Formulation Of Quantum Electrodynamics Research Articles

QED in dispersive and absorptive media

We develop a formulation of quantum electrodynamics in the presence of a dispersive and absorptive medium, giving a unified description of both relativistic and nonrelativistic interactions. It is based on using the electric field as the fundamental dynamical variable and introducing extra dynamical variables for the medium. As an application, we consider the Lamb shift in the presence a dielectric occupying a half-space.

MONTE CARLO CALCULATION OF THE LATERAL CASIMIR FORCES BETWEEN RECTANGULAR GRATINGS WITHIN THE FORMALISM OF LATTICE QUANTUM FIELD THEORY

We propose a new Monte Carlo method for calculation of the Casimir forces. Our method is based on the formalism of noncompact lattice quantum electrodynamics. This approach has been tested in the simplest case of two ideal conducting planes. After this the method has been applied to the calculation of the lateral Casimir forces between two ideal conducting rectangular gratings. We compare our calculations with the results of PFA and "Optimal" PFA methods.

Effect of Medium Chirality on the Rate of Resonance Energy Transfer

Resonance energy transfer (RET) between two chromophores in an absorptive and dispersive chiral medium is investigated using a quantum electrodynamical formulation. To accurately describe such an environment involves the introduction of electric displacement and auxiliary magnetic field operators that are solutions of the Drude-Born-Fedorov equations and the time-harmonic Maxwell equations. Perturbation theory within the electric and magnetic dipole approximation is used in the derivation of the probability amplitude for energy transfer. Expressions for the contributions to the RET rate arising from the pure electric dipole term, replacing one of the chiral chromophores by its corresponding enantiomer in the mixed electric-magnetic dipole term, and the pure magnetic dipole contribution are obtained. In the near-zone limit in a nonabsorptive medium, the medium chirality amplifies the pure electric dipole contribution to the rate relative to that in a racemic mixture and also increases the discriminatory contribution, but to a lesser extent relative to the pure electric dipole term. On the other hand, under the same conditions, the medium chirality does not affect the pure magnetic dipole contribution to the rate. Measurements of the rate could be used to obtain information on the magnitude of the chirality admittance or concentration of chiral species, by comparing with the rate in an environment comprised of a racemic mixture of the enantiomers. This method could allow for the analysis of macroscopically heterogeneous systems that are comprised of enantiomers and where the chromophores experiencing RET are located in regions of interest.

Compton scattering at high intensities

High-intensity Compton scattering takes place when an electron beam is brought into collision with a high power laser. We briefly review the main intensity signatures using the formalism of strong-field quantum electrodynamics.

Above-threshold ionization in the x-ray regime

Two-photon above-threshold ionization processes in the x-ray regime are studied using atomic hydrogen as a model system. Within the minimal-coupling formalism of nonrelativistic quantum electrodynamics, two distinct interactions---$\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{A}}\ensuremath{\cdot}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{p}}$ in second order and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{A}}}^{2}$ in first order---contribute to the two-photon absorption amplitude. The relative importance of these two interactions is assessed. It is found that above a photon energy of 6.8 keV, the contribution from ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{A}}}^{2}$ to the total two-photon absorption cross section dominates. In this high-energy regime, above-threshold ionization is a nonsequential purely nondipole process. Rate equations are employed to calculate the probabilities of ionization by Compton scattering, one-photon absorption, and two-photon absorption.

Theoretical and experimental investigation of radiative decay rates in active slot waveguides

We present a quantum-electrodynamical formalism to study the spontaneous emission from dipoles embedded in a non-absorbing and lossless multilayer dielectric structure. In this model the electromagnetic field is quantized by a proper choice of a complete and orthonormal set of classical modes and the analytical expressions for the emission rates are obtained within the framework of perturbation theory. We apply our model to investigate the 1.54??m transition of Er3+-doped SiO2 thin layers acting as active material in planar slot waveguides in polycrystalline silicon. The theoretical results show that a strong reduction of the radiative lifetime does occur in the slot waveguide. Furthermore, by using the theoretical analysis together with photoluminescence measurements, we estimate also the radiative efficiency which is found to be only slightly reduced with respect to the value for Er3+ in a bulk of SiO2. These results are important for future realization of silicon-compatible active optical devices and show the relevance of our model to study the spontaneous emission processes in multilayer structures.

