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Physical Review A

Dispersion interactions between excited atoms

Gyeong-il Kweon, N. M. Lawandy

Published May 1, 1993• 14 citations
Publisher

Abstract

We present results on the complete dispersion interaction between two neutral multilevel atoms in the same excited state. The calculations indicate that the dispersion interaction can produce a repulsive barrier of the order of \ensuremath{\simeq}7 \ensuremath{\mu}eV for intermediate separations and that long-range oscillations exist in the Casimir-Polder regime. The results may be of importance in laser-cooled atomic diffusion phenomena where translational energies well below this barrier height are achievable.

DOI
10.1103/physreva.47.4513

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We present results on the complete dispersion interaction between two neutral multilevel atoms in the same excited state. The calculations indicate that the dispersion interaction can produce a repulsive barrier of the order of \ensuremath{\simeq}7 \ensuremath{\mu}eV for intermediate separations and that long-range oscillations exist in the Casimir-Polder regime. The results may be of importance in laser-cooled atomic diffusion phenomena where translational energies well below this barrier height are achievable.
The potential of long-range interaction between two dissimilar atoms, one of which is excited, drops as 1/R 2 with the distance for the Casimir-Polder limit of large distances in comparison with the wave-length of atom transitions (E.A. Power and T. Thirunamachandran, Phys. Rev. A 51, 3660 (1995)). It is shown that such a dependence, obtained with the help of perturbation technique, results in a divergence for the interaction potential between an excited atom and a medium of dilute gas. We develop a nonperturbative method based upon quantum Green’s functions (Yu. Sherkunov, Phys. Rev. A 72, 052703 (2005)) to calculate the interaction potential for an excited atom and a ground-state atom embedded in a dielectric medium, taking into account the absorption of photons in the dielectric medium. The exponential suppression of the interaction between the atoms is demonstrated. The force acting on an excited atom near the interface of dilute gas medium is calculated. The result is no more divergent. The force between gas media in Casimir-Polder regime is calculated as well.
A complete description of the multipolar Casimir-Polder effects between two alkali-metal atoms in the ground state is presented. We give both general and particular expressions for the electric-electric, electric-magnetic, magnetic-magnetic, diamagnetic-electric, and diamagnetic-magnetic two-photon multipole processes, many of which have not been discussed previously in literature, to our knowledge. The asymptotic behavior of the Casimir-Polder potential is studied in terms of the K7,K9,{K}_{7}, {K}_{9},K7​,K9​, and K11{K}_{11}K11​ long-range coefficients. We have established the range of validity of the Casimir-Polder potential by analyzing the first-order correction to the energy given by the matrix element of the contact interaction term between the atomic charge distributions. Numerical values for the Casimir-Polder long-range interaction potentials for both homonuclear and heteronuclear alkali-metal dimers are presented. Comparisons with previous analytical and numerical results are included.
A complete description of the multipolar Casimir-Polder effects between two alkali-metal atoms in the ground state is presented. We give both general and particular expressions for the electric-electric, electric-magnetic, magnetic-magnetic, diamagnetic-electric, and diamagnetic-magnetic two-photon multipole processes, many of which have not been discussed previously in literature, to our knowledge. The asymptotic behavior of the Casimir-Polder potential is studied in terms of the K7,K9,{K}_{7}, {K}_{9},K7​,K9​, and K11{K}_{11}K11​ long-range coefficients. We have established the range of validity of the Casimir-Polder potential by analyzing the first-order correction to the energy given by the matrix element of the contact interaction term between the atomic charge distributions. Numerical values for the Casimir-Polder long-range interaction potentials for both homonuclear and heteronuclear alkali-metal dimers are presented. Comparisons with previous analytical and numerical results are included.
The van der Waals interaction between neutral atoms is typically studied using stationary perturbation theory for the short-distance (London) limit, while long-distance (Casimir-Polder) results are usually derived via semiclassical, time-dependent approaches. Here, we demonstrate that reformulating stationary perturbation theory calculations in terms of time-ordered correlation functions significantly simplifies the mathematical treatment. This reformulation is particularly advantageous for higher-order calculations required in the long-distance regime, where retardation effects become important. Our approach provides a unified framework connecting both limiting cases, and is intended as a bridge between advanced quantum mechanics and field-theoretic treatments of dispersion forces, suitable for graduate-level courses or specialized readers.
We consider the Casimir-Polder interaction between two atoms, one in the ground state and the other in its excited state. The interaction is time dependent for this system, because of the dynamical self-dressing and the spontaneous decay of the excited atom. We calculate the dynamical Casimir-Polder potential between the two atoms using an effective Hamiltonian approach. The results obtained and their physical meaning are discussed and compared with previous results based on a time-independent approach, which uses a nonnormalizable dressed state for the excited atom.
We study the Casimir-Polder potential of a multilevel alkali-metal atom near an optical nanofiber. We calculate the mean potential of the atom in a fine-structure state. We perform numerical calculations for the Casimir-Polder potentials of the ground state and a few low-lying excited states of a rubidium atom. We show that, unlike the potential of the ground state, which is negative and attractive, the potential of a low-lying excited state may take positive values, oscillate around the zero value with a decaying amplitude, and become repulsive in some regions of atom-to-surface distances. We observe that, for a nanofiber with a radius of 200 nm, the potential for the state 8S1/28{S}_{1/2}8S1/2​ of a rubidium atom achieves a positive peak value of about $17\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{K}$ at a distance of about 150 nm from the fiber surface and becomes strongly repulsive in the region of distances from 150 to 400 nm. We also calculate the nanofiber-induced shifts of the transition frequencies of the atomic rubidium D2{D}_{2}D2​ and D1{D}_{1}D1​ lines. We find that the shifts are negative in the region of short distances, become positive, and oscillate around the zero value with a decaying amplitude in the region of large distances.