Claudia Eberlein, Dieter Robaschik
We determine the photon propagator in the presence of a non-dispersive dielectric half-space and use it to calculate the self-energy of an electron near a dielectric surface.
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A new model for calculating the Casimir-Lifshitz force per unit length for two dielectric rods is proposed, based on the Green function method of classical electrodynamics and the Lorentz model for permittivity.
Integral Formulation of Macroscopic Quantum Electrodynamics in Dispersive Dielectric Objects
本文利用Hopfield型方法提出了有限尺寸线性色散介电物体在Heisenberg绘景下的宏观量子电动力学积分形式，通过真空推迟Green函数获得控制极化密度场算符演化的积分方程，从而允许直接应用经典电动力学计算技术在开放、色散和吸收环境中进行量子电动力学计算。
Quantum electrodynamics near a boundary is investigated by considering the inertial mass shift of an electron near a dielectric or conducting surface. We show that in all tractable cases the shift can be written in terms of integrals over the TE and TM reflection coefficients associated with the surface, in analogy to the Lifshitz formula for the Casimir effect. We discuss the applications and potential limitations of this formula, and provide exact results for several models of the surface.
We build up a consistent theory of quantum electrodynamics in the presence of macroscopic polarizable media. We use the Huttner-Barnett model of a dispersive and absorbing dielectric medium and formulate the theory in terms of interacting quantum fields. We integrate out the damped polaritons by using diagrammatic techniques and find an exact expression for the displacement field (photon) propagator in the presence of a dispersive and absorbing dielectric half-space. This opens a new route to traceable perturbative calculations of the same kind as in free-space quantum electrodynamics. As a wo…
Quantum Electrodynamics with Time-varying Dielectrics
本文提出一个框架，用于在时变介电介质中量子化电磁场，通过微观模型处理动态光-物质耦合，获得满足对易关系的简正模，并展示其与量子发射体的耦合及对原子辐射性质的影响，适用于多种时变边界条件平台。
We have fabricated an atom chip device which combines the circuitry for magnetic trapping of cold atoms with high-finesse optical resonators suitable for cavity QED in the single-atom strong coupling regime. Fabry-Perot optical resonators with finesse F > 2 X 10^5 were formed between a micropatterned on-chip planar mirror with lateral dimension of < 100 um and a curved mirror suspended above the chip. The strong and rapid thermal coupling between on-chip electrical and optical elements was utilized to stabilize the cavity mirror separation with servo bandwidth exceeding 100 kHz during simulate…
The macroscopic quantum theory of the electromagnetic field in a dielectric medium interacting with a dense collection of embedded two-level atoms fails to reproduce a result that is obtained from an application of the classical Lorentz local-field condition. Specifically, macroscopic quantum electrodynamics predicts that the Lorentz redshift of the resonance frequency of the atoms will be enhanced by a factor of the refractive index n of the host medium. However, an enhancement factor of (n*n+2)/3 is derived using the Bloembergen procedure in which the classical Lorentz local-field condition …
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…
Quantum Electrodynamics with a Nonmoving Dielectric Sphere: Quantizing Lorenz-Mie Scattering
本文量子化真空中非移动介质球体周围的电磁场，推导平面波与归一化本征模式的正则变换，并用于分析单光子、压缩光及双光子散射，揭示三维分束器的洪-欧-曼德尔干涉角分布，为光与介质球体机械自由度量子相互作用奠定理论。
The stress tensor for the quantized electromagnetic field is calculated in the region between a pair of dispersive, dielectric half-spaces. This generalizes the stress tensor for the Casimir energy to the case where the boundaries have finite reflectivity. We also include the effects of finite temperature. This allows us to discuss the circumstances under which the weak energy condition and the null energy condition can be violated in the presence of finite reflectivity and finite temperature.
