In this review the authors describe some of the advances in the quantum electrodynamical formulation of theory for molecular photonics. Earlier work has been extended and reformulated for application to real dispersive media—as reflected in the new treatment of refractive, dissipative, and resonance properties. Applications of the new theory have revealed new quantum optical features in two quite different aspects of the familiar process of second harmonic generation, one operating through local coherence within small particles and the other, a coherence between the quantum amplitudes for fundamental and harmonic excitation. Where the salient experiments have been performed, they exactly match the theoretical predictions.
In this review the authors describe some of the advances in the quantum electrodynamical formulation of theory for molecular photonics. Earlier work has been extended and reformulated for application to real dispersive media—as reflected in the new treatment of refractive, dissipative, and resonance properties. Applications of the new theory have revealed new quantum optical features in two quite different aspects of the familiar process of second harmonic generation, one operating through local coherence within small particles and the other, a coherence between the quantum amplitudes for fundamental and harmonic excitation. Where the salient experiments have been performed, they exactly match the theoretical predictions.
Interactions between light and molecular matter featuring photon absorption are commonly associated with excitation of individual chromophores. Subsequent relaxation is achieved through numerous mechanisms, such as scattering and energy transfer to neighbouring chromophores. The efficiency of such processes depends on many factors, including the intensity and wavelength of the optical input, the absorption cross-section of the molecule and the relative orientation of molecular components. New photonic materials are developed on the principle that such factors are controllable, duly tailoring the system to suit new technological applications. The parameters that determine the linear response in multicomponent materials are typically assessed within the theoretical framework of classical optics. However, with improved interest and capability in fabricating nanoscale structures (especially those that exhibit quantum effects), it is becoming increasingly relevant to develop theory that more faithfully represents how individual photons engage with matter. In such constructs, the interaction of materials with optical waves and photons is highly dependent on local molecular environment, therefore surrounding structures and ancillary species exert forms of influence on the photophysical processes inherent within dielectric media. At optical wavelengths where the secondary structure displays little intrinsic optical absorption, the role of such components is often interpreted as modifying the input through a corrective local index of refraction. Although expedient in the discussion of bulk properties of a macroscopic medium, it is reasonably supposed at a local chromophore-photon level that optical mechanisms operate in a different fashion. Using a fully quantized approach to the representation of local molecular electronic structure and electrodynamics, this research develops rigorous theory and a corresponding physical interpretation of how photon absorption, scattering and energy transfer are modified by vicinal, non-absorbing chromophores. The results provide insight into the mechanisms achieved within multi-chromophore systems, highlighting factors that assist in the optimization of optical characteristics in designer materials.
The theory of optical birefringence is discussed from the point of view of the scattering of polarized photons by molecules using the framework of formal scattering theory and quantum electrodynamics. In Part One, those features from noncovariant quantum electrodynamics relevant to the molecular scattering of photons are reviewed. Chapter One contains an outline of classical electrodynamics in the Coulomb gauge, including the Stokes parameter and density matrix formulations of polarization. Chapter Two deals with the quantization of the radiation field, and the occupation number representation is defined. The quantum mechanical description of polarized light is outlined in Chapter Three: operator equivalents of the density matrix and Stokes parameters are invoked, the parameters themselves being obtained from the expectation values of the Stokes operators with the state vector of the photon. The Stokes parameter and density matrix are then applied to the polarization of a general beam containing an arbitrary number of photons, and some new methods are developed. The interaction of the electromagnetic field with bound electrons is formulated in Chapter Four in terms of a canonically transformed interaction Hamiltonian in which the multipole terms are explicit. Since each term is then gauge-invariant, this Hamiltonian is particularly suited to the application of diagrammatic perturbation theory which follows from the iteration of the scattering matrix in the interaction representation (Chapter Five). Also the extension of the theory to multiphoton processes is facilitated "because the field strength is explicit in the transformed Hamiltonian. The S-matrix connects the initial and final asymptotic states of the scattering system, and in Chapter Six the state vector and density operator of the scattered photon beam are obtained from those of the incident beam. Part Two contains the application of the above methods to a variety of linear and nonlinear optical birefringence effects in the absence or presence of external fields. In Chapter Seven, general equations are obtained for the polarization changes imposed on a forward scattered photon in terms of matrix elements of the reaction operator between plane polarized photon base states; whereas Chapter Eight extends this treatment to an n-photon beam, thereby encompassing the hyperpolarizability contributions to the polarization changes of the forward scattered beam. It is then demonstrated that the fundamental process in optical birefringence can be interpreted as an infinitesimal unitary transformation of the polarization spinor. Also the S-matrix approach to birefringence is compared with the methods used in crystal optics, and with the classical treatments of the scattering of polarized light by molecules. The general equations obtained for the polarization changes of the forward scattered beam are subsequently interpreted in the light of the physical circumstances appropriate to the bire- fringence effect of interest. In Chapters Nine, Ten, and Eleven, diagrammatic perturbation theory is used to obtain explicit expressions, in terms of molecular polarizability and rotation tensors, for the linear and nonlinear contributions to the polarization changes involved in natural optical activity, and in birefringence phenomena induced by static and optical electric and magnetic fields. The nonforward scattering of polarized photons by molecules is discussed in Part Three. General equations are calculated in Chapter Twelve for the azimuth, ellipticity, and depolarization ratio of the Rayleigh beam at any scattering angle and for any polarization of the incident beam. Explicit expressions in terms of molecular quantities are then obtained for the polarization at scattering angles of 90° and almost zero from both optically inactive and optically active molecules. It is demonstrated that a determination of the precise polarization state of the scattered beam can provide useful molecular information additional to that obtained from depolarization ratios alone. This is because the depolarization ratio depends on only the diagonal elements of the polarization density matrix and so does not convey all the information about the system. Raman scattering processes are contained in the formulation and the polarization of the Raman light at any scattering angle can be obtained. This is shown to be particularly useful for predicting the polarization of stimulated Raman light for any Raman-active liquid placed within a laser cavity. By extending the nonforward scattering formulation to incorporate multiphoton processes, equations are obtained in Chapter Thirteen for the ellipticity, azimuth, and depolarization ratio of the second harmonic wave at any scattering angle as a function of the incident polarization. Several specific situations are subsequently investigated. Finally, it is shown in Chapter Fourteen that the near-forw- ard Rayleigh and Raman scattering formulations provide an explanation for the observed polarization, as a function of the initial polarization, of the self-trapped filaments that arise from the self-focusing of an intense laser beam.
