Symmetries, Conserved Properties, Tensor Representations, and Irreducible Forms in Molecular Quantum Electrodynamics
TL;DR: 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, and a variety of symmetry principles are drawn out with reference to applications.
Abstract: 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
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TL;DR: In this article, the orbital angular momentum (OAM) conveyed by optical vortices has been investigated in both chiral and achiral media, and the authors established mechanisms at play that entail an unconventional manifestation of optical spin-orbit interactions, engaging transition electric quadrupole moments.
Abstract: There is recurrent interest in the orbital angular momentum (OAM) conveyed by optical vortices, which are structured beams with a helically twisted wave front. Particular significance is attached to the issue of how material interactions with light conveying OAM might prove sensitive to the handedness and degree of twist in the optical wave front. As a result of recent experimental and theoretical studies, the supposition that beams with OAM might enable spectroscopic discrimination between oppositely handed forms of matter has become a renewed focus of attention. Some of the tantalizing conclusions that are beginning to emerge from this research have, however, not yet established a definitive basis for a supporting mechanism. To resolve this problem requires the development of theory to support a faithful representation, and a thorough understanding, of the fundamental molecule-photon physics at play in such optical processes - even for processes as basic as absorption. The present analysis establishes mechanisms at play that entail an unconventional manifestation of optical spin-orbit interactions, engaging transition electric-quadrupole moments. Powerful symmetry principles prove to render distinctively different criteria governing the exhibition of two-dimensional (2D) and 3D chirality. These results elucidate the operation of such effects, identifying their responsibility for discriminatory optical interactions of various forms in both chiral and achiral media.
41 citations
TL;DR: In this article, a broad guide to cutting-edge applications of quantum electrodynamics is provided, providing an outline of its underlying foundation and an examination of its role in photon science.
Abstract: One of the key frameworks for developing the theory of light–matter interactions in modern optics and photonics is quantum electrodynamics (QED). Contrasting with semiclassical theory, which depicts electromagnetic radiation as a classical wave, QED representations of quantized light fully embrace the concept of the photon. This tutorial review is a broad guide to cutting-edge applications of QED, providing an outline of its underlying foundation and an examination of its role in photon science. Alongside the full quantum methods, it is shown how significant distinctions can be drawn when compared to semiclassical approaches. Clear advantages in outcome arise in the predictive capacity and physical insights afforded by QED methods, which favors its adoption over other formulations of radiation–matter interaction.
36 citations
Cites background from "Symmetries, Conserved Properties, T..."
...[30,31]—their effect can also be correctly identified as the result of virtual photon coupling with static multipoles of the corresponding electric or magnetic kind....
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TL;DR: Casting the fundamental theory in terms of formal photon-molecule couplings enables the quantum mechanisms involved in all such phenomena to be clearly resolved and provide fresh physical insights.
Abstract: Optical polarization features associated with the fundamental processes of molecular fluorescence and resonance energy transfer are in general studied with reference to plane polarizations. When any of the species involved is chiral, the associated emission processes may exhibit an element of circular polarization-a degree of optical helicity. Although usually a minor effect, some systems can exhibit a sizeable component of circularly polarized luminescence, whose helicity correlates with the enantiomeric form. In studies of multi-component systems, in which initial excitation of a donor species-followed by energy transfer-leads to emission from an acceptor molecule, the handedness of both donor and acceptor may influence output circularity. In systems with an achiral acceptor, a degree of fluorescence circularity may be influenced by the handedness of a chiral donor, but this should not be construed in terms of 'conveying' chirality. Chiral molecules may also play a passive role by inducing helicity in the fluorescence from achiral neighbours, and further tiers of complexity arise if the initial excitation is itself of circular polarization. In all such processes, symmetry principles play a major role in determining a sensitivity to molecular handedness, and their detailed consideration enables a range of new experimental procedures to be identified. Casting the fundamental theory in terms of formal photon-molecule couplings enables the quantum mechanisms involved in all such phenomena to be clearly resolved. The results provide fresh physical insights, and establish connections across a range of indirectly related chiroptical phenomena including induced circular dichroism.
15 citations
Cites background from "Symmetries, Conserved Properties, T..."
...are the same as those we can draw from spatial symmetry [38, 39], while the...
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TL;DR: A photon-based perspective on these features enables regard to be given to the salient quantum operators, paying heed to quantum uncertainty limits of observables, and supports a persistence in features of significance for the material interactions of vortex beams.
Abstract: Optical vortices are beams of laser light with screw symmetry in their wavefront. With a corresponding azimuthal dependence in optical phase, they convey orbital angular momentum, and their methods of production and applications have become one of the most rapidly accelerating areas in optical physics and technology. It has been established that the quantum nature of electromagnetic radiation extends to properties conveyed by each individual photon in such beams. It is therefore of interest to identify and characterize the symmetry aspects of the quantized fields of vortex radiation that relate to the beam and become manifest in its interactions with matter. Chirality is a prominent example of one such aspect; many other facets also invite attention. Fundamental CPT symmetry is satisfied throughout the field of optics, and it plays significantly into manifestations of chirality where spatial parity is broken; duality symmetry between electric and magnetic fields is also involved in the detailed representation. From more specific considerations of spatial inversion, amongst which it emerges that the topological charge has the character of a pseudoscalar, other elements of spatial symmetry, beyond simple parity inversion, prove to repay additional scrutiny. A photon-based perspective on these features enables regard to be given to the salient quantum operators, paying heed to quantum uncertainty limits of observables. The analysis supports a persistence in features of significance for the material interactions of vortex beams, which may indicate further scope for suitably tailored experimental design.
