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arXiv:1802.10360 · Physical Review A

Casimir-Polder potential of a driven atom

Sebastian Fuchs, Robert G. Bennett, Stefan Yoshi Buhmann

Published Aug 20, 2018• 17 citations
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Abstract

We investigate theoretically the Casimir-Polder potential of an atom which is driven by a laser field close to a surface. This problem is addressed in the framework of macroscopic quantum electrodynamics using the Green's tensor formalism and we distinguish between two different approaches: a perturbative ansatz and a method based on Bloch equations. We apply our results to a concrete example, namely an atom close to a perfectly conducting mirror, and create a scenario where the tunable Casimir-Polder potential becomes similar to the respective potential of an undriven atom due to fluctuating field modes. Whereas the perturbative approach is restricted to large detunings, the ansatz based on Bloch equations is exact and yields an expression for the potential which does not exceed $1/2$ of the undriven Casimir-Polder potential.

DOI
10.1103/physreva.98.022514

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Optics and Spectroscopy•Sep 1, 2007•1 citation
We investigate theoretically the Casimir-Polder potential of an atom which is driven by a laser field close to a surface. This problem is addressed in the framework of macroscopic quantum electrodynamics using the Green's tensor formalism and we distinguish between two different approaches: a perturbative ansatz and a method based on Bloch equations. We apply our results to a concrete example, namely an atom close to a perfectly conducting mirror, and create a scenario where the tunable Casimir-Polder potential becomes similar to the respective potential of an undriven atom due to fluctuating field modes. Whereas the perturbative approach is restricted to large detunings, the ansatz based on Bloch equations is exact and yields an expression for the potential which does not exceed 1/21/21/2 of the undriven Casimir-Polder potential.
An atom irradiated by an off-resonant laser field near a surface is expected to experience the sum of two fundamental potentials, the optical potential of the laser field and the Casimir-Polder potential of the surface. Here, we report a new nonadditive potential, namely, the laser-induced Casimir-Polder potential, which arises from a correlated coupling of the atom with both the laser and the quantum vacuum. We apply this result to an experimentally realizable scenario of an atomic mirror with an evanescent laser beam leaking out of a surface. We show that the nonadditive term is significant for realistic experimental parameters, transforming potential barriers into potential wells, which can be used to trap atoms near surfaces.
The Casimir-Polder force on a single atom in the presence of microscopic magneto-electric bodies is studied within the framework of macroscopic quantum electrodynamics. In the first part, time-independent perturbation theory is used show that the static Casimir-Polder force on a ground-state atom in the presence of an arbitrary arrangement of bodies can be expressed in terms of the atom's polarisability and the scattering part of the Green tensor characterising the bodies. This result is used to verify the origin of the force and to study various bodies of simple shapes. In the second part, a genuinely dynamical approach is developed by starting from the operator Lorentz force. It is found that the dynamics of the force on initially excited atoms is governed by irreversible spontaneous decay in the case of weak atom-field coupling, while Rabi oscillations may arise for strong atom-field coupling.
We investigate the dynamics of Rydberg atoms trapped in front of an oscillating conducting mirror, that can be simulated by a wall with a periodically driven dielectric constant (dynamical mirror). We focus our attention on the probability of atomic excitation due to a dynamical Casimir-Polder effect, related to the near field of the image atom whose distance periodically changes as a consequence of the mirror's motion. The theoretical analysis of this system also aims to an experimental proposal to detect this new dynamical effect exploiting Rydberg atoms trapped in the vicinity of the dynamical mirror. Our results indicate that the number of excited atoms is high enough to allow detection of the dynamical effect.
We theoretically investigate Rydberg atom pair potentials of Rb atoms in front of a perfectly conducting plate. The pair potentials are perturbed by both the Casimir-Polder potential acting on a single atom and the scattering contribution to the interatomic interaction. In contrast to the pair potentials in free space, at atom-surface distances ${d}_{s}\ensuremath{\lesssim}4\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$, avoided crossings appear. In the associated potential wells that are entirely due to dispersion interactions with the surface, there exist vibrational bound states, i.e., Rydberg macrodimers, with ground-state energies of up to $E=\ensuremath{-}68\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$ and radial expectation values of the order of several $\ensuremath{\mu}\mathrm{m}$.
We consider the dynamical atom-surface Casimir-Polder force in the nonequilibrium configuration of an atom near a perfectly conducting wall, initially prepared in an excited state with the field in its vacuum state. We evaluate the time-dependent Casimir-Polder force on the atom and find that it shows an oscillatory behavior from attractive to repulsive both in time and in space. We also investigate the asymptotic behavior in time of the dynamical force and of related local field quantities, showing that the static value of the force, as obtained by a time-independent approach, is recovered for times much longer than the time scale of the atomic self-dressing but shorter than the atomic decay time. We then discuss the evolution of global quantities such as atomic and field energies and their asymptotic behavior. We also compare our results for the dynamical force on the excited atom with analogous results recently obtained for an initially bare ground-state atom. We show that new relevant features are obtained in the case of an initially excited atom, for example, much larger values of the dynamical force with respect to the static one, allowing for an easier way to single out and observe the dynamical Casimir-Polder effect.
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.