Van der Waals Interactions among Alkali Rydberg Atoms with Excitonic States

Zoubi, H.

Published Jan 1, 2015• 2 citations

Abstract

We investigate the influence of the appearance of excitonic states on van der Waals interactions among two Rydberg atoms. The atoms are assumed to be in different Rydberg states, e.g., in the $|ns\\rangle$ and $|np\\rangle$ states. The resonant dipole-dipole interactions yield symmetric and antisymmetric excitons, with energy splitting that give rise to new resonances as the atoms approach each other. Only far from these resonances the van der Waals coefficients, $C_6^{sp}$, can be defined. We calculate the $C_6$ coefficients for alkali atoms and present the results for lithium by applying perturbation theory. At short interatomic distances of several $\\mu m$, we show that the widely used simple model of two-level systems for excitons in Rydberg atoms breaks down, and the correct representation implies multi-level atoms. Even though, at larger distances one can keep the two-level systems but in including van der Waals interactions among the atoms.

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Van der Waals interactions among alkali Rydberg atoms with excitonic states

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Energy of van der Waals and dipole-dipole interactions between atoms in Rydberg states

Aleksandr A. Kamenski, Nikolai L. Manakov, Sergey N. Mokhnenko +1 more

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Resonance dispersion interaction of alkali metal atoms in Rydberg states

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Van der Waals Interaction of Alkaline Earth Atoms in Singlet Rydberg States

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Bulletin of the Lebedev Physics InstituteDec 1, 20251 citation

C6 coefficients for interacting Rydberg atoms and alkali-metal dimers

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arXiv:1912.01568Physical Review AMar 23, 20206 citations

van der Waals interaction in excited alkali-metal dimers

Mladen Movre, Robert Beuc

Physical Review AMay 1, 198530 citations

Van der Waals Interactions among Alkali Rydberg Atoms with Excitonic States

Zoubi, H.

Published Jan 1, 2015• 2 citations

OpenAlex

Abstract

We investigate the influence of the appearance of excitonic states on van der Waals interactions among two Rydberg atoms. The atoms are assumed to be in different Rydberg states, e.g., in the

|ns\\rangle

and

|np\\rangle

states. The resonant dipole-dipole interactions yield symmetric and antisymmetric excitons, with energy splitting that give rise to new resonances as the atoms approach each other. Only far from these resonances the van der Waals coefficients,

C_6^{sp}

, can be defined. We calculate the

C_6

coefficients for alkali atoms and present the results for lithium by applying perturbation theory. At short interatomic distances of several

\\mu m

, we show that the widely used simple model of two-level systems for excitons in Rydberg atoms breaks down, and the correct representation implies multi-level atoms. Even though, at larger distances one can keep the two-level systems but in including van der Waals interactions among the atoms.

Related papers

Van der Waals interactions among alkali Rydberg atoms with excitonic states

Hashem Zoubi

Abstract We investigate the influence of the appearance of excitonic states on van der Waals interactions among two Rydberg atoms. The atoms are assumed to be in different Rydberg states, e.g., in the and states. The resonant dipole-dipole interactions yield symmetric and antisymmetric excitons, with energy splitting that give rise to new resonances as the atoms approach each other. Only away from these resonances can the van der Waals coefficients, C 6 sp , be defined. We calculate the C 6 coefficients for alkali atoms and present the results for lithium by applying perturbation theory. At short interatomic distances of several , we show that the widely used simple model of two-level systems for excitons in Rydberg atoms breaks down, and the correct representation implies multi-level atoms. Even though, at larger distances one can keep the two-level systems but in including van der Waals interactions among the atoms .Abstract We investigate the influence of the appearance of excitonic states on van der Waals interactions among two Rydberg atoms. The atoms are assumed to be in different Rydberg states, e.g., in the and states. The resonant dipole-dipole interactions yield symmetric and antisymmetric excitons, with energy splitting that give rise to new resonances as the atoms approach each other. Only away from these resonances can the van der Waals coefficients, C 6 sp , be defined. We calculate the C 6 coefficients for alkali atoms and present the results for lithium by applying perturbation theory. At short interatomic distances of several , we show that the widely used simple model of two-level systems for excitons in Rydberg atoms breaks down, and the correct representation implies multi-level atoms. Even though, at larger distances one can keep the two-level systems but in including van der Waals interactions among the atoms .