Resonance energy transfer: When a dipole fails

The Coulombic coupling of electric dipole (E1) transition moments is the most commonly studied and widely operative mechanism for energy migration in multichromophore systems. However a significant number of exceptions exist, in which donor decay and/or acceptor excitation processes are E1-forbidden. The alternative transfer mechanisms that can apply in such cases include roles for higher multipole transitions, exciton- or phonon-assisted interactions, and non-Coulombic interactions based on electron exchange. A quantum electrodynamical formulation provides a rigorous basis to assess the first of these, specifically addressing the relative significance of higher multipole contributions to the process of energy transfer in donor-acceptor systems where electric dipole transitions are precluded by symmetry. Working within the near-zone limit, where donor-acceptor separations are small in comparison to the chromophore scale, the analysis highlights the contributions of both electric quadrupole-electric quadrupole (E2-E2) coupling and the seldom considered second-order electric dipole-electric dipole (E1(2)-E1(2)) coupling. For both forms of interaction, experimentally meaningful rate equations are secured by the use of orientational averaging, and the mechanisms are analyzed with reference to systems in which E1-forbidden transitions are commonly reported.

Modification of erbium radiative lifetime in planar silicon slot waveguides

The authors report a systematic study of the lifetime of the 1.54 μm transition of Er3+-doped SiO2 thin film as active material in planar slot waveguides in polycrystalline silicon. The lifetime shows a strong reduction when compared with values measured in three other configurations. The experimental results, combined with a rigorous quantum-electrodynamical formalism, are consistent with a sizable increase in both the radiative and nonradiative decay rates of Er3+ transition in slot waveguide. The radiative efficiency is only slightly reduced with respect to Er3+ in the bulk oxide, this result being important for future realization of Si-compatible active optical devices.

On the interactions between molecules in an off-resonant laser beam: Evaluating the response to energy migration and optically induced pair forces

Electronically excited molecules interact with their neighbors differently from their ground-state counterparts. Any migration of the excitation between molecules can modify intermolecular forces, reflecting changes to a local potential energy landscape. It emerges that throughput off-resonant radiation can also produce significant additional effects. The context for the present analysis of the mechanisms is a range of chemical and physical processes that fundamentally depend on intermolecular interactions resulting from second and fourth-order electric-dipole couplings. The most familiar are static dipole-dipole interactions, resonance energy transfer (both second-order interactions), and dispersion forces (fourth order). For neighboring molecules subjected to off-resonant light, additional forms of intermolecular interaction arise in the fourth order, including radiation-induced energy transfer and optical binding. Here, in a quantum electrodynamical formulation, these phenomena are cast in a unified description that establishes their inter-relationship and connectivity at a fundamental level. Theory is then developed for systems in which the interplay of these forms of interaction can be readily identified and analyzed in terms of dynamical behavior. The results are potentially significant in Forster measurements of conformational change and in the operation of microelectromechanical and nanoelectromechanical devices.

Relativisticn-fermion wave equations in quantum electrodynamics

The variational method in a reformulated Hamiltonian formalism of quantum electrodynamics is used to derive relativistic wave equations for a system consisting of $n$ fermions and antifermions. Simple Fock-space variational trial states are used to obtain the relativistic $n$-body equations. The derived kernels of these equations (i.e., momentum-space relativistic potentials) include one-photon exchange and virtual annihilation interactions. The equations are shown to have the Schr\odinger nonrelativistic limit. Application to the particular cases of positronium (Ps), positronium negative ion $({\text{Ps}}^{\ensuremath{-}})$, and positronium molecule (${\text{Ps}}_{2}$, ${e}^{\ensuremath{-}}{e}^{+}{e}^{\ensuremath{-}}{e}^{+}$) are discussed.

