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Analysis of the character of radiation transfer in a disordered three-dimensional ensemble of point scatterers in a waveguide

Пань Ичжэ

Published Jan 1, 2025• 0 citations
Publisher

Abstract

The subject of the graduate qualification work is «Analysis of the character of radiation transfer in a disordered three-dimensional ensemble of point scatterers in a waveguide». Object of study is waveguide. The aim is exploring the transmission properties of photons between atoms in waveguide. The following tasks were solved: 1. Calculation of the Green matrix for an ensemble of point-like stationary atoms in a waveguide; 2. Analysis of the nature of dipole-dipole interaction between two atoms; 3. Calculation of the dynamics of cooperative spontaneous decay of excited states of atoms in a waveguide; 4. Transition to the regime of stationary excitation of an atomic ensemble. Calculation of stationary amplitudes of singly excited atomic states; 5. Calculation and analysis of the dependence of the transmittance coefficient in the stationary regime on the size of the atomic medium in the waveguide. As a result of the study, we show how changing the size of messy waveguides controls how atoms emit light. These discoveries help us build better light-based computers and sensors. MATLAB is used to calculate and simulate the mathematical model of interatomic radiation transmission in waveguide.

DOI
10.18720/spbpu/3/2025/vr/vr25-4778

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•Jan 1, 2018•1 citation
The subject of the graduate qualification work is «Analysis of the character of radiation transfer in a disordered three-dimensional ensemble of point scatterers in a waveguide». Object of study is waveguide. The aim is exploring the transmission properties of photons between atoms in waveguide. The following tasks were solved: 1. Calculation of the Green matrix for an ensemble of point-like stationary atoms in a waveguide; 2. Analysis of the nature of dipole-dipole interaction between two atoms; 3. Calculation of the dynamics of cooperative spontaneous decay of excited states of atoms in a waveguide; 4. Transition to the regime of stationary excitation of an atomic ensemble. Calculation of stationary amplitudes of singly excited atomic states; 5. Calculation and analysis of the dependence of the transmittance coefficient in the stationary regime on the size of the atomic medium in the waveguide. As a result of the study, we show how changing the size of messy waveguides controls how atoms emit light. These discoveries help us build better light-based computers and sensors. MATLAB is used to calculate and simulate the mathematical model of interatomic radiation transmission in waveguide.
Light transport in a disordered ensemble of resonant atoms placed in a waveguide is found to be very sensitive to the sizes of the cross section of a waveguide. Based on a self-consistent quantum microscopic model treating atoms as coherent radiating dipoles, we have shown that the nature of radiation transfer changes from Anderson localization regime in a single-mode waveguide to a traditional diffuse transfer in a multimode one. Moreover, the transmittance magnitude undergoes complicated steplike nonmonotonic dependence on the transverse sizes of a waveguide.
Based on a consistent quantum microscopic approach, we investigate the peculiarities of collective polyatomic effects in atomic ensembles placed in a waveguide, caused by the presence of evanescent modes of electromagnetic field. We analyze the influence of these modes on the process of cooperative spontaneous decay, as well as on the nature of radiation transfer in the ensembles under consideration. We show that under certain conditions, their influence can be dominant compared to the role of radiation modes, and the mechanism for this influence is the modification of dipole-dipole interatomic interaction.
This work studies the cooperative Lamb shift in dense ensembles of point quasi-stationary atoms through a microscopic two-atom model. The objective of the work is to derive the finite interatomic part of the two atom reradiation matrix and use it to calculate distance-dependent cooperative frequency shifts. The tasks of the work are to formulate the atom-field Hamiltonian, specify the atomic level scheme and transition dipoles, include the one-photon virtual sector needed in the perturbative derivation, identify the ultraviolet problem of the off diagonal Green-matrix elements responsible for the cooperative Lamb shift, compare three derivation routes, and diagonalize the two-atom matrix for axial and arbitrary-coordinate geometries. The study uses analytical derivation in the electric-dipole and p·A gauges, direct principal-value analysis of the off-diagonal interaction integral, parameter differentiation, and numerical diagonalization of the 6×6 reradiation matrix. The main result is a consistent finite working formula for the off-diagonal interaction kernel and numerical curves showing how cooperative Lamb-shift branches depend on interatomic separation. MATLAB was used for numerical matrix construction, eigenvalue calculation, branch classification, and plotting.
Waveguide quantum electrodynamics (waveguide QED) describes the interaction between an electromagnetic field confined to a one-dimensional waveguide with atom-like quantum emitters close by. The characteristics of these kinds of systems are the possibility for strong and even ultrastrong interactions between the photonic and atom-like systems, and practically infinite range interactions between the emitters. These properties are valuable for a wide range of quantum optical applications, like quantum communication, quantum networks and quantum metrology. In this thesis we focus on two challenges in quantum optics, namely the generation and scattering of multiphoton states. In the first part of this thesis we demonstrate how waveguide QED systems can be exploited for the generation of multiphoton states, in particular of single-mode Fock states and superpositions thereof as well as multi-mode photonic states with metrological applications. The basic setup for this goal is an ensemble of quantum emitters coupled to a waveguide. In the so-called atomic mirror configuration symmetric Dicke states (or a superposition thereof) decay superradiantly to the ground state and emit the desired multiphoton state, which can be efficiently collected at the ends of the waveguide. We propose various protocols for the preparation of these Dicke states in waveguide QED systems and characterize the emitted photonic state. It turns out that in the low excitation regime, that is, if the number of photons is much lower than the ensemble size, the photonic state is emitted into a single mode. This single-mode structure is fundamental to current proposals for applications in quantum metrology with optical interferometers. Outside the low excitation regime, a multi-mode photonic state is generated, for which the metrological capabilities were unknown. We were able to show that these states still lead to quantum-enhanced optical interferometry. In the second part of this thesis we demonstrate how the scattering of multiphoton states on a single quantum emitter coupled to the waveguide can be used for testing the limits of the light-matter interaction strength. In particular, we investigate systems in the so-called ultrastrong coupling regime, where the coupling strength between the photonic and atom-like system is of the order of the emitter's transition energy. In this regime, many methods and approximations used in quantum optics, especially the Rotating Wave Approximation, break down and one needs to develop new analytical and numerical methods to study these systems. One approach is the so-called polaron Transformation. We show how this transformation can be applied for predicting the scattering amplitude of few photons scattering on the emitter. The comparison of these results with numerical simulations using matrix product states shows a good agreement for moderate coupling strengths. Both parts together show that waveguide QED systems are promising candidates for the generation of multiphoton states as well as for the investigation of fundamental limits probed through the scattering of multiphoton states. The latter also finds application in the implementation of photon-photon nonlinearities induced by the interaction with the quantum emitters. Apart from these and many other theoretical predictions, waveguide QED systems are also undergoing rapid progress in experiments. Therefore, we expect these kinds of systems to bring forth several advances in the field of quantum optics.