The Planck constant ($\hbar$) plays a pivotal role in quantum physics. Historically, it has been proposed as postulate, part of a genius empirical relationship $E=\hbar ω$ in order to explain the intensity spectrum of the blackbody radiation for which classical electrodynamic theory led to an unacceptable prediction: The ultraviolet catastrophe. While the usefulness of the Planck constant in various fields of physics is undisputed, its derivation (or lack of) remains unsatisfactory from a fundamental point of view. In this paper, the analysis of the blackbody problem is performed with a series expansion of the electromagnetic field in terms of TE, TM modes in a metallic cavity with small losses, that leads to developing the electromagnetic fields in a \textit{complete set of orthonormal functions}. This expansion, based on coupled power theory, maintains both space and time together enabling modeling of the blackbody's evolution toward equilibrium. Reaching equilibrium with a multimodal waveguide analysis brings into consideration the coupling between modes in addition to absorption and emission of radiation. The properties of the modes, such as spectral broadening, losses and lifetime, then progressively become independent of frequency and explains how equilibrium is allowed in good conductor metallic cavities. Based on the free electron relaxation time in gold, a value of $\hbar = 1.02 \times 10^{-34}$ J$\cdot$s for the reduced Planck constant is found and the uncertainty principle is also emerging from this \textit{a priori} classical study. The Planck constant is then obtained no longer as an ad hoc addition but as a natural consequence of the analysis taking boundary conditions into account as into optical resonators. That analysis based on finite-spacetime paradigm, also shine new light on the notion of decoherence in classical optics and electrodynamics.
Some consequences of a fully classical unified theory of gravity and electromagnetism are worked out for the electromagnetic sector such as the occurrence of classical light beams with spin and orbital angular momenta that are topologically quantized in units of $q_e q_m=σ$, independent of the beam size. Empirical fits require $σ= \hbar$. The theory also predicts a generalized coherency matrix whose consequences are testable.
Recent nanofabrication technologies have miniaturized optical and mechanical resonators, and have led to a variety of novel optomechanical systems in which optical and mechanical modes are strongly coupled. Here we hybridize an optomechanical resonator with two-level emitters and successfully demonstrate all-optical dynamic control of optical transition in the two-level system by the mechanical oscillation via the cavity quantum-electrodynamics (CQED) effect. Employing copper-doped silicon nanobeam optomechanical resonators, we have observed that the spontaneous emission rate of excitons bound…
We experimentally realize a Fabry-Perot-type optical microresonator near the cesium D2 line wavelength based on a tapered optical fiber, equipped with two fiber Bragg gratings which enclose a sub-wavelength diameter waist. Owing to the very low taper losses, the finesse of the resonator reaches F = 86 while the on-resonance transmission is T = 11 %. The characteristics of our resonator fulfill the requirements of non-linear optics and cavity quantum electrodynamics in the strong coupling regime. In combination with its demonstrated ease of use and its advantageous mode geometry, it thus opens …
While the postulate of covariance of Maxwell's equations for all inertial observers led Einstein to special relativity, it was the further demand of general covariance -- form invariance under general coordinate transformations, including between accelerating frames -- that led to general relativity. Several lines of inquiry over the past two decades, notably the development of metamaterial-based transformation optics, has spurred a greater interest in the role of geometry and space-time covariance for electrodynamics in ponderable media. I develop a generally covariant, coordinate-free framew…
We study light propagation through a slab of cold gas using both the standard electrodynamics of polarizable media, and massive atom-by-atom simulations of the electrodynamics. The main finding is that the predictions from the two methods may differ qualitatively when the density of the atomic sample $ρ$ and the wavenumber of resonant light $k$ satisfy $ρk^{-3}\gtrsim 1$. The reason is that the standard electrodynamics is a mean-field theory, whereas for sufficiently strong light-mediated dipole-dipole interactions the atomic sample becomes correlated. The deviations from mean-field theory app…
Invoking Maxwell's classical equations in conjunction with expressions for the electromagnetic (EM) energy, momentum, force, and torque, we use a few simple examples to demonstrate the nature of the EM angular momentum. The energy and the angular momentum of an EM field will be shown to have an intimate relationship; a source radiating EM angular momentum will, of necessity, pick up an equal but opposite amount of mechanical angular momentum; and the spin and orbital angular momenta of the EM field, when absorbed by a small particle, will be seen to elicit different responses from the particle…
Spontaneously generated coherence and enhanced dispersion in a V-type, three-level atomic system interacting with a single mode field can considerably reduce the radiative and cavity decay rates. This may eliminate the use of high finesse, miniaturized cavities in optical cavity quantum electrodynamics experiments under strong atom-field coupling conditions.
