Long-range Rydberg–Rydberg interactions in calcium, strontium and ytterbium

Abstract Long-range dipole–dipole and quadrupole–quadrupole interactions between pairs of Rydberg atoms are calculated perturbatively for calcium, strontium and ytterbium within the Coulomb approximation. Quantum defects, obtained by fitting existing laser spectroscopic data, are provided for all S, P, D and F series of strontium and for the 3P2 series of calcium. The results show qualitative differences with the alkali metal atoms, including isotropically attractive interactions of the strontium 1S0 states and a greater rarity of Förster resonances. Only two such resonances are identified, both in triplet series of strontium. The angular dependence of the long-range interaction is briefly discussed.Abstract Long-range dipole–dipole and quadrupole–quadrupole interactions between pairs of Rydberg atoms are calculated perturbatively for calcium, strontium and ytterbium within the Coulomb approximation. Quantum defects, obtained by fitting existing laser spectroscopic data, are provided for all S, P, D and F series of strontium and for the 3P2 series of calcium. The results show qualitative differences with the alkali metal atoms, including isotropically attractive interactions of the strontium 1S0 states and a greater rarity of Förster resonances. Only two such resonances are identified, both in triplet series of strontium. The angular dependence of the long-range interaction is briefly discussed.

arXiv:1203.3736Journal of Physics B Atomic Molecular and Optical PhysicsJun 7, 201274 citations

Long-range interactions in one- and two-electron Rydberg atoms

Christophe L. Vaillant

We present calculations of long-range interactions in Rydberg atoms, with a focus on the dipole-dipole interactions of strontium Rydberg states. The growing use of Rydberg states in the field of cold atoms necessitates a more detailed understanding of the effects of dipole-dipole interactions, which are currently being investigated in a number of research groups worldwide. Calculations of long-range interactions in Rydberg states of caesium, cal- cium, rubidium, strontium and ytterbium are presented. By taking the one active electron approximation we develop consistent models of these long- range interactions, and construct a survey of the Rydberg state dipole-dipole interactions and quadrupole-quadrupole interactions. We compare the inter- actions between series and between atoms, highlighting the importance of certain series for applications suggested in previous works. In order to include two-electron effects in the description of dipole-dipole interactions in divalent atoms, we use multichannel quantum defect theory (MQDT) to develop models of the Rydberg series of strontium. We use an empirical reactance matrix formalism, where the reactance matrix is fitted to reproduce experimentally measured values of the bound state energy levels. Models are found for all series of strontium with L ≤ 3. We extend the MQDT formalism to the description of the natural radiative lifetimes of strontium, where the perturbers are found to have a large quenching effect on these lifetimes. By incorporating the MQDT description of the Rydberg states of strontium into the calculation of dipole-dipole interactions, we find a spin-forbidden two-atom resonance in the 3D2 states of strontium. We consider a one- dimensional lattice of strontium atoms, and find that the internal dynamics of the Rydberg atoms demonstrates spin transport for large lattice spacings and a separation of the spin and total angular momentum dynamics for small lattice spacings. Spin-angular momentum separation (analogous to spin-charge separation in condensed matter) in strontium Rydberg atoms may have uses in the investigation of one-dimensional Fermi gases and their description using Luttinger liquid theory.We present calculations of long-range interactions in Rydberg atoms, with a focus on the dipole-dipole interactions of strontium Rydberg states. The growing use of Rydberg states in the field of cold atoms necessitates a more detailed understanding of the effects of dipole-dipole interactions, which are currently being investigated in a number of research groups worldwide. Calculations of long-range interactions in Rydberg states of caesium, cal- cium, rubidium, strontium and ytterbium are presented. By taking the one active electron approximation we develop consistent models of these long- range interactions, and construct a survey of the Rydberg state dipole-dipole interactions and quadrupole-quadrupole interactions. We compare the inter- actions between series and between atoms, highlighting the importance of certain series for applications suggested in previous works. In order to include two-electron effects in the description of dipole-dipole interactions in divalent atoms, we use multichannel quantum defect theory (MQDT) to develop models of the Rydberg series of strontium. We use an empirical reactance matrix formalism, where the reactance matrix is fitted to reproduce experimentally measured values of the bound state energy levels. Models are found for all series of strontium with L ≤ 3. We extend the MQDT formalism to the description of the natural radiative lifetimes of strontium, where the perturbers are found to have a large quenching effect on these lifetimes. By incorporating the MQDT description of the Rydberg states of strontium into the calculation of dipole-dipole interactions, we find a spin-forbidden two-atom resonance in the 3D2 states of strontium. We consider a one- dimensional lattice of strontium atoms, and find that the internal dynamics of the Rydberg atoms demonstrates spin transport for large lattice spacings and a separation of the spin and total angular momentum dynamics for small lattice spacings. Spin-angular momentum separation (analogous to spin-charge separation in condensed matter) in strontium Rydberg atoms may have uses in the investigation of one-dimensional Fermi gases and their description using Luttinger liquid theory.

