Dispersion Interactions between Neutral Atoms and the Quantum Electrodynamical Vacuum

Nonlocal Static and Dynamical Vacuum Field Correlations and Casimir-Polder Interactions

In this review, we investigate several aspects and features of spatial field correlations for the massless scalar field and the electromagnetic field, both in stationary and nonstationary conditions, and show how they manifest in two- and many-body static and dynamic dispersion interactions (van der Waals and Casimir-Polder). We initially analyze the spatial field correlations for noninteracting fields, stressing their nonlocal behavior, and their relation to two-body dispersion interactions. We then consider how field correlations are modified by the presence of a field source, such as an atom or in general a polarizable body, firstly in a stationary condition and then in a dynamical condition, starting from a nonstationary state. We first evaluate the spatial field correlation for the electric field in the stationary case, in the presence of a ground-state or excited-state atom, and then we consider its time evolution in the case of an initially nonstationary state. We discuss in detail their nonlocal features, in both stationary and nonstationary conditions. We then explicitly show how the nonlocality of field correlations can manifest itself in van der Waals and Casimir-Polder interactions between atoms, both in static and dynamic situations. We discuss how this can allow us to indirectly probe the existence and the properties of nonlocal vacuum field correlations of the electromagnetic field, a research subject of strong actual interest, also in consequence of recent measurements of spatial field correlations exploiting electro-optical sampling techniques. The subtle and intriguing relation between nonlocality and causality is also discussed.

Spectroscopy of Alkali Atoms in Solid Matrices of Rare Gases: Experimental Results and Theoretical Analysis

We present an experimental and theoretical investigation of the spectroscopy of dilute alkali atoms in a solid matrix of inert gases at cryogenic temperatures, specifically Rubidium atoms in a solid Argon or Neon matrix, and related aspects of the interaction energies between the alkali atoms and the atoms of the solid matrix. The system considered is relevant for matrix isolation spectroscopy, and it is at the basis of a recently proposed detector of cosmological axions, exploiting magnetic-type transitions between Zeeman sublevels of alkali atoms in a magnetic field, tuned to the axion mass, assumed in the meV range. Axions are one of the supposed constituents of the dark matter (DM) of the Universe. This kind of spectroscopy could be also relevant for the experimental search of new physics beyond the Standard Model, in particular the search of violations of time-reversal or parity-charge-conjugation (CP) symmetry. In order to efficiently resolve the axion-induced transition in alkali-doped solid matrices, it is necessary to reduce as much as possible the spectral linewidth of the electronic transitions involved. The theoretical investigation presented in this paper aims to estimate the order of magnitude of the inhomogeneous contribution to the linewidth due to the alkali–matrix interactions (Coulomb/exchange and dispersion), and to compare the theoretical results with our experimental measurements of spectra of dilute Rubidium atoms in Argon and Neon solid matrix. The comparison of the expected or measured spectral linewidths will be important for selecting the most appropriate combination of alkali atoms and matrix inert elements to be used in the proposed axion detection scheme. It is finally suggested that dilute Lithium atoms diffused in a cold parahydrogen solid matrix could be, overall, a good system upon which the proposed detector could be based.

Molecular Interactions Induced by a Static Electric Field in Quantum Mechanics and Quantum Electrodynamics

By means of quantum mechanics and quantum electrodynamics applied to coupled harmonic Drude oscillators, we study the interaction between two neutral atoms or molecules subject to a uniform static electric field. Our focus is to understand the interplay between leading contributions to field-induced electrostatics/polarization and dispersion interactions, as considered within the employed Drude model for both non-retarded and retarded regimes. For the first case, we present an exact solution for two coupled oscillators obtained by diagonalizing the corresponding quantum-mechanical Hamiltonian and demonstrate that the external field can control the strength of different intermolecular interactions and relative orientations of the molecules. In the retarded regime described by quantum electrodynamics, our analysis shows that field-induced electrostatic and polarization energies remain unchanged (in isotropic and homogeneous vacuum) compared to the non-retarded case. For interacting species modeled by quantum Drude oscillators, the developed framework based on quantum mechanics and quantum electrodynamics yields the leading contributions to molecular interactions under the combined action of external and vacuum fields.

Effective Hamiltonians in Nonrelativistic Quantum Electrodynamics

In this paper, we consider some second-order effective Hamiltonians describing the interaction of the quantum electromagnetic field with atoms or molecules in the nonrelativistic limit. Our procedure is valid only for off-energy-shell processes, specifically virtual processes such as those relevant for ground-state energy shifts and dispersion van der Waals and Casimir-Polder interactions, while on-energy-shell processes are excluded. These effective Hamiltonians allow for a considerable simplification of the calculation of radiative energy shifts, dispersion, and Casimir-Polder interactions, including in the presence of boundary conditions. They can also provide clear physical insights into the processes involved. We clarify that the form of the effective Hamiltonian depends on the field states considered, and consequently different expressions can be obtained, each of them with a well-defined range of validity and possible applications. We also apply our results to some specific cases, mainly the Lamb shift, the Casimir-Polder atom-surface interaction, and the dispersion interactions between atoms, molecules, or, in general, polarizable bodies.

