Quantum Electrodynamics Approach Research Articles

Opto-RF transduction in Er3+:CaWO4

We use an erbium doped CaWO4 crystal as a resonant transducer between the RF and optical domains at 12 GHz and 1532 nm respectively. We employ a RF resonator to enhance the spin coupling but keep a single-pass (non-resonant) optical setup. The overall efficiency is low but we carefully characterize the transduction process and show that the performance can be described by two different metrics that we define and distinguish: the electro-optics and the quantum efficiencies. We reach an electro-optics efficiency of -84 dB for 15.7 dBm RF power. The corresponding quantum efficiency is -142 dB for 0.4 dBm optical power. We develop the Schrödinger-Maxwell formalism, well-known to describe light-matter interactions in atomic systems, in order to model the conversion process. We explicitly make the connection with the cavity quantum electrodynamics (cavity QED) approach that are generally used to describe quantum transduction.

Non-linear QED approach for betatron radiation in a laser wakefield accelerator

Laser plasma-based accelerators provide an excellent source of collimated, bright, and adequately coherent betatron-type x-ray pulses with potential applications in science and industry. So far the laser plasma-based betatron radiation has been described within the concept of classical Liénard–Wiechert potentials incorporated in particle-in-cell simulations, a computing power-demanding approach, especially for the case of multi-petawatt lasers. In this work, we describe the laser plasma-based generation of betatron radiation at the most fundamental level of quantum mechanics. In our approach, photon emission from the relativistic electrons in the plasma bubble is described within a nonlinear quantum electrodynamics (QED) framework. The reported QED-based betatron radiation results are in excellent agreement with similar results using Liénard–Wiechert potentials, as well as in very good agreement with betatron radiation measurements, obtained with multi-10-TW lasers interacting with He and multielectron N_2 gas targets. Furthermore, our QED approach results in a dramatic reduction of the computational runtime demands, making it a favorable tool for designing betatron radiation experiments, especially in multi-petawatt laser facilities.

Coherent anharmonicity transfer from matter to light in the THz regime

Optical nonlinearities are fundamental in several types of optical information processing protocols. However, the high laser intensities needed for implementing phase nonlinearities using conventional optical materials represent a challenge for nonlinear optics in the few-photon regime. We introduce an infrared cavity quantum electrodynamics (QED) approach for imprinting nonlinear phase shifts on individual THz pulses in reflection setups, conditional on the input power. Power-dependent phase shifts on the order of can be achieved with femtosecond pulses of only a few µW input power. The proposed scheme involves a small number of intersubband quantum well transition dipoles evanescently coupled to the near field of an infrared resonator. The field evolution is nonlinear due to the dynamical transfer of spectral anharmonicity from material dipoles to the infrared vacuum, through an effective dipolar chirping mechanism that transiently detunes the quantum well transitions from the vacuum field, leading to photon blockade. We develop analytical theory that describes the dependence of the imprinted nonlinear phase shift on relevant physical parameters. For a pair of quantum well dipoles, the phase control scheme is shown to be robust with respect to inhomogeneities in the dipole transition frequencies and relaxation rates. Numerical results based on the Lindblad quantum master equation validate the theory in the regime where the material dipoles are populated up to the second excitation manifold. In contrast with conventional QED schemes for phase control that require strong light–matter interaction, the proposed phase nonlinearity works best in weak coupling, increasing the prospects for its experimental realization using current nanophotonic technology.

Polaritonic Chemistry: Hindering and Easing Ground State Polyenic Isomerization via Breakdown of σ-π Separation.

The ground state conformational isomerization in polyenes is a symmetry allowed process. Its low energy barrier is governed by electron density transfer from the formal single bond that is rotated to the nearby formal double bonds. Along the reaction pathway, the transition state is therefore destabilized. The rules of polaritonic chemistry, i.e., chemistry in a nanocavity with reflecting windows, are barely beginning to be laid out. The standing electric field of the nanocavity couples strongly with the molecular wave function and modifies the potential energy curve in unexpected ways. A quantum electrodynamics approach, applied to the torsional degree of freedom of the central bond of butadiene, shows that formation of the polariton mixes the σ-π frameworks thereby stabilizing/destabilizing the planar, reactant-like conformations. The values of the fundamental mode of the cavity field used in the absence of the cavity do not trigger this mechanism.

