The single-configuration, Hartree-Fock-term energy separations of the 2snd ${\mathrm{}}^{1}$ D and $^{3}\mathrm{D}$ Rydberg states in berylliumlike fluorine agree remarkably well with the observed separations. It is shown that, in the $^{1}\mathrm{D}$ series, interaction with 2 ${p}^{2}$ raises the energy of the 2snd levels whereas the remaining interactions lower the levels. The combined effect is such that the $^{1}\mathrm{\ensuremath{-}}^{3}$D separation remains essentially unchanged when correlation effects are added.The single-configuration, Hartree-Fock-term energy separations of the 2snd ${\mathrm{}}^{1}$D and $^{3}\mathrm{D}$ Rydberg states in berylliumlike fluorine agree remarkably well with the observed separations. It is shown that, in the $^{1}\mathrm{D}$ series, interaction with 2${p}^{2}$ raises the energy of the 2snd levels whereas the remaining interactions lower the levels. The combined effect is such that the $^{1}\mathrm{\ensuremath{-}}^{3}$D separation remains essentially unchanged when correlation effects are added.

Physical Review ANov 1, 19860 citations

Atomic Energy Levels

Francis F. Chen, Jane P. Chang

Springer eBooksJan 1, 20031 citation

Atomic clocks highly sensitive to the variation of the fine-structure constant based on Hf ii, Hf iv, and W vi ions

Saleh O. Allehabi, V. A. Dzuba, V. V. Flambaum

We demonstrate that several metastable excited states in Hf ii, Hf iv, and W vi ions may be good clock states since they are sufficiently long-living and are not sensitive to the perturbations. The cooling electric dipole ( $E1$ ) transition is available for Hf ii, while sympathetic cooling is possible for Hf iv and W vi using ${\mathrm{Ca}}^{+}$ or ${\mathrm{Sr}}^{+}$ ions. Energy levels; Land\'e $g$ factors; transition amplitudes for electric dipole ( $E1$ ), electric quadrupole ( $E2$ ), and magnetic dipole ( $M1$ ) transitions; lifetimes; and electric quadrupole moments for Hf ii, Hf iv, and W vi ions are investigated using a combination of several methods of relativistic many-body calculations including the configuration interaction (CI), linearized coupled-cluster single-doubles (SD), and many-body perturbation theory ( $\mathrm{CI}+\mathrm{SD}$ ), and also the configuration interaction with perturbation theory (CIPT). Scalar polarizabilities of the ground states and the clock states have been calculated to determine the blackbody radiation (BBR) shifts. We have found that the relative BBR shifts for these transitions range between ${10}^{\ensuremath{-}16}$ and ${10}^{\ensuremath{-}18}$. A linear combination of two clock transition frequencies allows one to further suppress BBR. Several $5d\text{\ensuremath{-}}6s$ single-electron clock transitions ensure high sensitivity of the transition frequencies to the variation of the fine-structure constant $\ensuremath{\alpha}$ and may be used to search for dark matter producing this variation of $\ensuremath{\alpha}$. The enhancement coefficient for the $\ensuremath{\alpha}$ variation reaches $K=8.3$ . Six stable isotopes of Hf and five stable isotopes in W allow one to make King plots and study its nonlinearities in order to put limits on the new interactions mediated by scalar particles or other mechanisms.We demonstrate that several metastable excited states in Hf ii, Hf iv, and W vi ions may be good clock states since they are sufficiently long-living and are not sensitive to the perturbations. The cooling electric dipole ($E1$) transition is available for Hf ii, while sympathetic cooling is possible for Hf iv and W vi using ${\mathrm{Ca}}^{+}$ or ${\mathrm{Sr}}^{+}$ ions. Energy levels; Land\'e $g$ factors; transition amplitudes for electric dipole ($E1$), electric quadrupole ($E2$), and magnetic dipole ($M1$) transitions; lifetimes; and electric quadrupole moments for Hf ii, Hf iv, and W vi ions are investigated using a combination of several methods of relativistic many-body calculations including the configuration interaction (CI), linearized coupled-cluster single-doubles (SD), and many-body perturbation theory ($\mathrm{CI}+\mathrm{SD}$), and also the configuration interaction with perturbation theory (CIPT). Scalar polarizabilities of the ground states and the clock states have been calculated to determine the blackbody radiation (BBR) shifts. We have found that the relative BBR shifts for these transitions range between ${10}^{\ensuremath{-}16}$ and ${10}^{\ensuremath{-}18}$. A linear combination of two clock transition frequencies allows one to further suppress BBR. Several $5d\text{\ensuremath{-}}6s$ single-electron clock transitions ensure high sensitivity of the transition frequencies to the variation of the fine-structure constant $\ensuremath{\alpha}$ and may be used to search for dark matter producing this variation of $\ensuremath{\alpha}$. The enhancement coefficient for the $\ensuremath{\alpha}$ variation reaches $K=8.3$. Six stable isotopes of Hf and five stable isotopes in W allow one to make King plots and study its nonlinearities in order to put limits on the new interactions mediated by scalar particles or other mechanisms.

