In this article we analyse the structure of Markov processes and reciprocal processes to underline their time symmetrical properties, and to compare them. Our originality consists in adopting a unifying approach of reciprocal processes, independently of special frameworks in which the theory was developped till now (diffusions, or pure jump processes). This leads to some new results, too.

This research investigates the characteristics of Parity Time symmetry breaking in two optically coupled, time delayed semiconductor lasers. A theoretical model is used to describe the controllable parameters in the experiment and intensity output of the coupled lasers. The PT parameters we control are the spatial separation between the two lasers, the frequency detuning, and the coupling strength. We find that the experimental data agrees with the predictions from the theoretical model confirming the intensity behaviors of the lasers, and the monotonic change in PT-threshold as a function of coupling scaled by the time delay. <br>

Indiana University-Purdue University Indianapolis (IUPUI) / Over the last two decades a new theory has been developed and intensively investigated in quantum physics. The theory stipulates that a non-Hermitian Hamiltonian can also represents a physical system as long as its energy spectra can be purely real in certain regime depending on the parameters of the Hamiltonian. It was demonstrated that the reality of the eigenenergy was conditioned by a certain kind of symmetry embedded in the actual non-Hermitian system. Indeed, such systems have a combined reflection (parity) symmetry (P) and time-reversal symmetry (T), PT-symmetry. The theory opens the door to new features particularly in open systems in which there could be gain and/or loss of particle or energy from and/or to the environment. A key property of the theory is the PT-symmetry breaking transition which occurs at the exceptional point (EP). The exceptional points are special degeneracies characterized by a coalescence of not only the eigenvalues but also of the corresponding eigenvectors of the system; and the coalescence happens when the gain-loss strength, a measure of the openness of the system, exceeds the intrinsic energy-scale of the system. In recent years, quantum walks with PT-symmetric non-unitary time evolution have been realized in systems with balanced gain and loss. These systems fall in two categories namely continuous time quantum walks (CTQW) that are characterized by a unitary or non-unitary time evolution Hamiltonian, and discrete-time quantum walks (DTQW) whose dynamic is described by a unitary or non-unitary time evolution operator consisting of a product of shift, coin, and gain-loss operations. In this thesis, we investigate the PT-symmetric phase of CTQW and DTQW in a variety of non-Hermitian lattice systems with both position-dependent and position independent, parity-symmetric tunneling functions in the presence of PT-symmetric impurities located at arbitrary parity-symmetric site on the lattice. Moreover, we explore the topological phase diagram and its novel features in non-Hermitian, homogeneous and non-homogeneous, PT-symmetric DTQW with closed and open boundary conditions. We conduct our study using analytical and numerical approaches that are directly and easily implementable in physical experiments. Among others, we found that, despite their non-unitary evolution, open systems governed by parity-time symmetric Hamiltonian support conserved quantities and that the PT-symmetry breaking threshold depends on the physical structure of the Hamiltonian and its underlying symmetries.

A time-reversible Maxwell's demon is demonstrated which creates a density difference between two chambers initialized to have equal density. The density difference is estimated theoretically and confirmed by computer simulations. It is found that the reversible Maxwell's demon compresses phase space volume even though its dynamics are time reversible. The significance of phase space volume compression in operating a microscopic heat engine is also discussed.

Quantum and classical frameworks form two perspectives for describing physical systems. Their formulation also presents interesting isomorphism: for example, the Schrodinger equation can find its classical correspondence in the paraxial Helmholtz equation, and coherent atomic population transfers is analogous to coupling dynamics in waveguides. In classical coupled mode systems, quantum notion can be manifested in the following ways: (1) adiabatic (i.e., sufficiently slow) evolution of the Hamiltonian enables robust mode conversion and light transfer, where the dynamics is carried out in predominantly one eigenmode; (2) non-Hermitian Hamiltonians give rise to peculiar singularities known as exceptional points (EPs), associated with not only degenerate eigenvalues but coalescent eigenvectors. In this dissertation, we explore the above principles in light manipulation, sensing, and photonic emulation. First, we numerically demonstrate two examples of photonic devices based on adiabatic evolution engineering. We present a coupled waveguide system analogous to the atomic physics process of stimulated Raman adiabatic passage, where the principle of adiabaticity not only allows high-extinction polarization mode splitting, but also counterintuitively mitigates the losses from the plasmonic structure involved. We show a modal hybridization effect in rib waveguide geometry that allows the mode to adiabatically evolve from one polarization to its orthogonal state upon electro-optic modulation in thin film lithium niobate, enabling an actively switchable polarization converter. We propose a generic EP emulator based on programmable photonics to tackle the challenging implementation of EP. Our approach combines on-chip operations of coupling, loss and detuning based on generic photonic modules (Mach-Zehnder interferometers), and a discrete scheme for mapping Hamiltonians to common mesh architecture. We demonstrate multiple exemplary EP functionalities, including loss-induced transparency, encircling second-order EPs in the PT and anti-PT symmetry picture, and a third-order EP. The proposed EP emulator marks a new paradigm for discrete, \textit{in situ} programming of EPs and multi-functional, repurposable EP devices. We also present our preliminary work on NV center-induced EPs. In contrast to conventional fluorescence-based schemes for addressing NV centers, we leverage NV centers' absorption to bring a coupled ring resonator system to an EP and numerically demonstrate the emerging dynamics. Our primary numerical results promise proof-of-concept magnetometry, combining NV centers' response to magnetic and microwave fields with the sensitivity enhancing nature of EP. This dissertation sheds light on unconventional photonics inspired by quantum-like principles. / 2025-08-29T00:00:00Z

