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Acta Physica Sinica

Van der Waals interaction between high excited states

Zhao Jian-Dong, Xin Jie

Published Jan 1, 2014• 0 citations
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Abstract

The highly excited atoms have a strong Van der Waals interaction as compared with the ground-state atoms, which can block the excitation of neighboring atoms and forming the blockade effect. In this work, the interaction between highly excited atoms is calculated using the perturbation theory, the interaction of nS and nD pair states and the dispersion coefficients are obtained. This shows that the interactions of the SS for both Rb and Cs atoms are repulsive, whereas the interaction of DD states is repulsive for Cs and attractive for Rb.

DOI
10.7498/aps.63.133201

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The highly excited atoms have a strong Van der Waals interaction as compared with the ground-state atoms, which can block the excitation of neighboring atoms and forming the blockade effect. In this work, the interaction between highly excited atoms is calculated using the perturbation theory, the interaction of nS and nD pair states and the dispersion coefficients are obtained. This shows that the interactions of the SS for both Rb and Cs atoms are repulsive, whereas the interaction of DD states is repulsive for Cs and attractive for Rb.
The authors report strong repulsive van der Waals and dipole-quadrupole interactions in the $\ensuremath{\Sigma}$ and $\ensuremath{\Pi}$ potentials of the LiCs molecule dissociating into Li 2P2P2P and Cs 6S6S6S atoms. Theoretical results derived from second-order perturbation theory are verified by investigating experimentally the wavelength dependence of the quasistatic wings of the Li resonance lines broadened by Cs ground-state atoms.
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.
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 (nA{n}_{A}nA​P) and the other is in the ground state (nB{n}_{B}nB​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 C6{C}_{6}C6​ constants for all heteronuclear alkali-metal-atom pairs. In the case of heavier perturbers (Rb and Cs) the C6{C}_{6}C6​ 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 C6{C}_{6}C6​ 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 analyze the effects of Zeeman degeneracies on the long-range interactions between like Rydberg atoms, with particular emphasis on applications to quantum-information processing using the van der Waals blockade. We present a general analysis of how degeneracies affect the primary error sources in blockade experiments, emphasizing that blockade errors are sensitive primarily to the weakest possible atom-atom interactions between the degenerate states, not the mean interaction strength. We present explicit calculations of the van der Waals potentials in the limit where the fine-structure interaction is large compared to the atom-atom interactions. The results are presented for all potential angular momentum channels involving s\mathit{s}s, p\mathit{p}p, and d\mathit{d}d states. For most channels there are one or more combinations of Zeeman levels that have extremely small dipole-dipole interactions and are therefore poor candidates for effective blockade experiments. Channels with promising properties are identified and discussed. We also present numerical calculations of Rb and Cs dipole matrix elements and relevant energy levels using quantum defect theory, allowing for convenient quantitative estimates of the van der Waals interactions to be made for principal quantum numbers up to 100. Finally, we combine the blockade and van der Waals results to quantitatively analyze the angular distribution of the blockade shift and its consequence for angular momentum channels and geometries of particular interest for blockade experiments with Rb.
van der Waals interactions between atoms and dielectric surfaces are reinvestigated. To describe the nonretarded interaction potential between a dispersive dielectric surface and an atom in an arbitrary internal energy state, we derive a general expression in terms of an integral, over real frequency, of the combined atom and surface polarizabilities. It is shown that, for excited atoms, the expression is equivalent to the one obtained by Wylie and Sipe [Phys. Rev. A 32, 2030 (1985)]. We thus demonstrate how to extend this approach to excited atoms interacting with birefringent dielectrics. For isotropic dielectrics, a method of integration in closed form allows us to derive an approximate formula for the van der Waals interaction constant in terms of resonance frequencies and oscillator strengths of both the atom and the dielectric. Frequency-dependent ``dielectric reflection'' coefficients are introduced for virtual atomic dipole couplings either in absorption or in emission. In absorption, the reflection coefficient is always positive and smaller than unity. In emission, it may take arbitrary values, positive or negative (corresponding to van der Waals repulsion). Such a behavior is shown to be related to resonant excitation exchange between the atomic system and the dielectric medium, when an atomic transition frequency gets in resonance with a dielectric absorption band. Numerical calculations performed for the cesium-sapphire system are shown to be in good agreement with data obtained by selective-reflection spectroscopy. Finally, experimental tests of the birefringent character of the sapphire response are discussed.
We use perturbation theory to directly calculate the van der Waals and dipole-dipole energy shifts of pairs of interacting Rb Rydberg atoms for different quantum numbers nnn, $\ensuremath{\ell}$, jjj, and mj{m}_{j}mj​, taking into account a large number of perturbing states. Our results can be used to identify good experimental parameters and illuminate important considerations for applications of the ``Rydberg-excitation blockade.'' We also use the results of the calculation to explain features of previous experimental data on the Rydberg-excitation blockade. To explore control methods for the blockade, we discuss energy shifts due to atom-atom interaction in an external electric field.