We study forces between two neutral atoms, modeled as three-dimensional harmonic oscillators, arising from mutual influences mediated by an electromagnetic field but not from their direct interactions. We allow as dynamical variables the center-of-mass motion of the atom, its internal degrees of freedom, and the quantum field treated relativistically. We adopt the method of nonequilibrium quantum field theory which can provide a first-principles, systematic, and unified description including the intrinsic and induced dipole fluctuations. The inclusion of self-consistent back-actions makes possible a fully dynamical description of these forces valid for general atom motion. In thermal equilibrium we recover the known forces---London, van der Waals, and Casimir-Polder---between neutral atoms in the long-time limit. We also reproduce a recently reported force between atoms when the system is out of thermal equilibrium at late times. More noteworthy is the discovery of the existence of a type of (or identification of the source of some known) interatomic force which we call the ``entanglement force,'' originating from the quantum correlations of the internal degrees of freedom of entangled atoms.
We study forces between two neutral atoms, modeled as three-dimensional harmonic oscillators, arising from mutual influences mediated by an electromagnetic field but not from their direct interactions. We allow as dynamical variables the center-of-mass motion of the atom, its internal degrees of freedom, and the quantum field treated relativistically. We adopt the method of nonequilibrium quantum field theory which can provide a first-principles, systematic, and unified description including the intrinsic and induced dipole fluctuations. The inclusion of self-consistent back-actions makes possible a fully dynamical description of these forces valid for general atom motion. In thermal equilibrium we recover the known forces---London, van der Waals, and Casimir-Polder---between neutral atoms in the long-time limit. We also reproduce a recently reported force between atoms when the system is out of thermal equilibrium at late times. More noteworthy is the discovery of the existence of a type of (or identification of the source of some known) interatomic force which we call the ``entanglement force,'' originating from the quantum correlations of the internal degrees of freedom of entangled atoms.
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 study the nonequilibrium dissipative dynamics of the center of mass of a particle coupled to a field via its internal degrees of freedom. We model the internal and external degrees of freedom of the particle as quantum harmonic oscillators in 1+1D, with the internal oscillator coupled to a scalar quantum field at the center of mass position. Such a coupling results in a nonlinear interaction between the three pertinent degrees of freedom---the center of mass, internal degree of freedom, and the field. It is typically assumed that the internal dynamics is decoupled from that of the center of mass owing to their disparate characteristic timescales. Here we use an influence functional approach that allows one to account for the self-consistent backaction of the different degrees of freedom on each other, including the coupled nonequilibrium dynamics of the internal degree of freedom and the field, and their influence on the dissipation and noise of the center of mass. Considering a weak nonlinear interaction term, we employ a perturbative generating functional approach to derive a second order effective action and a corresponding quantum Langevin equation describing the non-equilibrium dynamics of the center of mass. We analyze the resulting dissipation and noise arising from the field and the internal degree of freedom as a composite environment. Furthermore, we establish a generalized fluctuation-dissipation relation for the late-time dissipation and noise kernels. Our results are pertinent to open quantum systems that possess intermediary degrees of freedom between system and environment, such as in the case of optomechanical interactions.
This third paper in this series continues the investigation of atom-field interactions in the presence of a conductor or a dielectric medium, focusing on quantum information related basic issues such as decoherence and entanglement. Here we consider the entanglement between two atoms with internal degrees of freedom modeled by a harmonic oscillator, with varying separations between them and varying distances between them and a conducting surface. These are configurations familiar in the Casimir-Polder effect, but the behavior of atom-surface entanglement is quite different from the well-studied behavior of field-induced forces. For one, while the attractive force between an atom and a conducting surface increases as they come closer, the entanglement between the atom and the quantum field actually decreases as the atom gets closer to the conductor, as shown in \cite{Rong,AFD2}. We show how different factors play out, ranging from the coupling between the atoms and the field to the coupling between the atoms, going beyond the weak coupling restrictions often found necessary in the literature. Gathering our results for the entanglement dependence on each variable concerned, we can provide a spatial topography of quantum entanglement, thus enabling a visualized understanding of the behavior of quantum field-mediated entanglement. In particular we can quantify the definition of a three-dimensional \textit{entanglement domain} between the two atoms, how it varies with their coupling, their separation and their distances from the conducting surface, and for practical applications, how to exercise effective control of the entanglement between two atoms by changing these parameters. Our findings are expected to be useful for studies of atom-field-medium interactions in vacuum and surface physics.
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.
Abstract Students encounter harmonic-oscillator models in many aspects of basic physics, within widely varying theoretical contexts. Here we highlight the interconnections and varying points of view. We start with the classical mechanics of masses coupled by springs and trace how the same essential systems are reanalysed in the unretarded van der Waals interactions between dipole oscillators within classical and quantum theories. We note how classical-mechanical ideas from kinetic theory lead to energy equipartition which determines the high-temperature van der Waals forces of atoms and molecules modelled as dipole oscillators. In this case, colliding heat-bath particles can be regarded as providing local hidden variables for the statistical mechanical behaviour of the oscillators. Next we note how relativistic classical electrodynamical ideas conflict with the assumptions of nonrelativistic classical statistical mechanics. Classical electrodynamics which includes classical zero-point radiation leads to van der Waals forces between dipole oscillators, and these classical forces agree at all temperatures with the forces derived from quantum theory. However, the classical theory providing this agreement is not a local theory, but rather a non-local hidden-variables theory. The classical theory can be regarded as involving hidden variables in the random phases of the plane waves spreading throughout space which provide the source-free random radiation.
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.