We present a time-dependent quantum calculation of the van der Waals interaction between a pair of dissimilar atoms, one of which is initially excited while the other one is in its ground state. For small detuning, the interaction is predominantly mediated at all distances by the exchange of doubly resonant photons between the two atoms. We find that it presents both temporal and spatial oscillations. Spatially oscillating terms depend on the resonant frequencies of both atoms, while the frequency of the time oscillations is given by their detuning. We analyze the physical content of our findings and discuss to what extent previous conflicting stationary approaches provide compatible results. A proper account of causality is found essential in order to obtain the correct result.
We present a time-dependent quantum calculation of the van der Waals interaction between a pair of dissimilar atoms, one of which is initially excited while the other one is in its ground state. For small detuning, the interaction is predominantly mediated at all distances by the exchange of doubly resonant photons between the two atoms. We find that it presents both temporal and spatial oscillations. Spatially oscillating terms depend on the resonant frequencies of both atoms, while the frequency of the time oscillations is given by their detuning. We analyze the physical content of our findings and discuss to what extent previous conflicting stationary approaches provide compatible results. A proper account of causality is found essential in order to obtain the correct result.
I revisit the problem of the interaction between two dissimilar atoms with one atom in an excited state, recently addressed by Berman [Phys. Rev. A 91, 042127 (2015)], Donaire et al. [Phys. Rev. Lett. 115, 033201 (2015)], and Milonni and Rafsanjani [Phys. Rev. A 92, 062711 (2015)], for which precedent approaches have given conflicting results. In the first place, I discuss to what extent these works provide equivalent results. I show that the phase-shift rate of the two-atom wave function computed by Berman, the van der Waals potential of the excited atom by Donaire et al., and the level shift of the excited atom by Milonni and Rafsanjani possess equivalent expressions in the quasistationary approximation. In addition, I show that the level shift of the ground-state atom computed by Milonni and Rafsanjani is equivalent to its van der Waals potential. A diagrammatic representation of all those quantities is provided. The equivalences among them are, however, not generic. In particular, it is found that for the case of the interaction between two identical atoms excited, the phase-shift rate and the van der Waals potentials differ. Concerning the conflicting results of previous approaches in regards to the spatial oscillation of the interactions, I conclude, in agreement with Berman and with Milonni and Rafsanjani, that they refer to different physical quantities. The impacts of free-space dissipation and finite excitation rates on the dynamics of the potentials are analyzed. In contrast with Milonni and Rafsanjani, the oscillatory versus monotonic spatial forms of the potentials of each atom are found not to be related to the reversible versus irreversible nature of the excitation transfer involved.
We perform a time-dependent quantum computation of the van der Waals interaction between two free identical atoms, one of which is initially excited. Making use of the perturbative approach developed in Refs. It is shown that, in addition to an off-resonant interaction force between the two atoms, the two-atom system is subjected to a net force which oscillates periodically in time. We prove that the apparently missing momentum is carried by the resonant photons which mediate the periodic transfer of the excitation between the atoms, guaranteeing this way the satisfaction of the action-reaction principle in the quantum realm. Remarkably, since mediating photons remain virtual throughout the process, their momentum is virtual and thus unaccessible experimentally. Ultimately, as the de-excitation of the system takes place, that momentum turns into actual when carried off by the real photon which is emitted spontaneously. Hence, the directionality of such an emission constitutes a vestige of the net force acting upon the two-atom system while excited.
We present a time-dependent calculation of the velocity-dependent forces which act on an excited atomic dipole in relative motion with respect to ground state atoms of a different kind. Both its interaction with a single atom and with a dilute atomic plate are evaluated. In either case, the total force consists of a conservative van der Waals component and a nonconservative R\"ontgen component. On physical grounds, the former corresponds to the velocity-dependent recoil experienced by the excited atom in the processes of absorption and emission of the photons that it exchanges with the ground-state atoms on a periodic basis. The latter corresponds to the time-variation of the R\"ontgen momentum, which is also mediated by the periodic exchange of quasiresonant photons. We find that, at leading order, all these interactions are linear in velocity. In the nonretarded regime the van der Waals force dominates, being antiparallel to the velocity. On the contrary, in the retarded regime the velocity-dependent forces oscillate in space, van der Waals and R\"ontgen forces are of the same order in the atom-atom interaction, and the R\"ontgen component dominates in the atom-surface interaction.
We compute the conservative van der Waals forces between two atoms, one of which is initially excited, in the limit of identical atoms. Starting with the perturbative calculation of the interaction between two dissimilar atoms, we show that a time-dependent approach in the weak-interaction approximation is essential in considering the identical-atom limit in the perturbative regime. In this limit we find that, at leading order, the van der Waals forces are fully resonant and grow linearly in time, being different upon each atom. The resultant net force upon the two-atom system is related to the directionality of spontaneous emission, which results from the violation of parity symmetry. The strength of this force is much greater than that found in dissimilar atoms, raising the possibility of its experimental detection. In contrast to the usual stationary van der Waals forces, the time-dependent conservative forces cannot be written as the gradients of the expectation values of the interaction potentials, but as the expectation values of the gradients of the interaction potentials only.
We consider the van der Waals force involving excited atoms in general environments, constituted by magnetodielectric bodies. We develop a dynamical approach studying the dynamics of the atoms and the field, mutually coupled. When only one atom is excited, our dynamical theory suggests that for large distances the van der Waals force acting on the ground-state atom is monotonic, while the force acting in the excited atom is spatially oscillating. We show how this latter force can be related to the known oscillating Casimir-Polder force on an excited atom near a (ground-state) body. Our force also reveals a population-induced dynamics: for times much larger that the atomic lifetime the atoms will decay to their ground states leading to the van der Waals interaction between ground-state atoms.
We report the direct measurement of the van der Waals interaction between two isolated, single Rydberg atoms separated by a controlled distance of a few micrometers.Working in a regime where the single-atom Rabi frequency for excitation to the Rydberg state is comparable to the interaction, we observe partial Rydberg blockade, whereby the time-dependent populations of the various two-atom states exhibit coherent oscillations with several frequencies.Quantitative comparison of the data with a simple model based on the optical Bloch equations allows us to extract the van der Waals energy, and observe its characteristic C 6 =R 6 dependence.The measured C 6 coefficients agree well with ab initio calculations, and we observe their dramatic increase with the principal quantum number n of the Rydberg state.