Jan 1, 20144 citations

Tuning long-range interactions in Sr Rydberg atoms: the effect of series perturbations

Türker Topçu, Andrei Derevianko

We investigate the effect of series perturbation on the second-order dipole-dipole interactions between strontium atoms in the $5sns({^1}S_0)$ and $5snp({^1}P_1)$ Rydberg states as a means of engineering long-range interactions between atoms. The series perturbation in these atoms enables modifying the strength and the sign of the interaction by varying the principal quantum number $n$ of the Rydberg electron. We utilize experimentally available data to estimate the importance of perturber states, and find that van der Waals interaction between two strontium atoms in the $5snp({^1}P_1)$ states shows strong peaks outside the anticipated hydrogenic $n^{11}$ scaling. We identify this to be the result of the perturbation of $5snd({^1}D_2)$ intermediate states by the $4d^2({^1}D_2)$ and $4dn's({^1}D_2)$ states in the $n<20$ range. This demonstrates that divalent atoms offer a unique advantage for generating substantially stronger or weaker inter-atomic interactions than those that can be achieved using alkali metal atoms. This is due to the highly perturbed spectra of divalent atoms and other multivalent atoms that can persist up to high $n$ . Such irregularities can be especially useful in engineering asymmetric Ry blockade requiring the simultaneous presence of both ``weak'' and ``strong'' interactions.We investigate the effect of series perturbation on the second-order dipole-dipole interactions between strontium atoms in the $5sns({^1}S_0)$ and $5snp({^1}P_1)$ Rydberg states as a means of engineering long-range interactions between atoms. The series perturbation in these atoms enables modifying the strength and the sign of the interaction by varying the principal quantum number $n$ of the Rydberg electron. We utilize experimentally available data to estimate the importance of perturber states, and find that van der Waals interaction between two strontium atoms in the $5snp({^1}P_1)$ states shows strong peaks outside the anticipated hydrogenic $n^{11}$ scaling. We identify this to be the result of the perturbation of $5snd({^1}D_2)$ intermediate states by the $4d^2({^1}D_2)$ and $4dn's({^1}D_2)$ states in the $n<20$ range. This demonstrates that divalent atoms offer a unique advantage for generating substantially stronger or weaker inter-atomic interactions than those that can be achieved using alkali metal atoms. This is due to the highly perturbed spectra of divalent atoms and other multivalent atoms that can persist up to high $n$. Such irregularities can be especially useful in engineering asymmetric Ry blockade requiring the simultaneous presence of both ``weak'' and ``strong'' interactions.

arXiv:1505.07152May 26, 20151 citation

Calculations of long range interactions for 87 Sr Rydberg states

F. Robicheaux

Abstract A method for calculating the properties of Rydberg states and Rydberg–Rydberg interaction between two 87 Sr atoms is described. The method is based on a multichannel quantum defect theory description of the Rydberg states that accounts for the hyperfine splitting of the 87 Sr + ground state. Results are given for the scalar and tensor polarizabilities and the eigenvalues of the C 6 matrix for the 5 sns F T = 9/2 series. These results illustrate the new features that arise due to the hyperfine splitting of the thresholds. In particular, there should be several couple Förster resonances above n = 50 unlike the case of 88 Sr which has none.Abstract A method for calculating the properties of Rydberg states and Rydberg–Rydberg interaction between two 87 Sr atoms is described. The method is based on a multichannel quantum defect theory description of the Rydberg states that accounts for the hyperfine splitting of the 87 Sr + ground state. Results are given for the scalar and tensor polarizabilities and the eigenvalues of the C 6 matrix for the 5 sns F T = 9/2 series. These results illustrate the new features that arise due to the hyperfine splitting of the thresholds. In particular, there should be several couple Förster resonances above n = 50 unlike the case of 88 Sr which has none.