Quantum Field Theory and Beyond

It is a great pleasure and an honor to give the first talk at this symposium honoring Yukawa and Tomonaga, two giants, two pioneers of 20th century theoretical physics. I never had the pleasure of meeting them, and I look forward very much to hearing some of the stories of their lives and contributions, but I of course know very well their great contributions to elementary particle physics and to quantum field theory (QFT). Yukawa first applied QFT to the strong nuclear force, which was quite a step given that field theory had just been born a few years ago and only applied to the obvious case of electromagnetism. And he predicted the existence of the heavy meson as the carrier of the force, estimating roughly correctly its mass from the range of the nuclear force. In this sense, this was the first particle that was predicted, not on the basis of quantum theory as Einstein predicted the photon, or of symmetries as Dirac predicted the positron, but as a consequence of analysis of phenomena of elementary particle physics. It was certainly not the last particle to be predicted. Tomonaga of course developed the relativistically covariant formulation of quantum electrodynamics in parallel with Feynman and Schwinger and the theory of renormalization, thus establishing the foundations of the modern QFT. So in my talk, I am going to briefly discuss the triumph of QFT, which indeed by the end of the 20th century was triumphant as no physical theory has ever been in the past. I will also discuss the lessons that we have learned from the success of the standard model, most importantly the importance of symmetry, and the profound ways in which it appears in nature. The other important lesson we have learned goes under the name of the renormalization group or effective dynamics. Then I will briefly discuss the limitations of QFT as we turn to study the quantum dynamics of space and time, and go on to what lies beyond QFT, which I think is string theory.

Optically induced inter-particle forces: from the bonding of dimers to optical electrostriction in molecular solids

The quantum electrodynamical formulation of the Casimir–Polder interaction invites a consideration of optically induced inter-particle forces, which arise in the same level of perturbation theory. For the observation of such effects, quantitative assessments of the coupling mechanism suggest levels of intensity that are now routinely available from pulsed lasers. In this paper, a theoretical analysis of the principal mechanism is followed by a development for two specific systems, chosen to illustrate the broad significance and the range of systems in which such effects might be manifest. The first system is a van der Waals dimer, a loosely bound and essentially isolated molecular pair in which a small optically induced shift in the equilibrium bond length proves to be well within the limits of measurement by microwave rotational spectroscopy. The second system illustrates the opposite extreme, where an optically induced modification of the forces between densely packed molecules in the condensed phase is shown to produce anisotropic patterns of laser-induced compression and expansion, an effect termed optical electrostriction. Again, such an effect should be readily measurable, although the necessary conditions are such that a number of secondary effects might also be likely to arise. The experimental challenge of precluding those secondary effects in the condensed phase and unequivocally identifying optically induced intermolecular forces is discussed. Possible applications are also entertained, including optical actuators for nanoscale electromechanical systems.

Nonrelativistic QED approach to the Lamb shift

We calculate the one- and two-loop corrections of order alpha(Zalpha)^6 and alpha^2(Zalpha)^6 respectively, to the Lamb shift in hydrogen-like systems using the formalism of nonrelativistic quantum electrodynamics. We obtain general results valid for all hydrogenic states with nonvanishing orbital angular momentum and for the normalized difference of S-states. These results involve the expectation value of local effective operators and relativistic corrections to Bethe logarithms. The one-loop correction is in agreement with previous calculations for the particular cases of S, P, and D states. The two-loop correction in the order alpha^2(Zalpha)^6 includes the pure two-loop self-energy and all diagrams with closed fermion loops. The obtained results allow one to obtain improved theoretical predictions for all excited hydrogenic states.

Weak localization—an experimental tool to investigate electromagnetic vacuum fluctuations

In the present paper we demonstrate that some important experimentally observed features of so-called weak localization, a quantum-mechanical effect par excellence which is rather difficult to treat directly by application of formalism of quantum electrodynamics, may be alternatively on a quite elementary level treated quasi-classically using the concept of zero-point electromagnetic fluctuations as introduced in stochastic electrodynamics. Such an approach was applied to an analysis of original experimental data obtained on InP-based semiconductor structures with δ-layers, i.e. self-consistent two-dimensional system which is known to enable investigation of the WL effect at appreciably high temperatures.

Modification of electron-hole excitations for a quantum well embedded in an asymmetric dielectric structure

Starting from the conventional quantum electrodynamical formulation in Coulomb gauge we show that the Coulomb interaction of an electronhole in a quantum well (QW) embedded in an asymmetric dielectric structure with different dielectric constants in barrier regions yields a nondiagonal term of electron-hole pair excitation and the electron-hole vacuum state cannot be longer than the ground state of the system. A Bogoliubov transformation with a representation of new quasiparticles is provided to eliminate the nondiagonal term. The linear response function describing the modified exciton-polariton effect of the system is obtained. Analytical expressions are found for the effective mass of quasiparticles, the modified band gap, and the exciton coupling potential for a quasi-electron-hole pair. The exciton-polariton coupling turns out to contain an additional term originating from intraband processes. It is shown that the effect is significant for QW's with small thicknesses and for semiconductors with narrow band gaps.