Control of the Bright-Dark Exciton Splitting Using the Lamb Shift in a Two-Dimensional Semiconductor.

We investigate the exciton fine structure in atomically thin WSe_{2}-based van der Waals heterostructures where the density of optical modes at the location of the semiconductor monolayer can be tuned. The energy splitting Δ between the bright and dark exciton is measured by photoluminescence spectroscopy. We demonstrate that Δ can be tuned by a few meV as a result of a significant Lamb shift of the optically active exciton that arises from emission and absorption of virtual photons triggered by the vacuum fluctuations of the electromagnetic field. We also measure strong variations of the bright exciton radiative linewidth as a result of the Purcell effect. All these experimental results illustrate the strong sensitivity of the excitons to local vacuum field fluctuations. We find a very good agreement with a model that demonstrates the equivalence, for our system, of a classical electrodynamical transfer matrix formalism and quantum-electrodynamical approach. The bright-dark splitting control we demonstrate here in the weak light-matter coupling regime should apply to any semiconductor structures.

Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics.

When molecules are coupled to an optical cavity, new light-matter hybrid states, so-called polaritons, are formed due to quantum light-matter interactions. With the experimental demonstrations of modifying chemical reactivities by forming polaritons under strong light-matter interactions, theorists have been encouraged to develop new methods to simulate these systems and discover new strategies to tune and control reactions. This review summarizes some of these exciting theoretical advances in polariton chemistry, in methods ranging from the fundamental framework to computational techniques and applications spanning from photochemistry to vibrational strong coupling. Even though the theory of quantum light-matter interactions goes back to the midtwentieth century, the gaps in the knowledge of molecular quantum electrodynamics (QED) have only recently been filled. We review recent advances made in resolving gauge ambiguities, the correct form of different QED Hamiltonians under different gauges, and their connections to various quantum optics models. Then, we review recently developed ab initio QED approaches which can accurately describe polariton states in a realistic molecule-cavity hybrid system. We then discuss applications using these method advancements. We review advancements in polariton photochemistry where the cavity is made resonant to electronic transitions to control molecular nonadiabatic excited state dynamics and enable new photochemical reactivities. When the cavity resonance is tuned to the molecular vibrations instead, ground-state chemical reaction modifications have been demonstrated experimentally, though its mechanistic principle remains unclear. We present some recent theoretical progress in resolving this mystery. Finally, we review the recent advances in understanding the collective coupling regime between light and matter, where many molecules can collectively couple to a single cavity mode or many cavity modes. We also lay out the current challenges in theory to explain the observed experimental results. We hope that this review will serve as a useful document for anyone who wants to become familiar with the context of polariton chemistry and molecular cavity QED and thus significantly benefit the entire community.

Fluorescence in quantum dynamics: Accurate spectra require post-mean-field approaches.

Real time modeling of fluorescence with vibronic resolution entails the representation of the light-matter interaction coupled to a quantum-mechanical description of the phonons and is therefore a challenging problem. In this work, taking advantage of the difference in timescales characterizing internal conversion and radiative relaxation-which allows us to decouple these two phenomena by sequentially modeling one after the other-we simulate the electron dynamics of fluorescence through a master equation derived from the Redfield formalism. Moreover, we explore the use of a recent semiclassical dissipative equation of motion [C. M. Bustamante et al., Phys. Rev. Lett. 126, 087401 (2021)], termed coherent electron electric-field dynamics (CEED), to describe the radiative stage. By comparing the results with those from the full quantum-electrodynamics treatment, we find that the semiclassical model does not reproduce the right amplitudes in the emission spectra when the radiative process involves the de-excitation to a manifold of closely lying states. We argue that this flaw is inherent to any mean-field approach and is the case with CEED. This effect is critical for the study of light-matter interaction, and this work is, to our knowledge, the first one to report this problem. We note that CEED reproduces the correct frequencies in agreement with quantum electrodynamics. This is a major asset of the semiclassical model, since the emission peak positions will be predicted correctly without any prior assumption about the nature of the molecular Hamiltonian. This is not so for the quantum electrodynamics approach, where access to the spectral information relies on knowledge of the Hamiltonian eigenvalues.