Journal of Physics B Atomic Molecular and Optical PhysicsOct 8, 201926 citations

Multichannel quantum defect theory of strontium bound Rydberg states

Christophe L. Vaillant, M P A Jones, R. M. Potvliege

Abstract Using the reactance matrix approach, we systematically develop new multichannel quantum defect theory (MQDT) models for the singlet and triplet S, P, D and F states of strontium below the first ionization limit, based on improved energy level measurements. The new models reveal additional insights into the character of doubly excited perturber states, and the improved energy level measurements for certain series allow fine structure to be resolved for those series’ perturbers. Comparison between the predictions of the new models and those of previous empirical and ab initio studies reveals good agreement with most series; however, some discrepancies are highlighted. Using the MQDT wave functions derived from our models we calculate other observables such as Landé -factors and radiative lifetimes. The analysis reveals the impact of perturbers on the Rydberg state properties of divalent atoms, highlighting the importance of including two-electron effects in the calculations of these properties. The work enables future investigations of properties such as Stark maps and long-range interactions of Rydberg states of strontium.Abstract Using the reactance matrix approach, we systematically develop new multichannel quantum defect theory (MQDT) models for the singlet and triplet S, P, D and F states of strontium below the first ionization limit, based on improved energy level measurements. The new models reveal additional insights into the character of doubly excited perturber states, and the improved energy level measurements for certain series allow fine structure to be resolved for those series’ perturbers. Comparison between the predictions of the new models and those of previous empirical and ab initio studies reveals good agreement with most series; however, some discrepancies are highlighted. Using the MQDT wave functions derived from our models we calculate other observables such as Landé -factors and radiative lifetimes. The analysis reveals the impact of perturbers on the Rydberg state properties of divalent atoms, highlighting the importance of including two-electron effects in the calculations of these properties. The work enables future investigations of properties such as Stark maps and long-range interactions of Rydberg states of strontium.

arXiv:1402.5802Journal of Physics B Atomic Molecular and Optical PhysicsJul 15, 201440 citations

Long-range interactions between alkali Rydberg atom pairs correlated to thens–ns,np–np andnd–nd asymptotes

Kilian Singer, Jovica Stanojevic, Matthias Weidemüller +1 more

We have calculated the long-range interaction potential curves of highly excited Rydberg atom pairs for the combinations Li–Li, Na–Na, K–K, Rb–Rb and Cs–Cs in a perturbative approach. The dispersion C -coefficients are determined for all symmetries of molecular states that correlate to the n s– n s, n p– n p and n d– n d asymptotes. Fitted parameters are given for the scaling of the C -coefficients as a function of the principal quantum number n for all homonuclear pairs of alkali metal atoms.We have calculated the long-range interaction potential curves of highly excited Rydberg atom pairs for the combinations Li–Li, Na–Na, K–K, Rb–Rb and Cs–Cs in a perturbative approach. The dispersion C -coefficients are determined for all symmetries of molecular states that correlate to the n s– n s, n p– n p and n d– n d asymptotes. Fitted parameters are given for the scaling of the C -coefficients as a function of the principal quantum number n for all homonuclear pairs of alkali metal atoms.

Journal of Physics B Atomic Molecular and Optical PhysicsJan 6, 2005290 citations

We investigate the effect of series perturbation on the second-order dipole-dipole interactions between strontium atoms in the

5sns({^1}S_0)

and

5snp({^1}P_1)

Rydberg states as a means of engineering long-range interactions between atoms. The series perturbation in these atoms enables modifying the strength and the sign of the interaction by varying the principal quantum number

n

of the Rydberg electron. We utilize experimentally available data to estimate the importance of perturber states, and find that van der Waals interaction between two strontium atoms in the

5snp({^1}P_1)

states shows strong peaks outside the anticipated hydrogenic

n^{11}

scaling. We identify this to be the result of the perturbation of

5snd({^1}D_2)

intermediate states by the

4d^2({^1}D_2)

and

4dn's({^1}D_2)

states in the

n<20

range. This demonstrates that divalent atoms offer a unique advantage for generating substantially stronger or weaker inter-atomic interactions than those that can be achieved using alkali metal atoms. This is due to the highly perturbed spectra of divalent atoms and other multivalent atoms that can persist up to high

n

. Such irregularities can be especially useful in engineering asymmetric Ry blockade requiring the simultaneous presence of both ``weak'' and ``strong'' interactions.