arXiv:2206.14026Physical Review ASep 16, 202213 citations

Correlated Superposition States in Two-Atom Systems

Z. Ficek, R. Tanaś

Schemes proposed for the preparation of two two-level atoms in an entangled state are reviewed. The authors begin Section II with a derivation of the master equation for two nonidentical two-level atoms interacting with the quantized three-dimensional vacuum field and driven by a single-mode coherent laser field. Sections III and IV are concerned mainly with techniques proposed for the preparation of a two-atom system in entangled states. The cases of maximally and nonmaximally entangled states are discussed. Methods of detecting a particular entangled state are discussed in Section V and preparation of a two-atom system in two-photon entangled states is described in Section VI. A method of mapping of the entanglement of light on atoms is also presented.Schemes proposed for the preparation of two two-level atoms in an entangled state are reviewed. The authors begin Section II with a derivation of the master equation for two nonidentical two-level atoms interacting with the quantized three-dimensional vacuum field and driven by a single-mode coherent laser field. Sections III and IV are concerned mainly with techniques proposed for the preparation of a two-atom system in entangled states. The cases of maximally and nonmaximally entangled states are discussed. Methods of detecting a particular entangled state are discussed in Section V and preparation of a two-atom system in two-photon entangled states is described in Section VI. A method of mapping of the entanglement of light on atoms is also presented.

John Wiley & Sons, Inc. eBooksApr 2, 20031 citation

Atomic Physics

Theoretical and mathematical physicsNov 29, 20080 citations

The single-configuration, Hartree-Fock-term energy separations of the 2snd

{\mathrm{}}^{1}

D and

^{3}\mathrm{D}

Rydberg states in berylliumlike fluorine agree remarkably well with the observed separations. It is shown that, in the

^{1}\mathrm{D}

series, interaction with 2

{p}^{2}

raises the energy of the 2snd levels whereas the remaining interactions lower the levels. The combined effect is such that the $^{1}\mathrm{\ensuremath{-}}^{3}$D separation remains essentially unchanged when correlation effects are added.

E1

) transition is available for Hf ii, while sympathetic cooling is possible for Hf iv and W vi using

{\mathrm{Ca}}^{+}

{\mathrm{Sr}}^{+}

ions. Energy levels; Land\'e

g

factors; transition amplitudes for electric dipole (

E1

), electric quadrupole (

E2

), and magnetic dipole (

M1

) transitions; lifetimes; and electric quadrupole moments for Hf ii, Hf iv, and W vi ions are investigated using a combination of several methods of relativistic many-body calculations including the configuration interaction (CI), linearized coupled-cluster single-doubles (SD), and many-body perturbation theory (

\mathrm{CI}+\mathrm{SD}

), and also the configuration interaction with perturbation theory (CIPT). Scalar polarizabilities of the ground states and the clock states have been calculated to determine the blackbody radiation (BBR) shifts. We have found that the relative BBR shifts for these transitions range between ${10}^{\ensuremath{-}16}$ and ${10}^{\ensuremath{-}18}$. A linear combination of two clock transition frequencies allows one to further suppress BBR. Several $5d\text{\ensuremath{-}}6s$ single-electron clock transitions ensure high sensitivity of the transition frequencies to the variation of the fine-structure constant $\ensuremath{\alpha}$ and may be used to search for dark matter producing this variation of $\ensuremath{\alpha}$. The enhancement coefficient for the $\ensuremath{\alpha}$ variation reaches

K=8.3

. Six stable isotopes of Hf and five stable isotopes in W allow one to make King plots and study its nonlinearities in order to put limits on the new interactions mediated by scalar particles or other mechanisms.