Macroscopic quantum electrodynamics approach to multichromophoric excitation energy transfer. II. Polariton-mediated population dynamics in a dimer system.

In this study, based on the theory developed in Paper I, we explore the combined effects of molecular fluorescence and excitation energy transfer in a minimal model-a pair of single-vibration-mode chromophores coupled to surface plasmon polaritons. For the chromophores with zero Huang-Rhys factors and strong couplings to surface plasmon polaritons, we find that the frequencies of Rabi oscillations (the strengths of strong light-matter couplings) are associated with the initial excitation conditions. On the other hand, for the chromophores weakly coupled to surface plasmon polaritons, our numerical calculations together with analytical analysis elaborate on the conditions for the superradiant and subradiant decay behaviors. Moreover, we show that the modified decay rate constants can be explicitly expressed in terms of generalized spectral densities (or dyadic Green's functions), revealing a relationship between photonic environments and the collective effects such as superradiance and subradiance. For the chromophores with nonzero Huang-Rhys factors and strong coupling to surface plasmon polaritons, the effects of molecular vibrations emerge. We demonstrate that the low-frequency vibrational modes do not affect the excited state population dynamics, while the high-frequency vibrational modes can modify either the period of Rabi oscillation (Franck-Condon Rabi oscillation) or the amplitude of excited state population. Our study shows that the collective effects, including superradiance and subradiance, can be controlled via dielectric environments and initial excitation conditions, providing new insights into polariton chemistry and the design of quantum optical devices.

Macroscopic quantum electrodynamics approach to multichromophoric excitation energy transfer. I. Formalism.

In this study, we develop a theory of multichromophoric excitation energy transfer (MC-EET) in the framework of macroscopic quantum electrodynamics. The theory we present is general for studying the interplay between energy transfer and fluorescence in the presence of arbitrary inhomogeneous, dispersive, and absorbing media. The dynamical equations of MC-EET, including energy-transfer kernels and fluorescence kernels, allow us to describe the combined effects of molecular vibrations and photonic environments on excitation energy transfer. To demonstrate the universality of the MC-EET theory, we show that under specific conditions, the MC-EET theory can be converted to three representative theories. First, under the Markov approximation, we derive an explicit Förster-type expression for plasmon-coupled resonance energy transfer [Hsu et al., J. Phys. Chem. Lett. 8, 2357 (2017)] from the MC-EET theory. In addition, the MC-EET theory also provides a parameter-free formula to estimate transition dipole-dipole interactions mediated by photonic environments. Second, we generalize the theory of multichromophoric Förster resonance energy transfer [Jang et al., Phys. Rev. Lett. 92, 218301 (2004)] to include the effects of retardation and dielectric environments. Third, for molecules weakly coupled with photonic modes, the MC-EET theory recovers the previous main result in Chance-Prock-Silbey classical fluorescence theory [Chance et al., J. Chem. Phys. 60, 2744 (1974)]. This study opens a promising direction for exploring light-matter interactions in multichromophoric systems with possible applications in the exciton migration in metal-organic framework materials and organic photovoltaic devices.

Gauge invariance of the local phase in the Aharonov-Bohm interference: Quantum electrodynamic approach

In the Aharonov-Bohm (AB) effect, interference fringes are observed for a charged particle in the absence of the local overlap with the external electromagnetic field. This notion of the apparent “nonlocality” of the interaction or the significant role of the potential have recently been challenged and are under debate. The quantum electrodynamic approach provides a microscopic picture of the characteristics of the interaction between a charge and an external field. We explicitly show the gauge invariance of the local phase shift in the magnetic AB effect, which is in contrast to the results obtained using the usual semiclassical vector potential. Our study can resolve the issue of the locality in the magnetic AB effect. However, the problem is not solved in the same way in the electric counterpart wherein virtual scalar photons play an essential role.

