Generalized noise terms for the quantized fluctuational electrodynamics

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 describe the photon number also in the presence of magnetic field-matter interactions. It is shown that the magnetic fluctuations provide an additional degree of freedom in media where the magnetic coupling to the field is prominent. Therefore, the field quantization requires an additional independent noise operator that is commuting with the conventional bosonic noise operator describing the polarization current fluctuations in dielectric media. In addition to allowing the detailed description of field fluctuations, our methods provide practical tools for modeling optical energy transfer and the formation of thermal balance in general dielectric and magnetic nanodevices. We use the QFED to investigate the magnetic properties of microcavity systems to demonstrate an example geometry in which it is possible to probe fields arising from the electric and magnetic source terms. We show that, as a consequence of the magnetic Purcell effect, the tuning of the position of an emitter layer placed inside a vacuum cavity can make the emissivity of a magnetic emitter to exceed the emissivity of a corresponding electric emitter

Open geometry Fourier modal method: Modeling nanophotonic structures in infinite domains

We present an open geometry Fourier modal method based on a new combination of open boundary conditions and an efficient $k$-space discretization. The open boundary of the computational domain is obtained using basis functions that expand the whole space, and the integrals subsequently appearing due to the continuous nature of the radiation modes are handled using a discretization based on non-uniform sampling of the $k$-space. We apply the method to a variety of photonic structures and demonstrate that our method leads to significantly improved convergence with respect to the number of degrees of freedom, which may pave the way for more accurate and efficient modeling of open nanophotonic structures

Elektronikuljetus ballistisella ja Coulombin saarron alueilla

Tämän diplomityön ensimmäinen osa käsittelee konduktanssin laskemista ballistisella alueella nollalämpötilassa ja nollaa suuremmissa lämpötiloissa. Mode matching sekä rekursiivisen Greenin funktio -menetelmien soveltaminen valittujen kaksi- (2D) ja kolmiuloitteisten (3D) kanavien konduktanssien laskemiseen on esitetty yksityiskohtaisesti. Konduktanssilaskut on suoritettu lineaarisella alueella eli pienillä bias-jänitteen arvoilla. Lisäksi mode matching -menetelmällä laskettu piistä valmistetun (3D) kvanttipistekontaktin (QPC) konduktanssikuvaaja vastaa muodoltaan mitattuja tuloksia. Työn jälkimmäisessä osassa kuvataan Coulombin saarto -ilmiö sekä yhden elektronin transistorin (SET) rakenne ja toiminta. Lisäksi Monte Carlo (MC) - menetelmän käyttö SET piirien mallintamiseen ja simulointituloksia on esitetty. Esimerkkisovelluksena on esitetty monihila-SET:iin perustuvan loogisen ehdoton tai (XOR) -portin rakenne ja toiminta

Thermal balance and photon-number quantization in layered structures

The quantization of the electromagnetic field in lossy and dispersive dielectric media has been widely studied during the last few decades. However, several aspects of energy transfer and its relation to consistently defining position-dependent ladder operators for the electromagnetic field in nonequilibrium conditions have partly escaped the attention. In this work we define the position-dependent ladder operators and an effective local photon-number operator that are consistent with the canonical commutation relations and use these concepts to describe the energy transfer and thermal balance in layered geometries. This approach results in a position-dependent photon-number concept that is simple and consistent with classical energy conservation arguments. The operators are formed by first calculating the vector potential operator using Green's function formalism and Langevin noise source operators related to the medium and its temperature, and then defining the corresponding position-dependent annihilation operator that is required to satisfy the canonical commutation relations in arbitrary geometry. Our results suggest that the effective photon number associated with the electric field is generally position dependent and enables a straightforward method to calculate the energy transfer rate between the field and the local medium. In particular, our results predict that the effective photon number in a vacuum cavity formed between two lossy material layers can oscillate as a function of the position suggesting that also the local field temperature oscillates. These oscillations are expected to be directly observable using relatively straightforward experimental setups in which the field-matter interaction is dominated by the coupling to the electric field