arXiv:1507.04114Journal of Physics B Atomic Molecular and Optical PhysicsAug 11, 20156 citations

Energy of van der Waals and dipole-dipole interactions between atoms in Rydberg states

Aleksandr A. Kamenski, Nikolai L. Manakov, Sergey N. Mokhnenko +1 more

The van der Waals coefficient ${C}_{6}(\ensuremath{\theta};nlJM)$ of two like Rydberg atoms in their identical Rydberg states $|nlJM\ensuremath{\rangle}$ is resolved into four irreducible components called scalar ${R}_{ss}$ , axial (vector) ${R}_{aa}$ , scalar-tensor ${R}_{sT}={R}_{Ts}$ , and tensor-tensor ${R}_{TT}$ parts in analogy with the components of dipole polarizabilities. The irreducible components determine the dependence of ${C}_{6}(\ensuremath{\theta};nlJM)$ on the angle $\ensuremath{\theta}$ between the interatomic and the quantization axes of atoms. The spectral resolution for the biatomic Green's function with account of the most contributing terms is used for evaluating the components ${R}_{\ensuremath{\alpha}\ensuremath{\beta}}$ of atoms in their Rydberg series of doublet states of the low angular momenta ( $^{2}S, ^{2}P, ^{2}D, ^{2}F$ ). The polynomial presentations in powers of the Rydberg-state principal quantum number $n$ taking into account the asymptotic dependence ${C}_{6}(\ensuremath{\theta};nlJM)\ensuremath{\propto}{n}^{11}$ are derived for simplified evaluations of irreducible components. Numerical values of the polynomial coefficients are determined for Rb atoms in their $n{\phantom{\rule{0.222222em}{0ex}}}^{2}{S}_{1/2}, n{\phantom{\rule{0.222222em}{0ex}}}^{2}{P}_{1/2,3/2}, n{\phantom{\rule{0.222222em}{0ex}}}^{2}{D}_{3/2,5/2}$ , and $n{\phantom{\rule{0.222222em}{0ex}}}^{2}{F}_{5/2,7/2}$ Rydberg states of arbitrary high $n$ . The transformation of the van der Waals interaction law $\ensuremath{-}{C}_{6}/{R}^{6}$ into the dipole-dipole law ${C}_{3}/{R}^{3}$ in the case of close dipole-connected two-atomic states (the F\"orster resonance) is considered and the dependencies on the magnetic quantum numbers $M$ and on the angle $\ensuremath{\theta}$ of the constant ${C}_{3}(\ensuremath{\theta};nlJM)$ are determined together with the ranges of interatomic distances $R$ , where the transformation appears.The van der Waals coefficient ${C}_{6}(\ensuremath{\theta};nlJM)$ of two like Rydberg atoms in their identical Rydberg states $|nlJM\ensuremath{\rangle}$ is resolved into four irreducible components called scalar ${R}_{ss}$, axial (vector) ${R}_{aa}$, scalar-tensor ${R}_{sT}={R}_{Ts}$, and tensor-tensor ${R}_{TT}$ parts in analogy with the components of dipole polarizabilities. The irreducible components determine the dependence of ${C}_{6}(\ensuremath{\theta};nlJM)$ on the angle $\ensuremath{\theta}$ between the interatomic and the quantization axes of atoms. The spectral resolution for the biatomic Green's function with account of the most contributing terms is used for evaluating the components ${R}_{\ensuremath{\alpha}\ensuremath{\beta}}$ of atoms in their Rydberg series of doublet states of the low angular momenta ($^{2}S, ^{2}P, ^{2}D, ^{2}F$). The polynomial presentations in powers of the Rydberg-state principal quantum number $n$ taking into account the asymptotic dependence ${C}_{6}(\ensuremath{\theta};nlJM)\ensuremath{\propto}{n}^{11}$ are derived for simplified evaluations of irreducible components. Numerical values of the polynomial coefficients are determined for Rb atoms in their $n{\phantom{\rule{0.222222em}{0ex}}}^{2}{S}_{1/2}, n{\phantom{\rule{0.222222em}{0ex}}}^{2}{P}_{1/2,3/2}, n{\phantom{\rule{0.222222em}{0ex}}}^{2}{D}_{3/2,5/2}$, and $n{\phantom{\rule{0.222222em}{0ex}}}^{2}{F}_{5/2,7/2}$ Rydberg states of arbitrary high $n$. The transformation of the van der Waals interaction law $\ensuremath{-}{C}_{6}/{R}^{6}$ into the dipole-dipole law ${C}_{3}/{R}^{3}$ in the case of close dipole-connected two-atomic states (the F\"orster resonance) is considered and the dependencies on the magnetic quantum numbers $M$ and on the angle $\ensuremath{\theta}$ of the constant ${C}_{3}(\ensuremath{\theta};nlJM)$ are determined together with the ranges of interatomic distances $R$, where the transformation appears.

