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 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.
A net force on a system of two dissimilar atoms, one of which is excited, is shown to result from their van der Waals interaction. It is accompanied by a net transfer of linear momentum to the quantum fluctuations of the electromagnetic field. This momentum results from the asymmetric interference of the virtual photons scattered off each atom along the interatomic direction, which is in itself a manifestation of the optical theorem. Ultimately, the virtual photons' momentum, of equal strength and opposite direction to the momentum gained by the two-atom system while excited, is released through directional spontaneous emission, which allows for an indirect measure, a posteriori, of the total force on the excited system. A quantitative prediction is made in a two-alkali atom system. It is conjectured that a net force and hence a nonzero momentum of quantum fluctuations take place in any asymmetrically excited system.
The quantum description of the electromagnetic (EM) field, even in the absence of sources, reveals that the vacuum exhibits fluctuations in the energy and of the components of the field, known as quantum vacuum fluctuations. The coupling of these quantum fluctuations of the vacuum to electric charges leads to experimentally observable phenomena, such as the spontaneous emission of an excited atom, the Lamb effect, the Casimir effect, and the van der Waals interactions, which have been historically fundamental for the confirmation of the existence of these fluctuations. The optical response of simple atoms and the EM interaction between two atoms constitute the simplest realistic phenomena for studying these effects. This thesis focuses on the fundamental study of the properties of interatomic interactions, addressing aspects such as their dependence on the interatomic distance, their time dependence, and the emergence of nonreciprocal interatomic forces due to parity breaking. In particular, the detailed analysis of the electric dipole forces in a system of two atoms, one of which is initially excited, is carried out, along with the study of the implication of the resonant interactions in the appearance of collective effects in absorption and emission processes of many-atom systems. Due to the inherently time-dependent nature of the resonant forces between excited atoms, a time-dependent Hamiltonian approach is employed. The atomic interaction processes are represented with time-ordered diagrams. It is obtained that the atoms are subjected to resonant conservative forces, directed along the interatomic axis, which exert a net force on the system. This result implies an apparent violation of the action-reaction principle due to the lack of conservation of the kinetic momentum of the atoms. However, this net force on the atomic system is compensated by the time derivative of the transversal momentum of the EM field, associated with the resonant photons that mediate the interaction, ensuring the conservation of the total momentum of the system. In addition to these conservative forces, there are nonconservative forces which are a consequence of the time derivative of the so-called longitudinal momentum of the electromagnetic field and contain components perpendicular to the interatomic axis. We analyze the particular case of the interaction between identical atoms. In this scenario, the net force on the system becomes time-dependent. Furthermore, states with degenerate energy arise and evolve coherently through the periodic transfer of resonant photons between the atoms. This implies that in these degenerate states, there are contributions from interatomic interactions that cannot be expressed as an energy shift in the atomic wave functions. Consequently, these interactions give rise to collective phenomena observable in photon absorption and emission processes. At the same time, the strength of these forces is markedly superior to that calculated for different atoms, which makes this scenario a more favorable set-up for the experimental observation of the nonreciprocal forces and the associated coherent phenomena. Concerning collective effects and their application in the design of multi-atomic qubits, these phenomena have significant implications for the scalability and connectivity of such systems. To describe these collective properties, we have formulated a Hamiltonian that incorporates both the interaction processes, i.e., those that give rise to dynamic coherence and incoherence effects, and the stationary interaction processes that renormalize the energy of the atomic states. It is found that the photon absorption probability is determined by the ratio between the interatomic interaction and the intensity of the laser that excites the system. On the other hand, the spontaneous emission of photons is proportional to the number of decay channels, which decrease when the interatomic interaction between excited states breaks the degeneracy in the subspaces associated with the same number of excitations.
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 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 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 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.