This thesis employs molecular quantum electrodynamical theory to analyse the interactions between light and matter for four main processes. The first to be considered is Raman scattering, where the effect of the electrodynamic environment for the centre of spectroscopic interest is considered. This is achieved by engaging a retarded dipole-dipole interaction between the centre and a neighbouring molecule. Physically, this is explained by a virtual photon between the pair of centres. The results predict characteristic new lines on the Raman spectrum, for the species, arising from the engagement of selection rules not limited to those of a two-photon process. \nThe second process, is hyper-Rayleigh scattering, in which a single multipolar coupling is considered in place of the more familiar electric dipole. This modification to the theory subverts the standard selection rules for a three-photon process, which can allow for second-harmonic emission to be generated by a centre of high symmetry, such as a centrosymmetric molecule. \nThe third process offers another means of subverting the standard selection rules for second-harmonic generation, namely by incorporating six-wave mixing. First, the general mechanism is developed and pertinent results are expressed for the widely-deployed depolarisation ratio. Following this, structured light is considered and by utilising orbital angular momentum (OAM) conservation arguments, the pair of harmonic photons are found to display quantum entanglement. Moreover, the relative magnitudes of the possible emissions are found to correspond directly to that of the binomial coefficients. \nThis thesis concludes with a family of novel structures capable of directly generating OAM light. This work exploits symmetry characteristics for a delocalised excitonic structure that can allow for a more complex multipolar emission than that of any isolated centres. The phase of the exciton is shown to display an azimuthal phase progression, a vortex feature most commonly associated with Laguerre-Gaussian light.
ABSTRACT Molecular polaritons, hybrid quasiparticles formed through the strong coupling between molecular transitions and confined electromagnetic modes, have opened a new era by the combination of quantum electrodynamics (QED) with molecular photonics. This review deals with the theoretical, computational, and experimental developments that have put molecular polaritons at the forefront of next‐generation quantum information processing, photonics, and molecular‐scale qubit engineering. Starting from the Pauli–Fierz Hamiltonian, and other QED‐like macroscopic, ab initio, and QED‐coupled‐cluster methods which provide chemically accurate descriptions of correlated electron–photon states. A major focus is placed on dipole‐mediated quantum gates using rotational and polaritonic qubits, where long‐range dipole–dipole interactions enable scalable, room‐temperature logic operations. The article further discusses cutting‐edge spectroscopic methods such as 2D femtosecond stimulated Raman scattering, ultrafast pump‐probe, and cavity‐enhanced Raman reveals dark‐state dynamics, coherence transfer, and vacuum‐modified photo dynamics. Finally, we highlight recent advances in implementing polariton‐based logic gates, qubit analogs, and entanglement schemes that preserve coherence. Together, these advances establish molecular polaritons as chemically versatile and technologically promising candidates for on‐chip quantum logic and room‐temperature quantum photonic circuits, uniting the experimental realizations with quantum optical theory to chart a pathway for scalable, tunable, and coherent quantum information technologies.
Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications.
The standard mathematical formalism of cavity QED leads us to consider photons as excitations of a quantum harmonic oscillator. Although it is one of the most familiar problems of quantum mechanics, some aspects of the quantum harmonic oscillator remain difficult to visualize, particularly in the rather abstract context of an electromagnetic field. Recently, modern microfabrication and refrigeration techniques have begun to allow the creation of nanoscale mechanical oscillators which can be cooled close to the quantum regime. Despite the extreme physical differences between an electromagnetic cavity and a nanomechanical resonator, both systems may be approximated by the same quantum harmonic oscillator model. However, the conceptual consequences of quantum behavior, and the challenges to physical intuition, are quite different in the two cases. Taking a mechanical point of view therefore allows fresh insight into the quantum harmonic oscillator problem. To illustrate the connection and how it may aid our understanding of light, the mathematical parallelism between an electromagnetic cavity and a mechanical resonator is demonstrated. Current nanomechanics experiments are discussed, and some possible quantum measurements are introduced. Finally, the discrepancies between the predictions of quantum mechanics and our experience of classical vibrating beams are considered, with an emphasis on how nanomechanics may be able to offer a new perspective on the nature of photons.