Physical Review ASep 21, 201713 citations

Resonance dispersion interaction of alkali metal atoms in Rydberg states

Aleksandr A. Kamenski, Sergey N. Mokhnenko, V. D. Ovsyannikov

With the use of second-order perturbation theory in the long-range interatomic interaction for the degenerate states of two Rydberg atoms we have obtained a general formula for the dependence of atomic interaction energy on the interatomic distance R in the presence of the Förster resonance. Inside of the ‘Förster sphere’ ( R < R F ) this dependence transforms to the formula for electric dipole interaction energy Δ E d − d = C 3 / R 3 and for R > R F it transforms to the formula for the van der Waals interaction energy Δ E VdW = − C 6 / R 6 . The van der Waals constant C 6 is represented as an expansion in terms of irreducible components which define the dependence on the interatomic axis orientation relative to the quantisation axis of projections M of the total angular momentum J . The numerical values of the irreducible components of tensor C 6 were calculated for rubidium atoms in the same Rydberg states | nlJM 〉 with large quantum numbers n . We present the calculated resonance interaction energy of two rubidium atoms in the states |43D 5/2 M 〉, whose total energy exceeds by only 8 MHz the total energy of one of the atoms in the state |45P 3/2 M 〉 and of the other in the state |41F 7/2 M 〉.With the use of second-order perturbation theory in the long-range interatomic interaction for the degenerate states of two Rydberg atoms we have obtained a general formula for the dependence of atomic interaction energy on the interatomic distance R in the presence of the Förster resonance. Inside of the ‘Förster sphere’ ( R < R F ) this dependence transforms to the formula for electric dipole interaction energy Δ E d − d = C 3 / R 3 and for R > R F it transforms to the formula for the van der Waals interaction energy Δ E VdW = − C 6 / R 6 . The van der Waals constant C 6 is represented as an expansion in terms of irreducible components which define the dependence on the interatomic axis orientation relative to the quantisation axis of projections M of the total angular momentum J . The numerical values of the irreducible components of tensor C 6 were calculated for rubidium atoms in the same Rydberg states | nlJM 〉 with large quantum numbers n . We present the calculated resonance interaction energy of two rubidium atoms in the states |43D 5/2 M 〉, whose total energy exceeds by only 8 MHz the total energy of one of the atoms in the state |45P 3/2 M 〉 and of the other in the state |41F 7/2 M 〉.