Noiseless amplification of weak coherent fields without external energy

According to the fundamental laws of quantum optics, noise is necessarily added to the system when one tries to clone or amplify a quantum state. However, it has recently been shown that the quantum noise related to the operation of a linear phase-insensitive amplifier can be avoided when the requirement of a deterministic operation is relaxed. Nondeterministic noiseless linear amplifiers are therefore realizable. Usually nondeterministic amplifiers rely on using single photon sources. We have, in contrast, recently proposed an amplification scheme in which no external energy is added to the signal, but the energy required to amplify the signal originates from the stochastic fluctuations in the field itself. Applying our amplification scheme, we examine the amplifier gain and the success rate as well as the properties of the output states after successful and failed amplification processes. We also optimize the setup to find the maximum success rates in terms of the reflectivities of the beam splitters used in the setup. In addition, we discuss the nonidealities related to the operation of our setup and the relation of our setup with the previous setups.Comment: arXiv admin note: substantial text overlap with arXiv:1309.428

Quantum trajectory approach to statistics of amplified and damped cavity fields

Analysis of quantum optical experiments and the simulation of optical devices require detailed quantum mechanical models, especially in the case of weak optical fields. In this thesis the quantum dynamics of cavity fields are investigated and new tools for modeling cavity fields interacting with an energy reservoir are developed. Using the quantum trajectory approach the field dynamics during photon detection processes are investigated. Two experimentally feasible detector models, the resolving and the non-resolving detector scheme, are derived and applied to single photon detection and coincidence photon detection experiments. Furthermore, equivalence of the cavity field model to the beam splitter based single photon subtraction and addition schemes is shown. In addition to the detection schemes described above, a reduced model for fields in a non-ideal cavity interacting with a dissipative and amplifying reservoir through multiple two state systems is derived. The reduced model can be used to describe e.g. light emitting diodes and lasers depending on the relative strengths of the losses and energy injection. In these cases the model reproduces fields that approach a thermal or a coherent field, respectively. The derived models can be applied to wide variety of cavity field experiments. The reduced field model can be applied to modeling the optical fields of semiconductor devices or to describe cavity field based quantum information processing experiments. Furthermore, fundamental quantum optics experiments of single photon addition, single photon subtraction, coincidence detection, and their combinations can be analyzed using the derived models

Modeling open nanophotonic systems using the Fourier modal method: Generalization to 3D Cartesian coordinates

Recently, an open geometry Fourier modal method based on a new combination of an open boundary condition and a non-uniform $k$-space discretization was introduced for rotationally symmetric structures providing a more efficient approach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A 33, 1298 (2016)]. Here, we generalize the approach to three-dimensional (3D) Cartesian coordinates allowing for the modeling of rectangular geometries in open space. The open boundary condition is a consequence of having an infinite computational domain described using basis functions that expand the whole space. The strength of the method lies in discretizing the Fourier integrals using a non-uniform circular "dartboard" sampling of the Fourier $k$ space. We show that our sampling technique leads to a more accurate description of the continuum of the radiation modes that leak out from the structure. We also compare our approach to conventional discretization with direct and inverse factorization rules commonly used in established Fourier modal methods. We apply our method to a variety of optical waveguide structures and demonstrate that the method leads to a significantly improved convergence enabling more accurate and efficient modeling of open 3D nanophotonic structures

Photon momentum and optical forces in cavities

During the past century, the electromagnetic field momentum in material media has been under debate in the Abraham-Minkowski controversy as convincing arguments have been advanced in favor of both the Abraham and Minkowski forms of photon momentum. Here we study the photon momentum and optical forces in cavity structures in the cases of dynamical and steady-state fields. In the description of the single-photon transmission process, we use a field-kinetic one-photon theory. Our model suggests that in the medium photons couple with the induced atomic dipoles forming polariton quasiparticles with the Minkowski form momentum. The Abraham momentum can be associated to the electromagnetic field part of the coupled polariton state. The polariton with the Minkowski momentum is shown to obey the uniform center of mass of energy motion that has previously been interpreted to support only the Abraham momentum. When describing the steady-state nonequilibrium field distributions we use the recently developed quantized fluctuational electrodynamics (QFED) formalism. While allowing detailed studies of light propagation and quantum field fluctuations in interfering structures, our methods also provide practical tools for modeling optical energy transfer and the formation of thermal balance in nanodevices as well as studying electromagnetic forces in optomechanical devices