15 citations
TL;DR: In this paper, optical cavities for enhancing vibrational circular dichroism have been introduced to enhance the sensitivity of chiral molecules to incident left and right-handed circularly polarized light for sensing the handedness of molecules.
Abstract: The differential response of chiral molecules to incident left- and right-handed circularly polarized light is used for sensing the handedness of molecules. Currently, significant effort is directed toward enhancing weak differential signals from the molecules, with the goal of extending the capabilities of chiral spectrometers to lower molecular concentrations or small analyte volumes. Previously, optical cavities for enhancing vibrational circular dichroism have been introduced. Their enhancements are mediated by helicity-preserving cavity modes which maintain the handedness of light due to their degenerate TE and TM components. In this article, we simplify the design of the cavity and numerically compare it with the previous one using an improved model for the response of chiral molecules. We use parameters of molecular resonances to show that the cavities are capable of bringing the vibrational circular dichroism signal over the detection threshold of typical spectrometers for concentrations that are one to three orders of magnitude smaller than those needed without the cavities, for a fixed analyte volume. Frequency resolutions of current spectrometers result in enhancements of more than one order (two orders) of magnitude for the new (previous) design. With improved frequency resolution, the new design achieves enhancements of three orders of magnitude. We show that the TE/TM degeneracy in perfectly helicity-preserving modes is lifted by factors that are inherent to the cavities. More surprisingly, this degeneracy is also lifted by the molecules themselves due to their lack of electromagnetic duality symmetry, that is, due to the partial change of helicity during the light-molecule interactions.
11 citations
References
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Book•
01 Jan 1995
TL;DR: In this article, the authors present a systematic account of optical coherence theory within the framework of classical optics, as applied to such topics as radiation from sources of different states of coherence, foundations of radiometry, effects of source coherence on the spectra of radiated fields, and scattering of partially coherent light by random media.
Abstract: This book presents a systematic account of optical coherence theory within the framework of classical optics, as applied to such topics as radiation from sources of different states of coherence, foundations of radiometry, effects of source coherence on the spectra of radiated fields, coherence theory of laser modes, and scattering of partially coherent light by random media. The book starts with a full mathematical introduction to the subject area and each chapter concludes with a set of exercises. The authors are renowned scientists and have made substantial contributions to many of the topics treated in the book. Much of the book is based on courses given by them at universities, scientific meetings and laboratories throughout the world. This book will undoubtedly become an indispensable aid to scientists and engineers concerned with modern optics, as well as to teachers and graduate students of physics and engineering.
7,658 citations
TL;DR: The condition of self-adjointness as discussed by the authors ensures that the eigenvalues of a Hamiltonian are real and bounded below, replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive.
Abstract: The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive. These $\mathrm{PT}$ symmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase space. This paper describes the unusual classical and quantum properties of these theories.
5,626 citations
TL;DR: This work demonstrates experimentally passive PT-symmetry breaking within the realm of optics, which leads to a loss induced optical transparency in specially designed pseudo-Hermitian guiding potentials.
Abstract: In 1998, Bender and Boettcher found that a wide class of Hamiltonians, even though non-Hermitian, can still exhibit entirely real spectra provided that they obey parity-time requirements or PT symmetry. Here we demonstrate experimentally passive PT-symmetry breaking within the realm of optics. This phase transition leads to a loss induced optical transparency in specially designed pseudo-Hermitian guiding potentials.
2,409 citations
TL;DR: In this paper, it was shown that coupled optical microcavities bear all the hallmarks of parity-time symmetry; that is, the system dynamics are unchanged by both time-reversal and mirror transformations.
Abstract: It is now shown that coupled optical microcavities bear all the hallmarks of parity–time symmetry; that is, the system’s dynamics are unchanged by both time-reversal and mirror transformations. The resonant nature of microcavities results in unusual effects not seen in previous photonic analogues of parity–time-symmetric systems: for example, light travelling in one direction is resonantly enhanced but there are no resonance peaks going the other way.
2,061 citations
TL;DR: The physical mechanisms which can produce second-order dielectric polarization are discussed on the basis of a simple extension of the theory of dispersion in ionic crystals in this paper.
Abstract: The physical mechanisms which can produce second-order dielectric polarization are discussed on the basis of a simple extension of the theory of dispersion in ionic crystals. Four distinct mechanisms are described, three of which are related to the anharmonicity, second-order moment, and Raman scattering of the lattice. These mechanisms are strongly frequency dependent, since they involve ionic motions with resonant frequencies lower than the light frequency. The other mechanism is related to electronic processes of higher frequency than the light, and, therefore, is essentially flat in the range of the frequencies of optical masers. Since this range lies an order of magnitude higher than the ionic resonances, the fourth mechanism may be the dominant one. On the other hand, a consideration of the linear electro-optic effect shows that the lattice is strongly involved in this effect, and, therefore, may be very much less linear than the electrons. It is shown that the question of the mechanism involved in the second harmonic generation of light from strong laser beams may be settled by experiments which test the symmetry of the effect. The electronic mechanism is subject to further symmetry requirements beyond those for piezoelectric coefficients. In many cases, this would greatly reduce the number of independent constants describing the effect. In particular, for quartz and KDP there would be a single constant.
2,005 citations
"Symmetries, Conserved Properties, T..." refers background in this paper
...As a corollary to all such cases, however, it is of interest that in a specific case where all the photons involved in the interaction have identical polarization, then, for the same reasons discussed in Section 6, the results will indeed be consistent with Kleinman symmetry....
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...The essential flaws and general inapplicability of Kleinman symmetry were in fact quickly pointed out by Wagnière [118]....
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...Such an approach, which became widespread owing to its appealing simplicity, is largely credited to Kleinman [117], whose expressly limited intention was indeed to make the interpretation of early experiments in nonlinear optics more tractable....
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