Quantum ElectronicsMay 9, 20171 citation

Van der Waals Interaction of Alkaline Earth Atoms in Singlet Rydberg States

Igor L. Glukhov, Aleksandr A. Kamenski, A. S. Kornev +3 more

Abstract The numerical values of the van der Waals interaction constant C6 are determined between alkaline earth atoms in singlet Rydberg |n1S0〉 states with large principal quantum numbers, n > 20. The results of calculations using the semiempirical quantum defect theory (QDT) method are approximated by quadratic polynomials. The polynomial coefficients are tabulated and can be used for simplified quantitative estimates of interatomic interaction-induced energy shifts, determination of the Rydberg state excitation blockade radius, and limitations on the wavelengths of radiation forming Rydberg lattices for group IIA atoms. The numerical values of the contributions of various diatomic states to the constant C6 are calculated. States providing the main contribution, analogous to that of the Förster resonance, are identified.Abstract The numerical values of the van der Waals interaction constant C6 are determined between alkaline earth atoms in singlet Rydberg |n1S0〉 states with large principal quantum numbers, n > 20. The results of calculations using the semiempirical quantum defect theory (QDT) method are approximated by quadratic polynomials. The polynomial coefficients are tabulated and can be used for simplified quantitative estimates of interatomic interaction-induced energy shifts, determination of the Rydberg state excitation blockade radius, and limitations on the wavelengths of radiation forming Rydberg lattices for group IIA atoms. The numerical values of the contributions of various diatomic states to the constant C6 are calculated. States providing the main contribution, analogous to that of the Förster resonance, are identified.

Bulletin of the Lebedev Physics InstituteDec 1, 20251 citation

C6 coefficients for interacting Rydberg atoms and alkali-metal dimers

V. C. Olaya-Agudelo, Jesús Pérez‐Ríos, Felipe Herrera

We study the van der Waals interaction between Rydberg alkali-metal atoms with fine structure ( ${n}^{2}{L}_{j}$ ; $L\ensuremath{\le}2$) and heteronuclear alkali-metal dimers in the ground rovibrational state ($X^{1}\mathrm{\ensuremath{\Sigma}}^{+}$; $v=0, J=0$ ). We compute the associated ${C}_{6}$ dispersion coefficients of atom-molecule pairs involving $^{133}\mathrm{Cs}$ and $^{85}\mathrm{Rb}$ atoms interacting with KRb, LiCs, LiRb, and RbCs molecules. The obtained dispersion coefficients can be accurately fitted to a state-dependent polynomial $O({n}^{7})$ over the range of principal quantum numbers $40\ensuremath{\le}n\ensuremath{\le}150$. For all atom-molecule pairs considered, Rydberg states $n^{2}S_{j}$ and $n^{2}P_{j}$ result in attractive $1/{R}^{6}$ potentials. In contrast, $n^{2}D_{j}$ states can give rise to repulsive potentials for specific atom-molecule pairs. The interaction energy at the LeRoy distance approximately scales as ${n}^{\ensuremath{-}5}$ for $n>40$ . For intermediate values of $n\ensuremath{\lesssim}40$, both repulsive and attractive interaction energies of the order of 10--$1000\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ can be achieved with specific atomic and molecular species. The accuracy of the reported ${C}_{6}$ coefficients is limited by the quality of the atomic quantum defects, with relative errors $\mathrm{\ensuremath{\Delta}}{C}_{6}/{C}_{6}$ estimated to be no greater than 1% on average.We study the van der Waals interaction between Rydberg alkali-metal atoms with fine structure (${n}^{2}{L}_{j}$; $L\ensuremath{\le}2$) and heteronuclear alkali-metal dimers in the ground rovibrational state ($X^{1}\mathrm{\ensuremath{\Sigma}}^{+}$; $v=0, J=0$). We compute the associated ${C}_{6}$ dispersion coefficients of atom-molecule pairs involving $^{133}\mathrm{Cs}$ and $^{85}\mathrm{Rb}$ atoms interacting with KRb, LiCs, LiRb, and RbCs molecules. The obtained dispersion coefficients can be accurately fitted to a state-dependent polynomial $O({n}^{7})$ over the range of principal quantum numbers $40\ensuremath{\le}n\ensuremath{\le}150$. For all atom-molecule pairs considered, Rydberg states $n^{2}S_{j}$ and $n^{2}P_{j}$ result in attractive $1/{R}^{6}$ potentials. In contrast, $n^{2}D_{j}$ states can give rise to repulsive potentials for specific atom-molecule pairs. The interaction energy at the LeRoy distance approximately scales as ${n}^{\ensuremath{-}5}$ for $n>40$. For intermediate values of $n\ensuremath{\lesssim}40$, both repulsive and attractive interaction energies of the order of 10--$1000\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ can be achieved with specific atomic and molecular species. The accuracy of the reported ${C}_{6}$ coefficients is limited by the quality of the atomic quantum defects, with relative errors $\mathrm{\ensuremath{\Delta}}{C}_{6}/{C}_{6}$ estimated to be no greater than 1% on average.