Light absorption by interacting atomic gas in quantum optical regime

Quantum optical theory of absorption properties of interacting atoms is developed. The concept of local absorptance is introduced as a derivative of the logarithm of intensity with respect to the distance in the vicinity of a given spatial point and a moment of time. The intensity is represented by the quantum and statistically averaged normal product of creation and annihilation operators of the electromagnetic field. The development of an analytical method of the estimation for the kinetic and optical parameters for the system is proposed here. The calculation method of the absorption coefficient includes thermal atomic motion, Doppler effect, and the short-range interaction between atoms. The absorption coefficient explicitly takes into account the quantum nature of the optical field. The ability of the system to absorb or emit quanta is quantitatively expressed through the special form of interaction integrals. The specific form of integrals results from the structure of the quantum brackets. The interplay between the collective (virtual photon exchange) and binary (optically induced inter-particle bonding) processes determines the system behavior. The spectral profile of the local absorption coefficient for different atomic densities and time intervals is simulated for realistic parameters.

Gravitational Dispersion Forces and Gravity Quantization

The parallel development of the theories of electrodynamical and gravitational dispersion forces reveals important differences. The former arose earlier than the formulation of quantum electrodynamics so that expressions for the unretarded, van der Waals forces were obtained by treating the field as classical. Even after the derivation of quantum electrodynamics, semiclassical considerations continued to play a critical role in the interpretation of the full results, including in the retarded regime. On the other hand, recent predictions about the existence of gravitational dispersion forces were obtained without any consideration that the gravitational field might be fundamentally classical. This is an interesting contrast, as several semiclassical theories of electrodynamical dispersion forces exist although the electromagnetic field is well known to be quantized, whereas no semiclassical theory of gravitational dispersion forces was ever developed although a full quantum theory of gravity is lacking. In the first part of this paper, we explore this evolutionary process from a historical point of view, stressing that the existence of a Casimir effect is insufficient to demonstrate that a field is quantized. In the second part of the paper, we show that the recently published results about gravitational dispersion forces can be obtained without quantizing the gravitational field. This is done first in the unretarded regime by means of Margenau’s treatment of multipole dispersion forces, also obtaining mixed potentials. These results are extended to the retarded regime by generalizing to the gravitational field the approach originally proposed by McLachlan. The paper closes with a discussion of experimental challenges and philosophical implications connected to gravitational dispersion forces.

Fifty Years of the Dynamical Casimir Effect

This is a digest of the main achievements in the wide area, called the Dynamical Casimir Effect nowadays, for the past 50 years, with the emphasis on results obtained after 2010.

Dispersion Interaction between Two Hydrogen Atoms in a Static Electric Field

We consider the dispersion interaction between two ground-state hydrogen atoms, interacting with the quantum electromagnetic field in the vacuum state, in the presence of an external static electric field, both in the nonretarded and in the retarded Casimir-Polder regime. We show that the presence of the external field strongly modifies the dispersion interaction between the atoms, changing its space dependence. Moreover, we find that, for specific geometrical configurations of the two atoms with respect to the external field and/or the relative orientation of the fields acting on the two atoms, it is possible to change the character of the dispersion force, turning it from attractive to repulsive, or even make it vanishing. This new finding clearly shows the possibility to control and tailor interatomic dispersion interactions through external actions. By a numerical estimate of the field-modified interaction, we show that at typical interatomic distances the change of the interaction's strength can match or even outmatch the unperturbed interaction; this can be obtained for values of the external field that can be currently achieved in the laboratory, and sufficiently weak to be taken into account perturbatively.

Spontaneous Emission of an Atom Near an Oscillating Mirror

We investigate the spontaneous emission of one atom placed near an oscillating reflecting plate. We consider the atom modeled as a two-level system, interacting with the quantum electromagnetic field in the vacuum state, in the presence of the oscillating mirror. We suppose that the plate oscillates adiabatically, so that the time-dependence of the interaction Hamiltonian is entirely enclosed in the time-dependent mode functions, satisfying the boundary conditions at the plate surface, at any given time. Using time-dependent perturbation theory, we evaluate the transition rate to the ground-state of the atom, and show that it depends on the time-dependent atom–plate distance. We also show that the presence of the oscillating mirror significantly affects the physical features of the spontaneous emission of the atom, in particular the spectrum of the emitted radiation. Specifically, we find the appearance of two symmetric lateral peaks in the spectrum, not present in the case of a static mirror, due to the modulated environment. The two lateral peaks are separated from the central peak by the modulation frequency, and we discuss the possibility to observe them with actual experimental techniques of dynamical mirrors and atomic trapping. Our results indicate that a dynamical (i.e., time-modulated) environment can give new possibilities to control and manipulate also other radiative processes of two or more atoms or molecules nearby, for example their cooperative decay or the resonant energy transfer.

Off-Resonance Control and All-Optical Switching: Expanded Dimensions in Nonlinear Optics

The theory of non-resonant optical processes with intrinsic optical nonlinearity, such as harmonic generation, has been widely understood since the advent of the laser. In general, such effects involve multiphoton interactions that change the population of each input optical mode or modes. However, nonlinear effects can also arise through the input of an off-resonant laser beam that itself emerges unchanged. Many such effects have been largely overlooked. Using a quantum electrodynamical framework, this review provides detail on such optically nonlinear mechanisms that allow for a controlled increase or decrease in the intensity of linear absorption and fluorescence and in the efficiency of resonance energy transfer. The rate modifications responsible for these effects were achieved by the simultaneous application of an off-resonant beam with a moderate intensity, acting in a sense as an optical catalyst, conferring a new dimension of optical nonlinearity upon photoactive materials. It is shown that, in certain configurations, these mechanisms provide the basis for all-optical switching, i.e., the control of light-by-light, including an optical transistor scheme. The conclusion outlines other recently proposed all-optical switching systems.