THRESHOLD PHENOMENA IN INTENSE ELECTROMAGNETIC FIELDS

The influence of intense electromagnetic fields on the formation and decay of quasistationary states of different quantum systems is investigated based on exact solutions of quantum equations for charged particle motion. The method allows examining systems where a spontaneous decay may occur as well as phenomena that occur only under the action of the field. Different values of the total magnetic moment of the system are taken into account in this consideration. A consistent use of the analytic continuation method allows obtaining nonlinear equations that determine complex energies in an external field. The asymptotic expansions for real and imaginary energy values under the action of weak and strong electromagnetic fields are investigated. The developed approach allows establishing the characteristic values for the length parameters that determine the formation of the processes in superstrong fields. We note that a significant decrease of distances in strong fields may lead to effects with a new characteristic length scale, characterizing a modified quantum electrodynamics (QED) formalism, namely, the “QED with the fundamental mass” formalism.

Self-energy Effects on Nuclear Magnetic Resonance Parameters within Quantum Electrodynamics Perturbation Theory

A theory for the calculation of self-energy corrections to the nuclear magnetic parameters is given in this paper. It is based on the S-matrix formulation of bound-state quantum electrodynamics (QED). Explicit expressions for the various terms of the S-matrix are given. The interpretation of the self-energy, one- and two-vertex terms and some perspective for possible future developments are discussed.

A quantum electrodynamics framework for the nonlinear optics of twisted beams

A theory is presented for the detailed formulation of the nonlinear optics of laser beams endowed with orbital angular momentum. Following an introductory excursion into the general principles of such twisted beams, a quantum electrodynamical formulation is developed for representing the photonics of their interaction with matter. Detailed results are given for Laguerre–Gaussian beams in the large-Rayleigh-range limit. Utilization of the theory in nonlinear optics is illustrated by application to second-harmonic generation.

A THEORY OF LUMINESCENCE OF LIGHT-COLLECTING MOLECULAR SYSTEMS *

Expressions are obtained for the intensity and the quantum yield of the sensitized luminescence of the chromophore that plays the role of a reaction center in the simplest model trichromophore molecular [light‐collecting] antenna which is so constructed and so oriented in space that the irradiation photons coherently excite its other two chromophores‐pigments. The quantum electrodynamics formalism which takes into account the radiative dissipative interaction between the pigments and the reaction center of the antenna was used. The comparative analysis of the obtained expressions with the corresponding expressions for the luminescence of a bichromophore molecular system, differing from the trichromophore antenna by the absence of one of the pigments, has shown that the collective dissipative interaction of the pigments with the reaction center of the antenna can be considered as a highly efficient mechanism of [light collection] in molecular antennas.

On the use of many-body perturbation theory and quantum-electrodynamics in molecular electronic structure theory

Many-body perturbation theory is firmly established in molecular electronic structure studies both as a method of calculation in its own right and in underpinning other approaches to the electron correlation problem, such as coupled electron pair approximations and various cluster expansions. The central pillar of the many-body perturbation theory is the linked diagram theorem obtained by Goldstone using the method of Feynman graphs to enumerate the terms of the perturbation series. Feynman had introduced his graphs in his formulation of quantum electrodynamics. Goldstone restricted his analysis to the non-relativistic many-body problem, so that interactions were taken to be instantaneous and the effects of relativity were ignored. In recent years, the growing interest in the treatment of relativistic and quantum electrodynamic effects in atoms and molecules has necessitated the re-introduction of physics that has been known for over forty years. A key to this development for molecular systems is a rigorous and robust implementation of the algebraic approximation for Dirac and Dirac-like equations. The algebraic approximation provides a representation of both the positive-energy and the negative-energy branches of the Dirac spectrum. Relativistic many-body perturbation theory, relativistic coupled pair approximations and relativistic coupled cluster theories can be formulated within the ‘no-virtual-pair’ approximation. Such formulations are restricted to the positive energy branch of the spectrum. However, the negative energy states make an essential contribution to the description of atomic and molecular electronic structure. The investigation of this contribution is facilitated by proper implementation of the algebraic approximation using formulations which are amenable to systematic refinement.