Molecular quantum electrodynamics in the Heisenberg picture: A field theoretic viewpoint

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.

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.

Resonance energy transfer mediated by a chiral molecule

The problem of resonant energy transfer (RET) between an electric dipole donor, D, and an electric dipole acceptor, A, mediated by a passive, chiral third-body, T, is considered within the framework of molecular quantum electrodynamics theory. To account for the optical activity of the mediator, magnetic dipole and electric quadrupole coupling terms are included in addition to the leading electric dipole interaction term. Fourth-order diagrammatic time-dependent perturbation theory is used to obtain the matrix element. It is found that the Fermi golden rule rate depends on pure multipole moment polarizabilities and susceptibilities of T, as well as on various mixed electric and magnetic multipole moment response functions. The handedness of T manifests through mixed electric-magnetic dipole and mixed electric dipole-quadrupole polarizabilities, which affect the rate and, respectively, require the use of fourth-rank and sixth-rank Cartesian tensor averages over T, yielding non-vanishing isotropic rate formulae applicable to a chiral fluid medium. Terms of a similar order of magnitude proportional to the product of electric dipole polarizability and either magnetic dipole susceptibility or electric quadrupole polarizability of T are also computed for oriented and freely tumbling molecules. Migration rates dependent upon the product of the pure electric dipole or magnetic dipole polarizability with the mixed electric-magnetic or electric dipole-quadrupole analogs, which require fourth- and fifth-rank Cartesian tensor averaging, vanish for randomly oriented systems. Asymptotically limiting rate expressions are also evaluated. Insight is gained into RET occurring in complex media.

Bridge-Mediated RET between Two Chiral Molecules

Molecular quantum electrodynamics (QED) theory is employed to calculate the rate of resonance energy transfer (RET) between a donor, D, described by an electric dipole and quadrupole, and magnetic dipole coupling, and an identical acceptor molecule, A, that is mediated by a third body, T, which is otherwise inert. A single virtual photon propagates between D and T, and between T and A. Time-dependent perturbation theory is used to compute the matrix element, from which the transfer rate is evaluated using the Fermi golden rule. This extends previous studies that were limited to the electric dipole approximation only and admits the possibility of the exchange of excitation between a chiral emitter and absorber. Rate terms are computed for specific pure and mixed multipole-dependent contributions of D and A for both an oriented arrangement of the three particles and for the freely tumbling situation. Mixed multipole moment contributions, such as those involving electric–magnetic dipole or electric dipole–quadrupole coupling at one center, do not survive random orientational averaging. Interestingly, the mixed electric–magnetic dipole D and A rate term is non-vanishing and discriminatory, exhibiting a dependence on the chirality of the emitter and absorber, and is entirely retarded. It vanishes, however, if D and A are oriented perpendicularly to one another. Near- and far-zone asymptotes of isotropic contributions to the rate are also evaluated, demonstrating radiationless short-range transfer and inverse-square radiative exchange at very large separations.

Polariton mediated resonance energy transfer in a fluid

The focus of this work is on a microscopic quantum electrodynamical understanding of cumulative quantum effects in resonance energy transfer occurring in an isotropic and disordered medium. In particular, we consider quantum coherence, defined in terms of interferences between Feynman pathways, and analyze pure-amplitude and phase cross terms that appear in the Fermi golden rule rate equation that results from squaring the matrix element for mediated energy transfer. It is shown that pure-amplitude terms dominate in the near-zone when chromophores are close in proximity to one another (within a few nanometers), and phase cross terms dominate toward the far-zone when phase differences between different Feynman pathways begin to emerge. This can be understood in terms of physical attributes of the mediating photon, whose character becomes more real at long distances, coinciding with vanishing longitudinal components of the field, as transverse components begin to dominate.

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.

A Quantum Electrodynamics Description of Quantum Coherence and Damping in Condensed-Phase Energy Transfer

Quantum coherence in condensed-phase electronic resonance energy transfer (RET) is described within the context of quantum electrodynamics (QED) theory. Mediating dressed virtual photons (polaritons) are explicitly incorporated into the treatment, and coherence is understood within the context of interfering Feynman pathways connecting the initial and final states for the RET process. The model investigated is that of an oriented three-body donor, acceptor, and mediator RET system embedded within a dispersive and absorbing polarizable medium. We show how quantum coherence can significantly enhance the rate of RET and give a rigorous picture for subsequent decoherence that is driven by both phase and amplitude damping. Energy-conserving phase damping occurs as a result of geometric and dispersive effects and is associated with destructive interference between Feynman pathways. Dissipative amplitude damping, on the other hand, is attributed to vibronic relaxation and absorptivity of the medium and can be understood as virtual photons (polaritons) leaking into the environment. This model offers insights into the emergence of coherence and subsequent decoherence for energy transfer in photosynthetic systems.