A diffraction problem for a flat Chern-Simons layer at plane boundary of a dielectric half space is solved. The Casimir energy of two dielectric half spaces with Chern-Simons layers at plane-parallel boundaries separated by a vacuum slit is derived. Crossing from the repulsive to the attractive Casimir force is analyzed for two Au and two Si half spaces with boundary Chern-Simons layers. Boundary quantum Hall layers in external magnetic field lead to Casimir repulsion at nanoscales. We discuss features that make systems with boundary quantum Hall layers unique for force measurements and search…
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…
Microscopic theory of exciton-polariton model involving multiple molecules: Macroscopic quantum electrodynamics formulation and essence of direct intermolecular interactions
本文通过宏观量子电动力学推导出包含自由空间偶极子-偶极子相互作用的有效耗散CQED模型，揭示了在研究多分子极子-极化子系统时直接分子间相互作用的重要性。
The recent development of a scanning thermal microscope (SThM) has led to measurements of radiative heat transfer between a heated sensor and a cooled sample down to the nanometer range. This allows for comparision of the known theoretical description of radiative heat transfer, which is based on fluctuating electrodynamics, with experiment. The theory itself is a macroscopic theory, which can be expected to break down at distances much smaller than 10-8m. Against this background it seems to be reasonable to revisit the known macroscopic theory of fluctuating electrodynamics and of radiative h…
Within the framework of exact quantum electrodynamics in dielectric, we study the topological Berry phase of a classically pumped $Λ$-type three-level atom, prepared initially in a superposition of its two pumped levels and located near a planar dielectric half-space with model permittivity of Lorentz type, interacts with a vacuum field. The effects of material losses, expressed in terms of the Green tensor of the dielectric-matter formation including dispersion and absorption, on the topological Berry phase of the photon transition between the pumped levels have been studied. The outcomes are…
We study the Brownian motion of a charged test particle driven by quantum electromagnetic fluctuations in the vacuum region near a non-dispersive and non-absorbing dielectric half-space and calculate the mean squared fluctuations in the velocity of the test particle. Our results show that a nonzero susceptibility of the dielectrics has its imprints on the velocity dispersions of the test particles. The most noteworthy feature in sharp contrast to the case of an idealized perfectly conducting interface is that the velocity dispersions in the parallel directions are no longer negative and does n…
The quantization of optical fields in vacuum has been known for decades, but extending the field quantization to lossy and dispersive media in nonequilibrium conditions has proven to be complicated due to the position-dependent electric and magnetic responses of the media. In fact, consistent position-dependent quantum models for the photon number in resonant structures have only been formulated very recently and only for dielectric media. Here we present a general position-dependent quantized fluctuational electrodynamics (QFED) formalism that extends the consistent field quantization to desc…
The possibility of repulsive Casimir forces between small metal spheres and a dielectric half-space is discussed. We treat a model in which the spheres have a dielectric function given by the Drude model, and the radius of the sphere is small compared to the corresponding plasma wavelength. The half-space is also described by the same model, but with a different plasma frequency. We find that in the retarded limit, the force is quasi-oscillatory. This leads to the prediction of stable equilibrium points at which the sphere could levitate in the Earth's gravitational field. This seems to lead t…
Predicting electric-field noise in ion traps using fluctuation electrodynamics
本文提出一种基于涨落电动力学的方法，用于预测离子阱中由材料体涨落引起的电场噪声，适用于任意几何结构，并验证了介电材料贡献主导，预测误差在四倍以内。
We theoretically study the properties of highly prolate shaped dielectric microresonators. Such resonators sustain whispering gallery modes that exhibit two spatially well separated regions with enhanced field strength. The field per photon on the resonator surface is significantly higher than e.g. for equatorial whispering gallery modes in microsphere resonators with a comparable mode volume. At the same time, the frequency spacing of these modes is much more favorable, so that a tuning range of several free spectral ranges should be attainable. We discuss the possible application of such res…
Resonance energy transfer between chiral molecules can be used to discriminate between different enantiomers. The transfer rate between chiral molecules consists of a non-discriminatory and discriminatory parts. We derive these two rate contributions in the framework of macroscopic quantum electrodynamics. We show that their ratio is usually larger in the retarded regime or far-zone of large separation distances and that the degree of discrimination can be modified when considering a surrounding medium. We highlight the importance of local field effects onto the degree of discrimination and pr…