Le développement des systèmes photoniques aucours des dernières décennies, rendu possible parl’évolution des technologies de nanofabrication, a vul’apparition de nouveaux matériaux synthétiques tels queles cristaux photoniques, les métamatériaux, les plasmonsde surface, et plus récemment les structures dites « àsymétrie Parité-Temps ». La caractéristique de ces derniersmatériaux synthétiques est que bien qu’ils soient décrits parun Hamiltonien non-Hermitien, leurs valeurs proprespeuvent toutefois être réelles. En optique plusieursphénomènes physiques sont connus pour la ressemblancedes équations les décrivant, avec l’expression de ce typed’Hamiltonien en mécanique quantique. C’est le cas deséquations de modes couplés dans les lasers DFB.Ce travail de thèse a porté sur la conception, fabrication etétude de lasers DFB à couplage complexe, dans l’optiqued’appliquer le principe de symétrie Parité Temps (PT) à uncomposant fonctionnel. Ces lasers sont combinent un réseaupar l’indice et par les pertes, avec un déphasage spécifique.La simulation des modes dans la cavité, effectuée parméthode matricielle de Ables, a dévoilé l’avantageuxfiltrage apporté par les lasers DFB à couplage complexe, engardant un seuil faible. Le cas spécifique d’un déphasaged’un quart de période entre les deux réseaux, correspondantà une condition de symétrie PT, induit des effetsunidirectionnels d’amplification en réflexion.Des lasers DFB à couplage par l’indice, par les pertes et àcouplage complexe avec différentes phases entre les réseauxont été fabriqués selon les techniques courantes deréalisation de circuits photonique intégrés : lithographieélectronique et gravure ICP notamment.Les mesures de caractéristiques courant /puissancemontrent une diminution du courant de seuil des lasers àcouplage complexe en comparaison de leur équivalent àcouplage par les pertes, et un comportement monomodeplus robuste et plus systématique en comparaison de leuréquivalent à couplage par l’indice.Les variations d’indice réelle et imaginaire dans les cavitésont été mesurés à l’aide d’un laser externe.La résistance au retour optique de nos lasers a également étéétudiée. Les résultats montrent une corrélation entre latolérance au retour optique et le déphasage des réseauxd’indice et de pertes, sans montrer d’améliorationsignificative de cette résistance par rapport aux lasers DFBà couplage par l’indice.Ce premier « véhicule test » sur l’application de la symétriePT aux lasers à contre réaction répartie a permis d’obtenirdes perspectives encourageantes quant à l’amélioration desperformances des technologies existantes. Ce travailconforte l’intérêt de ce concept pour la conception de lasersDFB tolérant au feedback et leur intégration dans unsystème laser-modulateur fonctionnant sur la même base. / The development of photonics during the pastdecades, enabled by the advent of nanofabricationtechnologies, witnessed the appearance of new types ofartificial materials such as photonic crystals,metamaterials, plasmonic circuits, and more recently the socalled “PT symmetry” structures. The characteristic featureof this new type of artificial structures is that though theyare described by non-Hermitian Hamiltonians theireigenvalues can still be real. In optics, several physicalphenomena are known to obey equations that are formallyequivalent to that of Hamiltonians in quantum mechanics.During this work, we investigated the design, fabricationand characterization of complex-coupled DFB lasers, withthe intent to apply Parity-Time (PT) symmetry to apractical device. The mode selectivity inside the cavity isbrought by the combination of a gain-coupled and indexcoupledBragg grating, under the form of respectively acorrugated waveguide and a metallic absorbing surfacegrating.Through the simulation of the mode evolution insideconventional DFB lasers and complexe-coupled DFBlasers using Ables matrix method, the advantages ofefficient mode filtering while keeping a low thresholdcurrent was observed. The specific phase shift of a quarterperiod, matching the PT-symmetric configuration, is foundto show highly asymmetric mode selection, with unidirectionalamplification in reflection.Index, gain and complex-coupled DFB lasers with differentphase shifts between loss and index grating profiles werefabricated, using photonics integrated circuits fabricationbuilding blocks: electron beam lithography and inducedcoupled plasma dry etching to name but a few.The characterization of the fabricated lasers shows areduction in threshold compared to equivalent third ordergain-coupled DFB lasers, and improved monomodeoperation and yield compared to third order index-coupledDFB lasers.Real and imaginary parts of the index modulation as wellas reflection spectral response was investigated by externaloptical probing of the laser cavities.The resistance of the CC DFB lasers to external opticalfeedback was studied. If results show an apparentcorrelation between the gratings phase shift and thefeedback resistance, but no significant improvement wasfound with regards to IC DFB lasers.This first milestone on the application of PT-symmetry tothe design and fabrication of DFB lasers provide interestingprospects on the improvement of existing technologies.This work reinforces the interest of this concept for thedesign of feedback tolerant DFB lasers, and theirintegration in an all PT-symmetric laser-modulator system.