Effects of Reservoir Input Fields on the Non-Classical Features of Quantum Beat Cascade Laser

The quantum features and quantum statistical properties of a cavity-mode radiation emitted from the coherently prepared degenerate three-level laser have been investigated, by using the standard quantum electrodynamics approach and accounting for the light-matter interaction. We considered the vacuum reservoir, squeezed vacuum reservoir, and thermal reservoir to see the effect of reservoir input fields on the statistical and squeezing nature on the cavity radiation. It is found that the squeezed vacuum reservoir has enhancement effect on the squeezing property, as well as the brightness of the cavity radiation compared to those of the vacuum and thermal reservoirs. It is also observed that the radiation emitted from the cavity is in the squeezed state with super-Poissonian photon statistics regardless of the reservoir nature.

Lowest-Order Thermal Correction to the Hydrogen Recombination Cross-Section in Presence of Blackbody Radiation

In the present paper, the correction of the recombination and ionization processes of the hydrogen atom due to the thermal interaction of two charges was considered. The evaluation was based on a rigorous quantum electrodynamic (QED) approach within the framework of perturbation theory. The lowest-order radiative correction to the recombination/ionization cross-section was examined for a wide range of temperatures corresponding to laboratory and astrophysical conditions. The found thermal contribution was discussed both for specific states and for the total recombination and ionization coefficients.

Potency dependent activity of homeopathic nanomedicine- classical and quantum electrodynamical approach

The effect of homeopathic medicine on biological and physical system is directly related to its potency [1]. However, from physico-chemical point of view it is difficult to explain this effect at such high dilution, as then the existence of even trace amount of particle is questionable. 
 It has been reported that during the process of potentization, a large amount of mechanical energy gets transferred to the medium due to succussion [2]. This energy in all probability reduces the size of the drug aggregates. The drug then penetrates easily through the membrane barrier, and thereby gives rise to enhanced activity of the medicine.
 It has been experimentally proved by us and supported by others that indeed a reduction of size of the aggregates takes place with increase in potency [3]. Using five different homeopathic medicines, their sizes at three different potencies have been estimated and a general mathematical expression relating the size of the particle (Y) and the corresponding potency (X) has been derived as follows
 Y = a X -n

Quantum sensing protocol for motionally chiral Rydberg atoms

A quantum sensing protocol is proposed for demonstrating the motion-induced chirality of circularly polarised Rydberg atoms. To this end, a cloud of Rydberg atoms is dressed by a bichromatic light field. This allows to exploit the long-lived ground states for implementing a Ramsey interferometer in conjunction with a spin echo pulse sequence for refocussing achiral interactions. Optimal parameters for the dressing lasers are identified. Combining a circularly polarised dipole transition in the Rydberg atom with atomic centre-of-mass motion, the system becomes chiral. The resulting discriminatory chiral energy shifts induced by a chiral mirror are estimated using a macroscopic quantum electrodynamics approach. The presented quantum sensing protocol will also provide an indirect proof for Casimir–Polder quantum friction.

Many-body photoemission theory for organic molecular crystals

A many-body photoemission theory based on Keldysh nonequilibrium Green's functions is developed and applied to photoemission from extended states of organic molecules and their crystals, in particular excited by ultraviolet and soft X-ray radiation. In this energy region, electron-phonon interaction and radiation filed screening play some important roles. To incorporate the latter effects, we should use quantum electrodynamics (QED) approach. To discuss the electron-phonon interaction, we apply the Hedin equation including the screened Coulomb interaction mediated by the electron-phonon interaction. This theoretical framework gives us a unified picture of the UPS spectra from organic solids. Furthermore some illustrative numerical calculations are shown to discuss the relative importance of the multiple scatterings, Debye-Waller factors, the peak width of the quasi-particles, and the angular dependence of the phonon satellites. We demonstrate some specific features of ultraviolet photoemission spectroscopy (UPS) spectra from particularly anisotropic organic solids.

Probability Calculations Within Stochastic Electrodynamics

Several stochastic situations in stochastic electrodynamics (SED) are analytically calculated from first principles. These situations include probability density functions, as well as correlation functions at multiple points of time and space, for the zero-point (ZP) electromagnetic fields, as well as for ZP plus Planckian (ZPP) electromagnetic fields. More lengthy analytical calculations are indicated, using similar methods, for the simple harmonic electric dipole oscillator bathed in ZP as well as ZPP electromagnetic fields. The method presented here makes an interesting contrast to Feynman’s path integral approach in quantum electrodynamics (QED). The present SED approach directly entails probabilities, while the QED approach involves summing weighted paths for the wave function.

