A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical Sellmeir equations obtained from the Drude-Lorentz model. In the homogeneous (plane-wave) case, we obtain the detailed quantum mode structure of the coupled polariton fields, and show that the mode expansion in all branches of the dispersion relation is completely defined by the refractive index and the group-velocity for the polaritons. We demonstrate a straightforward procedure for exactly diagonalizing the Hamiltonian in one, two or three-dimensional environments, even in the presence of longitudinal phonon-exciton dispersion, and an arbitrary number of resonant transitions with different frequencies. This is essential, since it is necessary to include at least one phonon (I.R.) and one exciton (U.V.) mode, in order to accurately represent dispersion in transparent solid media. Our method of diagonalization does not require an explicit solution of the dispersion relation, but relies instead on the analytic properties of Cauchy contour integrals over all possible mode frequencies. When there is longitudinal phonon dispersion, the relevant group-velocity term is modified so that it only includes the purely electromagnetic part of the group velocity.
A comparison of different master equations for driven-dissipative dynamics in composite quantum systems: Dispersive readout in structured electromagnetic environments
Sorbonne Université（索邦大学）；Institut des NanoSciences de Paris（巴黎纳米科学研究所）；LPENS, Département de Physique, École Normale Supérieure, Centre Automatique et Systèmes (CAS), MINES ParisTech, Université PSL, Sorbonne Université, CNRS, Inria（物理与能源环境研究实验室，巴黎高等师范学院，自动系统与中央研究院，国立巴黎高等矿业学校，巴黎文理研究大学，索邦大学，法国国家科学研究中心，法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）
This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first family of solutions describe the shape-preserving translation of a wavepacket along any desired trajectory in the x-y plane. In particular, we show that the dispersionless motion of a Gaussian wavepacket along both elliptical and circular paths can be achieved with rather simple electromagnetic field configurations. A second family of solutions involves a plan…
We present a new math-physics modeling approach, called canonical quantization with numerical mode-decomposition, for capturing the physics of how incoming photons interact with finite-sized dispersive media, which is not describable by the previous Fano-diagonalization methods. The main procedure is to (1) study a system where electromagnetic (EM) fields are coupled to non-uniformly distributed Lorentz oscillators in Hamiltonian mechanics, (2) derive a generalized Hermitian eigenvalue problem for conjugate pairs in coordinate space, (3) apply computational electromagnetics methods to find a c…
Modified Langevin noise formalism for multiple quantum emitters in dispersive electromagnetic environments out of equilibrium
Scuola Superiore Meridionale（南方高等学院）；Department of Electrical Engineering and Information Technology, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学电气与信息工程学院）
Electro-optical sampling has been recently used to perform spectrally-resolved measurements of electromagnetic vacuum fluctuations. In order to understand which information on the ground state of an interacting system can be acquired thanks to this technique, in this paper we will develop the quantum theory of electro-optical sampling in arbitrary dispersive dielectrics. Our theory shows that a measure of the time correlations of the vacuum fluctuations effectively implements an ellipsometry measurement on the quantum vacuum, allowing to access the frequency-dependent dielectric function. We d…
A dual-Lagrangian description adapted to quantum optics in dispersive and dissipative dielectric media
我们发展了一种适用于无磁介质系统的量子光学的对偶描述。我们的形式主义，这是等价于标准的文章中讨论的一些偶极近似，适用于电介质中的极化激元的描述。我们证明了对偶形式导致Huttner-Barnett方程[B. Huttner，S. M. Barnett，Phys. Rev. A \textbf{46}，4306（1992）]中关于电介质系统中的QED的研究。更一般地说，我们讨论的作用，电磁对偶性的量子化过程中的光学系统，并推导出结构的动力学定律的各种表示。
In this paper we deal with the macroscopic electromagnetic response of a finite size dispersive dielectric object, in unbounded space, in the framework of quantum electrodynamics using the Heisenberg picture. We apply a Hopfield type scheme to account for the dispersion and dissipation of the matter. We provide a general expression of the polarization density field operator as functions of the initial conditions of the matter field operators and of the electromagnetic field operators. It is a linear functional whose kernel is a linear expression of the impulse response of the dielectric object…
Full-Wave Green's-Function Modeling of Collective Single-Photon Emission in Non-Markovian Open-System QED with Finite-Bandwidth Compensation of Dispersive Interactions
Pohang University of Science and Technology（韩国科学技术院）；Purdue University（普渡大学）
Cavity optomechanics represents a flexible platform for the implementation of quantum technologies, useful in particular for the realization of quantum interfaces, quantum sensors and quantum information processing. However, the dispersive, radiation-pressure interaction between the mechanical and the electromagnetic modes is typically very weak, harnessing up to now the demonstration of interesting nonlinear dynamics and quantum control at the single photon level. It has already been shown both theoretically and experimentally that if the interaction is mediated by a Josephson circuit, one ca…
The quantum thermodynamical properties of (quasi-normal) overdamped electromagnetic modes (eddy currents) are investigated in the context of the magnetic Casimir-Polder interaction. The role of the material response in terms of spatially local and nonlocal material models is discussed. In particular, the focus is set on the system's entropy in the limit of low temperatures. In specific circumstances the spatially local (Drude) model reveals an "entropy defect", while spatial dispersion leads to a more regular behavior. We present a detailed description of this phenomenon and of the different m…
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…
Fluctuational Quantum Electrodynamics of Dispersive Time-Varying Media
Universidad Autónoma de Madrid（马德里自治大学）；Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid（马德里自治大学凝聚态物理中心 (IFIMAC)）；Instituto Nicolás Cabrera (INC), Universidad Autónoma de Madrid（马德里自治大学尼古拉斯·卡布雷拉研究所 (INC)）
