The dynamical and radiative features of an excited system of two identical atoms are analyzed. The metastability of the system, the directionality of its emission, and its internal forces are studied. Closed-form expressions are derived for the time propagator of the system, for the angular distribution of its spontaneous emission, and for its internal dipole forces, both conservative and nonconservative. The latter reveals the presence of nonreciprocal forces, which leads to a net time-dependent force upon the system. We estimate that, for a free binary system of Li Rydberg atoms, the net internal force may cause a displacement of its center of mass as large as 120 nm over a lifetime.
The dynamical and radiative features of an excited system of two identical atoms are analyzed. The metastability of the system, the directionality of its emission, and its internal forces are studied. Closed-form expressions are derived for the time propagator of the system, for the angular distribution of its spontaneous emission, and for its internal dipole forces, both conservative and nonconservative. The latter reveals the presence of nonreciprocal forces, which leads to a net time-dependent force upon the system. We estimate that, for a free binary system of Li Rydberg atoms, the net internal force may cause a displacement of its center of mass as large as 120 nm over a lifetime.
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 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.
The spontaneous emission of a set of N identical two-level atoms interacting with a quantized electromagnetic field is studied. The atoms are assumed to be close together compared to the mean wavelength of the emitted radiation, and their initial state is either a Dicke state or a superposition of the ground and excited state for each atom. Approximate expressions are obtained for transition probabilities, expectation values, and correlations as functions of time. The spontaneous emission for a very large separation of the atoms is also studied. In this case the directional properties of the emitted radiation, as well as the time within which the atoms decay to their ground state, depend on the position of each atom.
The usual form of electromagnetic forces is given by but for neutral atoms q = 0. The next order of force is the dipole term, but this also vanishes because neutral atoms have no inherent dipole moment. However, a dipole moment can be induced by a field, and this is most efficient if the field is alternating near the atomic resonance frequency. Since these frequencies are typically in the optical range, dipole moments are efficiently induced by shining nearly resonant light on the atoms. Laser cooling and trapping rely on the interaction between laser light and atoms to exert a controllable force on the atoms, and many sophisticated schemes have been developed using the special properties of the interaction. This chapter begins with the simplest schemes for exerting optical forces on atoms, namely a single-frequency light field interacting with a two-level atom. Although this is the simplest possible scheme, it is pedagogically valuable because it shows many of the features that will be encountered further on. The ultimate temperature using such a scheme is limited, but lower temperatures can be achieved with multilevel atoms. This topic is addressed later in the chapter. Two kinds of optical forces When an atom absorbs nearly resonant light, it makes a transition to the excited state, and its subsequent return to the ground state can be either by spontaneous or by stimulated emission. The nature of the optical force that arises from these two different processes is quite different, and will be described separately [1]. The spontaneous emission case is different from the familiar quantum mechanical calculations using state vectors to describe the state of the system, because spontaneous emission causes the state of the system to evolve from a pure state into a mixed state (see Exercise 6.9). Spontaneous emission is an essential ingredient for the dissipative nature of the optical forces in monochromatic light, and the density matrix is needed to describe it (see Chap. 6). When an atom absorbs light, its energy excites the atom and its angular momentum changes the electron's orbit. Both of these are internal atomic properties. However, the linear momentum of the light, can change only the external, translational motion of the atom.
The momentum exchange between a standing wave laser field and an atomic center-of-mass is dominated by the internal dynamics of an atomic electron in the exciting laser field. Rydberg atoms are one of the simplest physical systems where the dependence of this radiative force on the electronic dynamics can be investigated in detail. The characteristics of the momentum transfer between an atomic center-of-mass and a standing wave laser field strongly depend on whether the “particle” or the “wave” aspect of the electronic dynamics prevail. In this review recent theoretical advances in the description of the mechanical action of laser light on Rydberg atoms are discussed. These advances have become possible by the application of semiclassical path integral techniques with respect to the electronic dynamics which clearly exhibit the “particle” and “wave” aspects of this momentum transfer.