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 〉.
We calculate the interaction strength of the van der Waals force between two Rydberg atoms by applying the applications of quantum information processing using for Rydberg blockade. The alkali metals (Cs and K) in states of principal quantum number n were used to calculate the interaction strength. We use some possible angular momentum channels involving s, p, and d states for measuring interaction strength. The obtained results were then generalized for all angular momentum channels which mostly have small interactions and therefore a poor candidate for blockade experiments. The interaction strength in the atoms of Cs and K dipole matrix elements was calculated first and then relevant energy levels were determined by using the quantum defects theory. The radial wave function was calculated numerically with the integration of the radial Schrodinger equation. Also, the interaction coefficients of van der Waals for various channels were calculated here.
Abstract Förster resonances provide a highly flexible tool to tune both the strength and the angular shape of interactions between two Rydberg atoms. We give a detailed explanation about how Förster resonances can be found by searching through a large range of possible quantum number combinations. We apply our search method to SS , SD and DD pair states of 87 Rb with principal quantum numbers from 30 to 100, taking into account the fine structure splitting of the Rydberg states. We find various strong resonances between atoms with a large difference in principal quantum numbers. We quantify the strength of these resonances by introducing a figure of merit C ˜ 3 which is independent of the magnetic quantum numbers and geometry to classify the resonances by interaction strength. We further predict to what extent excitation exchange is possible on different resonances and point out limitations of the coherent hopping process. Finally, we discuss the angular dependence of the dipole–dipole interaction and its tunability near resonances.
We study the van der Waals interaction between Rydberg alkali-metal atoms with fine structure (
n2Lj; $L\ensuremath{\le}2$) and heteronuclear alkali-metal dimers in the ground rovibrational state ($X^{1}\mathrm{\ensuremath{\Sigma}}^{+}$;
v=0,J=0). We compute the associated
C6 dispersion coefficients of atom-molecule pairs involving
133Cs and
85Rb atoms interacting with KRb, LiCs, LiRb, and RbCs molecules. The obtained dispersion coefficients can be accurately fitted to a state-dependent polynomial
O(n7) over the range of principal quantum numbers $40\ensuremath{\le}n\ensuremath{\le}150$. For all atom-molecule pairs considered, Rydberg states
n2Sj and
n2Pj result in attractive
1/R6 potentials. In contrast,
n2Dj 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
C6 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 review experimental and theoretical tools to excite, study and understand strongly interacting Rydberg gases. The focus lies on the excitation of dense ultracold atomic samples close to, or within quantum degeneracy, high-lying Rydberg states. The major part is dedicated to highly excited S-states of rubidium, which feature an isotropic van der Waals potential. Nevertheless, the setup and the methods presented are also applicable to other atomic species used in the field of laser cooling and atom trapping.
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
∣nsrangle and
∣nprangle 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,
C6sp, can be defined. We calculate the
C6 coefficients for alkali atoms and present the results for lithium by applying perturbation theory. At short interatomic distances of several
mum, 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.