arXiv:1912.01568Physical Review AMar 23, 20206 citations

van der Waals interaction in excited alkali-metal dimers

Mladen Movre, Robert Beuc

We have studied the long-range interaction potentials of the heteronuclear alkali-metal-atom dimers in the case when one of the atoms is in the first excited state ( ${n}_{A}$ P) and the other is in the ground state ( ${n}_{B}$ S). The presentation of the general expressions for the interaction energies in the Hund's case (c) is followed by the calculation of the corresponding ${C}_{6}$ constants for all heteronuclear alkali-metal-atom pairs. In the case of heavier perturbers (Rb and Cs) the ${C}_{6}$ constants are found to be significantly influenced by the perturber's fine structure. The van der Waals interaction in the K-Rb system is exceptionally strong resulting in ${C}_{6}$ constants considerably larger than in all other alkali-metal-atom heteronuclear systems. The intermediate-coupling region (ICR) is defined as the region of internuclear separation R where the interaction energy is of the order of the atomic spin-orbit splitting, while the exchange energy is still negligible. Analysis of the general form of the energy matrices in the ICR shows that the homonuclear alkali-metal-atom dimers can be treated as a special case. In the large-R limit, the ICR results reduce to those obtained in Hund's case (c). As an example, we have calculated the ICR interaction potentials of the K-Rb system, taking into account only the leading dipole-dipole interaction. Finally we have discussed the construction of the absorption coefficient in the wings of the resonance lines, both in the impact and in the quasistatic approximation.We have studied the long-range interaction potentials of the heteronuclear alkali-metal-atom dimers in the case when one of the atoms is in the first excited state (${n}_{A}$P) and the other is in the ground state (${n}_{B}$S). The presentation of the general expressions for the interaction energies in the Hund's case (c) is followed by the calculation of the corresponding ${C}_{6}$ constants for all heteronuclear alkali-metal-atom pairs. In the case of heavier perturbers (Rb and Cs) the ${C}_{6}$ constants are found to be significantly influenced by the perturber's fine structure. The van der Waals interaction in the K-Rb system is exceptionally strong resulting in ${C}_{6}$ constants considerably larger than in all other alkali-metal-atom heteronuclear systems. The intermediate-coupling region (ICR) is defined as the region of internuclear separation R where the interaction energy is of the order of the atomic spin-orbit splitting, while the exchange energy is still negligible. Analysis of the general form of the energy matrices in the ICR shows that the homonuclear alkali-metal-atom dimers can be treated as a special case. In the large-R limit, the ICR results reduce to those obtained in Hund's case (c). As an example, we have calculated the ICR interaction potentials of the K-Rb system, taking into account only the leading dipole-dipole interaction. Finally we have discussed the construction of the absorption coefficient in the wings of the resonance lines, both in the impact and in the quasistatic approximation.

Physical Review AMay 1, 198530 citations

We investigate the influence of the appearance of excitonic states on van der Waals interactions among two Rydberg atoms. The atoms are assumed to be in different Rydberg states, e.g., in the

|ns\\rangle

and

|np\\rangle

C_6^{sp}

, can be defined. We calculate the

C_6

coefficients for alkali atoms and present the results for lithium by applying perturbation theory. At short interatomic distances of several

\\mu m

{R}_{ss}

, axial (vector)

{R}_{aa}

, scalar-tensor

{R}_{sT}={R}_{Ts}

, and tensor-tensor

{R}_{TT}

parts in analogy with the components of dipole polarizabilities. The irreducible components determine the dependence of ${C}_{6}(\ensuremath{\theta};nlJM)$ on the angle $\ensuremath{\theta}$ between the interatomic and the quantization axes of atoms. The spectral resolution for the biatomic Green's function with account of the most contributing terms is used for evaluating the components ${R}_{\ensuremath{\alpha}\ensuremath{\beta}}$ of atoms in their Rydberg series of doublet states of the low angular momenta (