Dispersion Interactions between Neutral Atoms and the Quantum Electrodynamical Vacuum

Dispersion interactions are long-range interactions between neutral ground-state atoms or molecules, or polarizable bodies in general, due to their common interaction with the quantum electromagnetic field. They arise from the exchange of virtual photons between the atoms, and, in the case of three or more atoms, are not additive. In this review, after having introduced the relevant coupling schemes and effective Hamiltonians, as well as properties of the vacuum fluctuations, we outline the main properties of dispersion interactions, both in the nonretarded (van der Waals) and retarded (Casimir–Polder) regime. We then discuss their deep relation with the existence of the vacuum fluctuations of the electromagnetic field and vacuum energy. We describe some transparent physical models of two- and three-body dispersion interactions, based on dressed vacuum field energy densities and spatial field correlations, which stress their deep connection with vacuum fluctuations and vacuum energy. These models give a clear insight of the physical origin of dispersion interactions, and also provide useful computational tools for their evaluation. We show that this aspect is particularly relevant in more complicated situations, for example when macroscopic boundaries are present. We also review recent results on dispersion interactions for atoms moving with noninertial motions and the strict relation with the Unruh effect, and on resonance interactions between entangled identical atoms in uniformly accelerated motion.

The Unified Theory of Resonance Energy Transfer According to Molecular Quantum Electrodynamics

An overview is given of the molecular quantum electrodynamical (QED) theory of resonance energy transfer (RET). In this quantized radiation field description, RET arises from the exchange of a single virtual photon between excited donor and unexcited acceptor species. Diagrammatic time-dependent perturbation theory is employed to calculate the transfer matrix element, from which the migration rate is obtained via the Fermi golden rule. Rate formulae for oriented and isotropic systems hold for all pair separation distances, R, beyond wave function overlap. The two well-known mechanisms associated with migration of energy, namely the R−6 radiationless transfer rate due to Förster and the R−2 radiative exchange, correspond to near- and far-zone asymptotes of the general result. Discriminatory pair transfer rates are also presented. The influence of an environment is accounted for by invoking the polariton, which mediates exchange and by introducing a complex refractive index to describe local field and screening effects. This macroscopic treatment is compared and contrasted with a microscopic analysis in which the role of a neutral, polarizable and passive third-particle in mediating transfer of energy is considered. Three possible coupling mechanisms arise, each requiring summation over 24 time-ordered diagrams at fourth-order of perturbation theory with the total rate being a sum of two- and various three-body terms.

Symmetries, Conserved Properties, Tensor Representations, and Irreducible Forms in Molecular Quantum Electrodynamics

In the wide realm of applications of quantum electrodynamics, a non-covariant formulation of theory is particularly well suited to describing the interactions of light with molecular matter. The robust framework upon which this formulation is built, fully accounting for the intrinsically quantum nature of both light and the molecular states, enables powerful symmetry principles to be applied. With their origins in the fundamental transformation properties of the electromagnetic field, the application of these principles can readily resolve issues concerning the validity of mechanisms, as well as facilitate the identification of conditions for widely ranging forms of linear and nonlinear optics. Considerations of temporal, structural, and tensorial symmetry offer significant additional advantages in correctly registering chiral forms of interaction. More generally, the implementation of symmetry principles can considerably simplify analysis by reducing the number of independent quantities necessary to relate to experimental results to a minimum. In this account, a variety of such principles are drawn out with reference to applications, including recent advances. Connections are established with parity, duality, angular momentum, continuity equations, conservation laws, chirality, and spectroscopic selection rules. Particular attention is paid to the optical interactions of molecules as they are commonly studied, in fluids and randomly organised media.