Macroscopic quantum electrodynamics approach to nonlinear optics and application to polaritonic quantum-vacuum detection

We provide an in-depth discussion of a theoretical framework recently introduced [Lindel et al., Phys. Rev. A 102, 041701(R) (2020)] which is capable of predicting the electromagnetic field emerging from a nonlinear crystal through which a coherent laser pulse is shone. This framework is based on macroscopic quantum electrodynamics and includes dispersion and absorption effects inside the crystal and allows for arbitrary optical environments through the classical Green's tensor. We introduce a diagrammatic approach with which the nonlinear processes contributing to the electric field operator up to certain orders in the perturbation series can be represented in a convenient way. Applying this framework to the setup of electro-optic sampling experiments of the polaritonic quantum vacuum, we derive analytical results for the electro-optic sampling between distinct spatiotemporal regions. Also, we discuss different approximations and the parameter ranges in which they apply including angled or diverging beams, thermal fluctuations, as well as (linear) absorption effects upon the polaritonic quantum vacuum. Finally, we compare these theoretical results to experimental data.

Bridging nano-optics and condensed matter formalisms in a unified description of inelastic scattering of relativistic electron beams

In the last decades, the blossoming of experimental breakthroughs in the domain of electron energy loss spectroscopy (EELS) has triggered a variety of theoretical developments. Those have to deal with completely different situations, from atomically resolved phonon mapping to electron circular dichroism passing by surface plasmon mapping. All of them rely on very different physical approximations and have not yet been reconciled, despite early attempts to do so. As an effort in that direction, we report on the development of a scalar relativistic quantum electrodynamic (QED) approach of the inelastic scattering of fast electrons. This theory can be adapted to describe all modern EELS experiments, and under the relevant approximations, can be reduced to most of the last EELS theories. In that aim, we present in this paper the state of the art and the basics of scalar relativistic QED relevant to the electron inelastic scattering. We then give a clear relation between the two once antagonist descriptions of the EELS, the retarded dyadic Green function, usually applied to describe photonic excitations and the quasi-static mixed dynamic form factor (MDFF), more adapted to describe core electronic excitations of material. Using the photon propagator in a material, expressed in the relevant gauges, as a tool to understand the interaction between a fast electron and a material, we extend this relation to a newly defined quantity, the relativistic MDFF. The relation between the dyadic Green function and the relativistic MDFF does depend only on the photon propagator and not on the specifics of the particle (here, a fast electron) probing the target. Therefore, it can be adapted to any spectroscopy where a relation between the electromagnetic and electronic properties of a material is needed. We then use this theory to establish two important EELS-related equations. The first one relates the spatially resolved EELS to the imaginary part of the photon propagator and the incoming and outgoing electron beam wavefunction, synthesizing the most common theories developed for analyzing spatially resolved EELS experiments. The second one shows that the evolution of the electron beam density matrix is proportional to the mutual coherence tensor, proving that quite universally, the electromagnetic correlations in the target are imprinted in the coherence properties of the probing electron beam.

Limitations of the semiclassical approach for the problem of two-level atomic ensemble emission in a resonant laser field

Both quantum-electrodynamical (QED) and semiclassical approaches are applied to study the spontaneous emission of an atom or atomic ensemble driven by the strong external laser field. It is demonstrated that the semiclassical approach typically used for analyzing the emission of dressed atomic systems is inconsistent with the QED approach and does not provide a proper description of the emission of two-level atoms in a strong external laser field. That is, aside from a situation where the external radiation is nonresonant, weak enough and does not cause the essential population of the excited atomic level.

Equilibrium radiation in a plasma medium with spatial and frequency dispersion

Examination of equilibrium radiation in plasma media shows that the spectral energy distribution of such radiation differs from that of Planck equilibrium radiation. Using the quantum electrodynamic approach, the general relation for the spectral energy density of equilibrium radiation in a system of charged particles is found. The obtained result takes into account the influence of plasma on equilibrium radiation through the explicit transverse dielectric permittivity which includes spatial and frequency dispersion, as well as the finite collision damping. For the limiting case of infinitesimal damping the result is identical with the known expression.