Quantum communication schemes widely use dielectric four-port devices as basic elements for constructing optical quantum channels. Since for causality reasons the permittivity is necessarily a complex function of frequency, dielectrics are typical examples of noisy quantum channels in which quantum coherence will not be preserved. Basing on quantization of the phenomenological electrodynamics, we construct the transformation relating the output quantum state to the input quantum state without placing frequency restrictions. Knowledge of the full transformed quantum state enables us to compute …
Microwave amplification via interfering multi-photon processes in a half-waveguide quantum electrodynamics system
本文提出在半无限传输线末端利用 transmon 的 Rabi 边带相长干涉实现微波探测放大，获得约18%的单人工原子最高振幅放大率，并表征自发辐射噪声。
We devise new optical antennas that reduce the excited-state radiative lifetimes of emitters to the order of 100 femtoseconds while maintaining quantum efficiencies of about 80% at a broadband operation. Here, we combine metallic nanoparticles with planar dielectric structures and exploit design strategies from plasmonic nanoantennas and concepts from Cavity Quantum Electrodynamics to maximize the local density of states and minimize the nonradiative losses incurred by the metallic constituents. The proposed metallo-dielectric hybrid antennas promise important impact on various fundamental and…
The repulsive nature of the static Casimir force between two half-spaces, one perfectly dielectric and the other purely magnetic, has been known since Boyer's work [T. H. Boyer, Phys. Rev. A {\bf 9}, 2078 (1974)]. We here analyze the corresponding friction force in the magnetodielectric case. Our main method is that of quantum mechanical statistical mechanics. The basic model we introduce is a harmonic oscillator model: an electric dipole oscillating in the $x$ direction and a magnetic one oscillating in the $y$ direction, while their separation is in the $z$ direction. This is then extended t…
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…
Classical electromagnetism is linear. However, fields can polarize the vacuum Dirac sea, causing quantum nonlinear electromagnetic phenomena, e.g., scattering and splitting of photons, that occur only in very strong fields found in neutron stars or heavy ion colliders.We show that strong nonlinearity arises in Dirac materials at much lower fields $\sim 1\:\text{T}$, allowing us to explore the nonperturbative, extremely high field limit of quantum electrodynamics in solids. We explain recent experiments in a unified framework and predict a new class of nonlinear magneto-electric effects, includ…
Despite tremendous advances in the fundamentals and applications of cavity quantum electrodynamics (CQED), investigations in this field have primarily been limited to optical cavities composed of purely dielectric materials. Here, we demonstrate a hybrid metal-dielectric nanocavity design and realize it in the InAs/GaAs quantum photonics platform utilizing angled rotational metal evaporation. Key features of our nanometallic light-matter interface include: (i) order of magnitude reduction in mode volume compared to that of leading photonic crystal CQED systems; (ii) surface-emitting nanoscale …
We study from a critical perspective several quantum-electrodynamic phenomena commonly related to vacuum electromagnetic (EM) fluctuations in complex media. We compute the resonance-shift, the spontaneous emission rate, the local density of states and the van-der-Waals-Casimir pressure in a dielectric medium using a microscopic diagrammatic approach. We find, in agreement with some recent works, that these effects cannot be attributed to variations on the energy of the EM vacuum but to variations of the dielectric self-energy. This energy is the result of the interaction of the bare polarizabi…
We investigate the suitability of toroidal microcavities for strong-coupling cavity quantum electrodynamics (QED). Numerical modeling of the optical modes demonstrate a significant reduction of modal volume with respect to the whispering gallery modes of dielectric spheres, while retaining the high quality factors representative of spherical cavities. The extra degree of freedom of toroid microcavities can be used to achieve improved cavity QED characteristics. Numerical results for atom-cavity coupling strength, critical atom number N_0 and critical photon number n_0 for cesium are calculated…
We consider a general quantum field relativistic scattering involving two half spin fermions, $A$ and $B$, which are initially entangled with another fermion $C$ that does not participate in the scattering dynamics. We construct general expressions for the reduced spin matrices for the out-state considering a general tripartite spin-entangled state. In particular we study an inelastic QED process at tree-level, namely $e^-e^+\rightarrow μ^- μ^+$ and a half spin fermion $C$ as an spectator particle which can be entangled to the $AB$ system in the following ways: W state, GHZ state, $|\text{A}^α…