Resonance interaction energy between two entangled atoms in a photonic bandgap environment

We consider the resonance interaction energy between two identical entangled atoms, where one is in the excited state and the other in the ground state. They interact with the quantum electromagnetic field in the vacuum state and are placed in a photonic-bandgap environment with a dispersion relation quadratic near the gap edge and linear for low frequencies, while the atomic transition frequency is assumed to be inside the photonic gap and near its lower edge. This problem is strictly related to the coherent resonant energy transfer between atoms in external environments. The analysis involves both an isotropic three-dimensional model and the one-dimensional case. The resonance interaction asymptotically decays faster with distance compared to the free-space case, specifically as 1/r² compared to the 1/r free-space dependence in the three-dimensional case, and as 1/r compared to the oscillatory dependence in free space for the one-dimensional case. Nonetheless, the interaction energy remains significant and much stronger than dispersion interactions between atoms. On the other hand, spontaneous emission is strongly suppressed by the environment and the correlated state is thus preserved by the spontaneous-decay decoherence effects. We conclude that our configuration is suitable for observing the elusive quantum resonance interaction between entangled atoms.

One- and two-photon absorption in solution: the effects of a passive auxiliary beam

The efficiencies of one- and two-photon absorption by chromophores in solution may be significantly modified by a sufficiently intense beam of off-resonant light. A molecular analysis based on quantum electrodynamics (QED) fully accounts for this phenomenon of laser-modified absorption. A time-dependent perturbation-theory treatment describes the process in terms of stimulated forward Rayleigh-scattering of the auxiliary beam occurring simultaneously with the absorption interaction(s). Our formulation accommodates media modifications to the basic character of light-matter interactions, taking into account the refractive and dispersive properties of a solution-phase environment. This introduces the bulk refractive index of the solvent directly into the QED framework. The measurable electronic response of molecules freely rotating in solution is defined by an average of all orientations. We explicitly derive fixed-orientation and rotationally averaged calculations for the Fermi-rule rate of laser-modified one- and two-photon absorption. For a given beam polarization geometry, the solution-phase molecular response is expressible as a set of natural invariant scalars. These results reveal details of the dependence on the beam polarisations and on the rotationally averaged molecular response: we illustrate the breadth of variation available via geometric manipulation of beam polarization, and raise new possibilities for quantum weak measurements of laser states.

UNUSUAL LASER-INDUCED ABSORPTIONS OF Ca+-FORMALDEHYDE: MOLECULAR ORBITAL INTERACTION

We have theoretically studied the photodissociation spectroscopy of Ca +-formaldehyde complex using the TD-B2-PLYP method. The SDD pseudopotential and basis sets for Ca and 6-31++G (2df, 2pd) basis sets for C , H , and O atoms were employed in all calculations. In this way, we have reassigned the photodissociation spectroscopy of this complex. All experimentally observed spectral features can be well explained by our calculation. Besides the charge–dipole interaction, a strong molecule–orbital interaction also exists in the excited states and plays an important role in photoexcitation of the Ca+–CH2O complex.

A molecular theory for two-photon and three-photon fluorescence polarization

In the analysis of molecular structure and local order in heterogeneous samples, multiphoton excitation of fluorescence affords chemically specific information and high-resolution imaging. This report presents the results of an investigation that secures a detailed theoretical representation of the fluorescence polarization produced by one-, two-, and three-photon excitations, with orientational averaging procedures being deployed to deliver the fully disordered limits. The equations determining multiphoton fluorescence response prove to be expressible in a relatively simple, generic form, and graphs exhibit the functional form of the multiphoton fluorescence polarization. Amongst other features, the results lead to the identification of a condition under which the fluorescence produced through the concerted absorption of any number of photons becomes completely unpolarized. It is also shown that the angular variation of fluorescence intensities is reliable indicator of orientational disorder.

Macroscopic quantum electrodynamics and duality

We discuss under what conditions the duality between electric and magnetic fields is a valid symmetry of macroscopic quantum electrodynamics. It is shown that Maxwell's equations in the absence of free charges satisfy duality invariance on an operator level, whereas this is not true for Lorentz forces and atom-field couplings in general. We prove that derived quantities such as Casimir forces, local-field corrected decay rates, as well as van der Waals potentials are invariant with respect to a global exchange of electric and magnetic quantities. This exact symmetry can be used to deduce the physics of new configurations on the basis of already established ones.

Macroscopic quantum electrodynamics - Concepts and applications

In this article, we review the principles of macroscopic quantum electrodynamics and discuss a variety of applications of this theory to medium-assisted atom-field coupling and dispersion forces. The theory generalises the standard mode expansion of the electromagnetic fields in free space to allow for the presence of absorbing bodies. We show that macroscopic quantum electrodynamics provides the link between isolated atomic systems and magnetoelectric bodies, and serves as an important tool for the understanding of surface-assisted atomic relaxation effects and the intimately connected position-dependent energy shifts which give rise to Casimir—Polder and van der Waals forces.