. From our data, singlet-triplet mixing coefficients have been deduced. A three-channel quantum-defect model has been used to analyze the resonance in singlet-triplet mixing of 6snd1D2and3D26snd^{1}D_{2} \mathrm{and} ^{3}D_{2}6snd1D2​and3D2​ Rydberg states in the vicinity of the 5d7d1D25d7d^{1}D_{2}5d7d1D2​ perturber. For the determination of the scattering matrix, hyperfine-structure data were found to be essential. Good agreement has been achieved between calculated and experimental singlet-triplet mixing coefficients.
By combining the quantum theory of radiative transition with multichannel quantum-defect theory, we have derived a general formula to calculate the lifetimes of highly excited states for atoms. As an example, we have evaluated the lifetimes for the perturbed 6snd 1D2^{1}D_{2}1D2​ (n=8--40) and 6snd 3D2^{3}D_{2}3D2​ (n=10--26) Rydberg levels, and the perturbers of the ytterbium atom. We have not only obtained results that are in perfect agreement with the recent measurements, but also predicted the lifetimes of 18 other highly excited states. The results indicate that the dramatic variation for lifetimes of Rydberg states in the vicinity of perturbing states is due to the strong channel interaction.
Three-photon ionization spectra of Ba were studied which result from two-photon resonances between the 6s2{s}^{2}s2 1{\mathrm{}}^{1}1S0{S}_{0}S0​ ground state and the 6snd J=2,6s(n+1)s 1{\mathrm{}}^{1}1S0{S}_{0}S0​ (16\ensuremath{\le}n40) Rydberg states and 5d7d 1{\mathrm{}}^{1}1D2{D}_{2}D2​,3{\mathrm{}}^{3}3P0{P}_{0}P0​,2 perturber states. A tunable laser with field strength ${10}^{\mathrm{\ensuremath{-}}(4\mathrm{\ensuremath{-}}5)}$ a.u. was used to drive the excitation in a low-density atomic beam (n\ensuremath{\lesssim}3\ifmmode\times\else\texttimes\fi{}108{10}^{8}108 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$). Resonant line shapes were systematically studied as a function of light polarization and intensity. Studies with linearly polarized light find all resonant line shapes manifest the same peak shift and asymmetry which is traced to the ac Stark shift of the ground state. The resonant peak height, shift, and linewidth scale linearly with light intensity which is accounted for with a rate-equation formulation.For the case of circular polarization, a distinct minimum of ionization occurs between each J=2 doublet of the 6snd series. One level (generally 3D2^{3}\mathrm{D}_{2}3D2​) is significantly broadened in comparison to the laser linewidth (0.1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) with increasing intensity while its sister level remains narrow (\ensuremath{\sim}0.2 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$). Further, light shifts of the 3D2^{3}\mathrm{D}_{2}3D2​ states are generally \ensuremath{\gtrsim}1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ to the red while shifts of 1D2^{1}\mathrm{D}_{2}1D2​ states are negligible. This behavior switches for the n=27 doublet. Lastly, the dynamic shifts are not quadratic with the field strength. These effects are attributed in part to cancellation due to channel interference and a two-photon Raman process which mixes each J=2 doublet. These processes act in conjunction with the ac Stark effect to produce the observed profile behavior. The shifts and coupling of the excited states are attributed to the influence of the 6pnd ${J}^{\ensuremath{\pi}}$${=3}^{\mathrm{\ensuremath{-}}}$ autoionization series and are shown to be sensitive to the singlet-triplet mixing coefficient \ensuremath{\beta} of the J=2 doublets. A perturbation analysis is introduced which accounts for the salient features of the data, although it does not include bandwidth and saturation effects. Calculations of light shifts of the 6snd J=2 levels based on this analysis require \ensuremath{\beta} be modified from previous assignments based on hfs measurements for n in the vicinity of the 5d7d 1{\mathrm{}}^{1}1D2{D}_{2}D2​ perturber.
The diamagnetic and Stark shifts of strongly perturbed Rydberg spectra such as those of the alkaline earths are expressed in terms of multichannel---quantum-defect parameters. The theory is applicable when the shifts produced by the external fields are smaller than the neighboring Rydberg separations. It is applied to evaluate the diamagnetic shifts in Ba, an atom in which Rydberg and doubly excited channels are strongly mixed. In such complex spectra, the diamagnetic effect can serve a useful purpose as a tool to disentangle the interacting series. The radial sizes and, therefore, the diamagnetic shifts are quite different for singly and doubly excited states even when they are at the same energy. In fact, for the field strengths considered ($\ensuremath{\simeq}40$ kG), the diamagnetic contribution of the doubly excited configuration is quite negligible. As a result, the observed shift is a direct measure of the amount of singly excited configuration in the state of interest. Exactly similar conclusions apply to Stark shifts. The last part of this paper considers states of very high excitation further up in the spectrum which are no longer in a perturbative regime. Spectra of atoms in a magnetic field have shown equally spaced resonances near the ionization threshold with characteristic spacings. By the consideration of the effects of electric fields which are also often simultaneously present, a criterion is established for the nature of these spacings depending on the relative strengths of the crossed electric and magnetic fields. The spacing seen in any particular experiment is shown to depend on the mass and quantum defect of the atom, the strengths of the external fields, and experimental conditions such as the temperature of the atomic vapor whose absorption spectrum is being studied.
The 877.5-nm electric-field-induced quench radiation on a thermal beam of Ba atoms in the metastable 6s5d 1^{1}1D2{\mathit{D}}_{2}D2​ state for transition to the 5s2{\mathit{s}}^{2}s2 1^{1}1S0{\mathit{S}}_{0}S0​ ground state has been measured at the 3% precision level. The Stark-enhanced dipole radiation yields a simple relationship between the field-free-decay rates for transitions between the metastable 1^{1}1D2{\mathit{D}}_{2}D2​ state and the nearby states that are mixed in by the field. Using the known decay rates, we obtain a decay rate of A(6s6p 3^{3}3P1{\mathit{P}}_{1}P1​--6s5d 1^{1}1D2{\mathit{D}}_{2}D2​)\ensuremath{\sim}7\ifmmode\times\else\texttimes\fi{}103{10}^{3}103 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$.