^{2}S, ^{2}P, ^{2}D, ^{2}F

). The polynomial presentations in powers of the Rydberg-state principal quantum number

n

taking into account the asymptotic dependence ${C}_{6}(\ensuremath{\theta};nlJM)\ensuremath{\propto}{n}^{11}$ are derived for simplified evaluations of irreducible components. Numerical values of the polynomial coefficients are determined for Rb atoms in their

n{\phantom{\rule{0.222222em}{0ex}}}^{2}{S}_{1/2}, n{\phantom{\rule{0.222222em}{0ex}}}^{2}{P}_{1/2,3/2}, n{\phantom{\rule{0.222222em}{0ex}}}^{2}{D}_{3/2,5/2}

, and

n{\phantom{\rule{0.222222em}{0ex}}}^{2}{F}_{5/2,7/2}

Rydberg states of arbitrary high

n

. The transformation of the van der Waals interaction law $\ensuremath{-}{C}_{6}/{R}^{6}$ into the dipole-dipole law

{C}_{3}/{R}^{3}

in the case of close dipole-connected two-atomic states (the F\"orster resonance) is considered and the dependencies on the magnetic quantum numbers

M

and on the angle $\ensuremath{\theta}$ of the constant ${C}_{3}(\ensuremath{\theta};nlJM)$ are determined together with the ranges of interatomic distances

R

, where the transformation appears.

We study the van der Waals interaction between Rydberg alkali-metal atoms with fine structure (

{n}^{2}{L}_{j}

; $L\ensuremath{\le}2$) and heteronuclear alkali-metal dimers in the ground rovibrational state ($X^{1}\mathrm{\ensuremath{\Sigma}}^{+}$;

v=0, J=0

). We compute the associated

{C}_{6}

dispersion coefficients of atom-molecule pairs involving

^{133}\mathrm{Cs}

and

^{85}\mathrm{Rb}

atoms interacting with KRb, LiCs, LiRb, and RbCs molecules. The obtained dispersion coefficients can be accurately fitted to a state-dependent polynomial

O({n}^{7})

over the range of principal quantum numbers $40\ensuremath{\le}n\ensuremath{\le}150$. For all atom-molecule pairs considered, Rydberg states

n^{2}S_{j}

and

n^{2}P_{j}

result in attractive

1/{R}^{6}

potentials. In contrast,

n^{2}D_{j}

states can give rise to repulsive potentials for specific atom-molecule pairs. The interaction energy at the LeRoy distance approximately scales as ${n}^{\ensuremath{-}5}$ for

n>40

. For intermediate values of $n\ensuremath{\lesssim}40$, both repulsive and attractive interaction energies of the order of 10--$1000\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ can be achieved with specific atomic and molecular species. The accuracy of the reported

{C}_{6}

coefficients is limited by the quality of the atomic quantum defects, with relative errors $\mathrm{\ensuremath{\Delta}}{C}_{6}/{C}_{6}$ estimated to be no greater than 1% on average.

We have studied the long-range interaction potentials of the heteronuclear alkali-metal-atom dimers in the case when one of the atoms is in the first excited state (

{n}_{A}

P) and the other is in the ground state (

{n}_{B}

S). The presentation of the general expressions for the interaction energies in the Hund's case (c) is followed by the calculation of the corresponding

{C}_{6}

constants for all heteronuclear alkali-metal-atom pairs. In the case of heavier perturbers (Rb and Cs) the

{C}_{6}

constants are found to be significantly influenced by the perturber's fine structure. The van der Waals interaction in the K-Rb system is exceptionally strong resulting in

{C}_{6}

constants considerably larger than in all other alkali-metal-atom heteronuclear systems. The intermediate-coupling region (ICR) is defined as the region of internuclear separation R where the interaction energy is of the order of the atomic spin-orbit splitting, while the exchange energy is still negligible. Analysis of the general form of the energy matrices in the ICR shows that the homonuclear alkali-metal-atom dimers can be treated as a special case. In the large-R limit, the ICR results reduce to those obtained in Hund's case (c). As an example, we have calculated the ICR interaction potentials of the K-Rb system, taking into account only the leading dipole-dipole interaction. Finally we have discussed the construction of the absorption coefficient in the wings of the resonance lines, both in the impact and in the quasistatic approximation.