We experimentally realize an optical fiber ring resonator that includes a tapered section with subwavelength-diameter waist. In this section, the guided light exhibits a significant evanescent field which allows for efficient interfacing with optical emitters. A commercial tunable fiber beam splitter provides simple and robust coupling to the resonator. Key parameters of the resonator such as its out-coupling rate, free spectral range, and birefringence can be adjusted. Thanks to the low taper- and coupling-losses, the resonator exhibits an unloaded finesse of F=75+/-1, sufficient for reaching…
We present a canonical quantization of macroscopic electrodynamics. The results apply to inhomogeneous media with a broad class of linear magneto-electric responses which are consistent with the Kramers-Kronig and Onsager relations. Through its ability to accommodate strong dispersion and loss, our theory provides a rigorous foundation for the study of quantum optical processes in structures incorporating metamaterials, provided these may be modeled as magneto-electric media. Previous canonical treatments of dielectric and magneto-dielectric media have expressed the electromagnetic field opera…
Electrodynamical processes induced in complex systems like semiconductors by strong electromagnetic fields, have traditionally/conventionally been described using semi-classical approaches. Although these approaches, allowed the investigation of ultrafast dynamics in solids culminating in multi-petahertz electronics, they do not provide any access in the quantum optical nature of the interaction as they treat the driving-field classically and unaffected by the interaction. Here, using a full quantum-optical approach, we demonstrate that the sub-cycle electronic response in a strongly driven se…
We address two issues in the quantum electrodynamical description of photonic media with some disorder, neglecting material dispersion. When choosing a gauge in which the static potential vanishes, the normal modes of the medium with disorder satisfy another transversality condition than the modes of the ideal medium. Our first result is an integral equation for optical modes such that all perturbation-theory solutions automatically satisfy the desired transversality condition. Secondly, when expanding the vector potential for the medium with disorder in terms of the normal modes of the ideal …
The equations of electromagnetic fields in a medium is usually written in the rest frame of the medium. We outline a method of generalizing the discussion to arbitrary inertial frames. In the discussion, we also include the possibility that the medium is optically active, a possibility that is often overlooked in discussions of electromagnetic fields in a medium.
In this work we give a comprehensive derivation of an exact and numerically feasible method to perform ab-initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierachy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac f…
A major challenge in quantum optics and quantum information technology is to enhance the interaction between single photons and single quantum emitters. Highly engineered optical cavities are generally implemented requiring nanoscale fabrication precision. We demonstrate a fundamentally different approach in which disorder is used as a resource rather than a nuisance. We generate strongly confined Anderson-localized cavity modes by deliberately adding disorder to photonic crystal waveguides. The emission rate of a semiconductor quantum dot embedded in the waveguide is enhanced by a factor of 1…
We show that the Higgs mode of a superconductor, which is usually challenging to observe by far-field optics, can be made clearly visible using near-field optics by harnessing ultraconfined graphene plasmons. As near-field sources we investigate two examples: graphene plasmons and quantum emitters. In both cases the coupling to the Higgs mode is clearly visible. In the case of the graphene plasmons, the coupling is signaled by a clear anticrossing stemming from the interaction of graphene plasmons with the Higgs mode of the superconductor. In the case of the quantum emitters, the Higgs mode is…