We have observed a distance-dependent absorption linewidth of cold $^{87}$Rb atoms close to a dielectric-vacuum interface. This is the first observation of modified radiative properties in vacuum near a dielectric surface. A cloud of cold atoms was created using a magneto-optical trap (MOT) and optical molasses cooling. Evanescent waves (EW) were used to observe the behavior of the atoms near the surface. We observed an increase of the absorption linewidth with up to 25% with respect to the free-space value. Approximately half the broadening can be explained by cavity-quantum electrodynamics (…
We present a new approach to incorporate self-assembled quantum dots into a Fabry-Pérot-like microcavity. Thereby a 3$λ$/4 GaAs layer containing quantum dots is epitaxially removed and attached by van der Waals bonding to one of the microcavity mirrors. We reach a finesse as high as 4,100 with this configuration limited by the reflectivity of the dielectric mirrors and not by scattering at the semiconductor - mirror interface, demonstrating that the epitaxial lift-off procedure is a promising procedure for cavity quantum electrodynamics in the solid state. As a first step in this direction, we…
In this paper, we propose an effective model including a macroscopic Hamiltonian to describe the interactions between a two-level atom and scattered light in a 1-D dielectric waveguide. The proposed formalism allows us to incorporate the effect of changing optical media inside the continuum while demonstrating a non-classical derivation of Fresnel Law. We obtain the transport characteristics of the two-level system, explore its high-Q bandreject filter property and discuss the implications of radiative and non-radiative dissipation. In addition, we apply our formalism to a modified Fabry-Pérot…
An ad hoc quantization scheme for the electromagnetic field in a weakly dispersive, transparent dielectric leads to the definition of canonical and kinetic forms for the momentum of the electromagnetic field in a dispersive medium. The canonical momentum is uniquely defined as the operator that generates spatial translations in a uniform medium, but the quantization scheme suggests two possible choices for the kinetic momentum operator, corresponding to the Abraham or the Minkowski momentum in classical electrodynamics. Another implication of this procedure is that a wave packet containing a s…
We have designed and fabricated a half-wavelength reflection line resonator (RLR) that consists of a pair of two coupled microstrip lines on a GaAs/AlGaAs heterostructure. By changing the top gate voltage on a square of two dimensional electron gas under the resonator, a large range of the quality factors can be obtained. Energy loss in the two-dimensional electron gas can be minimized, thus realizing a versatile resonator suitable for integration with semiconductor quantum circuits.
Cavity quantum electrodynamics of photonic temporal crystals
本文提出光子时晶的量子电动力学模型，揭示经典与量子动量间隙的联系，并展示两能级原子在其中的不可逆衰减现象，为非平衡量子光子学研究提供新方法。
Dissipation in the Broadband and Ultrastrong Coupling Regimes of Cavity Quantum Electrodynamics: An Ab Initio Quantized Quasinormal Mode Approach
该研究针对宽带光-物质相互作用下腔QED唯象耗散方法的不足，从头推导了基于准简正模量化的量子主方程，验证了其有效性并揭示了宽带耗散区域的新判据与单模模型的限制。
Spectral densities of a dispersive dielectric sphere in the modified Langevin noise formalism
本文在修正朗之万噪声形式主义的宏观量子电动力学框架下，推导了均匀色散介质球的介质辅助、散射辅助及温度相关有效谱密度的解析表达式，解决了两库不同初始热态下标准方法失效问题，并研究了量子发射器动力学。
Electromagnetic waves at grazing incidence onto a planar medium are analogous to zero energy quantum particles incident onto a potential well. In this limit waves are typically completely reflected. Here we explore dielectric profiles supporting optical analogues of `half-bound states', allowing for zero reflection at grazing incidence. To obtain these profiles we use two different theoretical approaches: supersymmetric quantum mechanics, and direct inversion of the Helmholtz equation.
Quantum emitter interacting with a dispersive dielectric object: a model based on the modified Langevin noise formalism
本文在宏观量子电动力学框架下，用修正朗之万噪声形式主义建模量子发射器与有限色散介质物体的相互作用，揭示其耦合的两个玻色库特性及等效单玻色库条件，为相关系统动力学研究提供基础。
We consider the electric and magnetic field fluctuations in the vacuum state in the region external to a half-space filled with a homogeneous non-dissipative dielectric. We discuss an appropriate limit to an ideal metal and concentrate our interest on the renormalized field fluctuations, or equivalently to renormalized electric and magnetic energy densities, in the proximity of the dielectric-vacuum interface. We show that surface divergences of field fluctuations arise at the interface in an appropriate ideal conductor limit, and that our limiting procedure allows to discuss in detail their s…
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