The local-field renormalization of the spontaneous emission rate in a dielectric is explicitly obtained from a fully microscopic quantum-electrodynamical, many-body derivation of Langevin-Bloch operator equations for two-level atoms embedded in an absorptive and dispersive, linear dielectric host. We find that the dielectric local-field enhancement of the spontaneous emission rate is smaller than indicated by previous studies.
We investigate spontaneous emission of a two-level atom with an arbitrarily polarized electric dipole in front of a flat dielectric surface. We treat the general case where the atomic dipole matrix element is a complex vector, that is, the atomic dipole can rotate with time in space. We calculate the rates of spontaneous emission into evanescent and radiation modes and study the angular densities of the rates in the space of wave vectors for the field modes. We show that, when the ellipticity of the atomic dipole is not zero, the angular density of the spontaneous emission rate of the atom may…
We develop a dual description of quantum optics adapted to dielectric systems without magnetic property. Our formalism, which is shown to be equivalent to the standard one within some dipolar approximations discussed in the article, is applied to the description of polaritons in dielectric media. We show that the dual formalism leads to the Huttner-Barnett equations [B. Huttner, S. M. Barnett, Phys. Rev. A \textbf{46}, 4306 (1992)] for QED in dielectric systems. More generally, we discuss the role of electromagnetic duality in the quantization procedure for optical systems and derive the struc…
By a generalization of the Hopfield model, we construct a microscopic Lagrangian describing a dielectric medium with dispersion and dissipation. This facilitates a well-defined and unambiguous $\textit{ab initio}$ treatment of quantum electrodynamics in such media, even in time-dependent backgrounds. As an example, we calculate the number of photons created by switching on and off dissipation in dependence on the temporal switching function. This effect may be stronger than quantum radiation produced by variations of the refractive index $Δn(t)$ since the latter are typically very small and yi…
Mathematical Foundation for Quantum Computing of Electromagnetic Wave Propagation in Dielectric Media
Plasma Science and Fusion Center Massachusetts Institute of Technology（麻省理工学院等离子体科学与聚变中心）；School of Electrical and Computer Engineering National Technical University of Athens（雅典国立技术大学电气与计算机工程学院）；Department of Physics College of William & Mary（威廉玛丽学院物理系）
The Quantum Vacuum of Complex Media. A Unified Approach to the Dielectric Constant, the Spontaneous Emission and the Zero-Temperature Electromagnetic Pressure
The emission properties of atoms lie at the foundations of both quantum theory and light-matter interactions. In the context of macroscopic media, exact knowledge thereof is important both in current quantum technologies as well as in fundamental studies. While for isotropic media, this is a very well-studied problem, there are still big gaps in the theory of anisotropic media. In particular, to the best of our knowledge, an explicit expression for the spontaneous emission rate in general anisotropic media has not been presented. In this work, we first derive the quantised electromagnetic fiel…
A rigorous description of volume and surface spontaneous parametric down-conversion in 1D nonlinear layered structures is developed considering exact continuity relations for the fields' amplitudes at the boundaries. The nonlinear process is described by the quantum momentum operator that provides the Heisenberg equations which solution is continuous at the boundaries. The transfer-matrix formalism is applied. The volume and surface contributions are clearly identified. Numerical analysis of a structure composed of 20 alternating GaN/AlN layers is given as an example.
We measured photon absorption in dielectric media and proposed the photon-version Beer-Lambert's law to quantify the absorption. We used a Hong-Ou-Mandel interferometer and 810 nm twin-photons. We found that the depth ratio of the null point in the interference patterns of the interferometer agreed with the classical transmittance of the samples. We established a statistical model of the photon absorption process and proposed an information entropy interpretation to understand the meaning of the Beer-Lambert law. Comparisons of the results of the photon absorption experiments with classical ex…
We consider the so-called Hopfield model for the electromagnetic field in a dielectric dispersive medium in a framework in which one allows a space-time dependence of microscopic parameters, aimed to a phenomenological description of a space-time varying dielectric perturbation induced by means of the Kerr effect. We discuss the analogue Hawking effect, by first analyzing the geometrical optics for the Hopfield model, and then by introducing a simplified model which has the bonus to avoid many difficulties which are involved in the full Hopfield model, still keeping the same dispersion relatio…
Acoustic spontaneous emission into bulk dielectrics can be a strong source of decoherence in quantum devices, especially when a qubit is in the presence of piezoelectric materials. We study the dynamics of a qubit coupled to an acoustic resonator by a piezoelectric film. By varying the surface topography of the resonator from rough to polished to shaped, we explore the crossover from fast decay of an excited qubit to quantum-coherent coupling between the qubit and an isolated phonon mode. Our experimental approach may be used for precision measurements of crystalline vibrations, the design of …
Quantum-statistical effects occur during the propagation of electromagnetic (EM) waves inside the dielectric media or metamaterials, which include a large class of nanophotonic and plasmonic waveguides with dissipation and noise. Exploiting the formal analogy between the Schrodinger equation and the Maxwell equations for dielectric linear media, we rigorously derive the effective Hamiltonian operator which describes such propagation. This operator turns out to be essentially non-Hermitian in general, and pseudo-Hermitian in some special cases. Using the density operator approach for general no…
A broad class of planar dielectric media with complex permittivity profiles that are fully invisible, for both left and right incidence sides, is introduced. Such optical media are locally isotropic, non-magnetic and belong to the recently discovered class of Kramers-Kronig media [{\it Nature Photon.} 9, 436 (2015)], i.e. the spatial profiles of the real and imaginary parts of the dielectric permittivity are related each other by a Hilbert transform. The transition from unidirectional to bidirectional invisibility, and the possibility to realize sharp reflection above a cut-off incidence angle…
Creation of correlated photon pairs is one of the key topics in contemporary quantum optics. Here, we theoretically describe the generation of photon pairs in the process of spontaneous parametric down-conversion in a resonant spherical nanoparticle made of a dielectric material with bulk $χ^{(2)}$ nonlinearity. We pick the nanoparticle size that satisfies the condition of resonant eigenmodes described by Mie theory. We reveal that highly directional photon-pair generation can be observed utilising the nonlinear Kerker-type effect, and that this regime provides useful polarisation correlations…
We demonstrate a fundamental breakdown of the photonic spontaneous emission (SE) formula derived from Fermi's golden rule, in absorptive and amplifying media, where one assumes the SE rate scales with the local photon density of states, an approach often used in more complex, semiclassical nanophotonics simulations. Using a rigorous quantization of the macroscopic Maxwell equations in the presence of arbitrary linear media, we derive a corrected Fermi's golden rule and master equation for a quantum two-level system (TLS) that yields a quantum pumping term and a modified decay rate that is net …
We study a two-level quantum system embedded in a dispersive environment and coupled with the electromagnetic field. We expand the theory of light-matter interactions to include the spatial extension of the system, taken into account through its wavefunctions. This is a development beyond the point-dipole approximation. This ingredient enables us to overcome the divergence problem related to the Green tensor propagator. Hence, we can reformulate the expressions for the spontaneous emission rate and the Lamb shift. In particular, the inclusion of the spatial structure of the atomic system clari…
