Cavity quantum electrodynamics (QED) is the study of the interaction between light conned in a microcavity and material modes (such as single atoms or electrons in quantum wells), where the quantum nature of light is crucial.This thesis theoretically examines four dierent systems where light becomes strongly coupled with dierent material modes leading to dierent eects stemming from the dierent dimensionality and natures of the systems.The rst system consists of a semiconductor slab embedded into a zero-dimensional microcavity, leading to vacuum band gap opening of the electron dispersion caused by the interactions with the cavity photon mode.The second system is a quantum ring coupled to polarized light, calculated non-perturbatively.Since the polarization breaks time reversal symmetry, the particles in the ring will exhibit an energy dierence of particles with the same magnitude of angular momentum but dierent directions.The viability of these resulting in Aharonov-Bohm oscillations in large rings is considered.The third system consists of an array of quantum wires embedded into a planar microcavity.The inhomogeneity of the two directions along and perpendicular to the wires, coupled with the homogeneous two-dimensional photon mode, leads to an emergence of a hyperbolic region and many peculiar eects.The fourth and last work considers an algorithm to modify systems, leading to a ladder of equidistant energies.To illustrate, a radially symmetric nanoparticle with a hydrogenic impurity is analysed.The material composition along the radius can be altered to achieve a cascade of transitions in the Terahertz range.When multiple such particles are embedded into a resonant microcavity, one can convert photons of a higher energy to multiple Terahertz photons.
Cavity quantum electrodynamics (QED) is the study of the interaction between light conned in a microcavity and material modes (such as single atoms or electrons in quantum wells), where the quantum nature of light is crucial.This thesis theoretically examines four dierent systems where light becomes strongly coupled with dierent material modes leading to dierent eects stemming from the dierent dimensionality and natures of the systems.The rst system consists of a semiconductor slab embedded into a zero-dimensional microcavity, leading to vacuum band gap opening of the electron dispersion caused by the interactions with the cavity photon mode.The second system is a quantum ring coupled to polarized light, calculated non-perturbatively.Since the polarization breaks time reversal symmetry, the particles in the ring will exhibit an energy dierence of particles with the same magnitude of angular momentum but dierent directions.The viability of these resulting in Aharonov-Bohm oscillations in large rings is considered.The third system consists of an array of quantum wires embedded into a planar microcavity.The inhomogeneity of the two directions along and perpendicular to the wires, coupled with the homogeneous two-dimensional photon mode, leads to an emergence of a hyperbolic region and many peculiar eects.The fourth and last work considers an algorithm to modify systems, leading to a ladder of equidistant energies.To illustrate, a radially symmetric nanoparticle with a hydrogenic impurity is analysed.The material composition along the radius can be altered to achieve a cascade of transitions in the Terahertz range.When multiple such particles are embedded into a resonant microcavity, one can convert photons of a higher energy to multiple Terahertz photons.
In modern physics, the investigation of the interaction between light and matter is important from both a fundamental and an applied point of view. Cavity quantum electrodynamics (cavity QED) is the study of the interaction between light confined in a reflective cavity and atoms or other particles where the quantum nature of light photons is significant. The strong interaction between an exciton and cavity photon in a high-finesse microcavity can induce a hybrid light-matter eigenstate which is usually named as polariton in solid-state systems. This strong light-matter interaction can be achieved when this interaction is larger than all broadenings caused by other various factors e.g. electron phonon scattering and cavity loss. The polariton is now stimulating tremendous research interests due to its high potential in cavity quantum electrodynamics (QED) and the achievement of polaritonic devices. Moreover, when the interaction strength between an excitation and the cavity photon, quantified by vacuum Rabi frequency, becomes comparable to or larger than the corresponding electronic transition frequency in a cavity, the system can enter an ultrastrong coupling regime, which has been experimentally observed. In this regime, the standard rotating-wave approximation is no longer valid and the antiresonant term of the interaction Hamiltonian starts to play an important role, giving rise to exciting effects in cavity QED. The Aharonov-Bohm (AB) effect is a fundamental quantum phenomenon that bears the significance of the nature of electromagnetic fields and potentials. Besides its fundamental significance in quantum theory, its importance for applications in interferometric devices is omnipresent. Recently, since the 2D materials have triggered immense interest, some work has been done to integrate the AB effect with the electronic and transport properties of 2D materials. This thesis consists of two parts. In the first part, the light-matter coupling between cyclotron transition and photon is theoretically investigated in some 2-D materials such as the monolayer MoS2, graphene and monolayer black phosphorene (BP) systems. The results show that, in these 2-D materials, the ultrastrong light-matter coupling can be achieved at a high filling factor of Landau levels. Furthermore, we show that, in contrast to the case for conventional semiconductor resonators, the MoS2 system shows a vacuum instability. In monolayer MoS2 resonator, the diamagnetic term can still play an important role in determining magnetopolariton dispersion which is different from monolayer graphene system. The diamagnetic term arises from electron-hole asymmetry which indicates that electron-hole asymmetry can influence the quantum phase transition. Meanwhile, we show that, similar with some other 2D materials such as graphene and MoS2, the monolayer BP system shows a vacuum instability. However, in contrast with other 2D materials, the BP system displays a large energy gap between three branches of polaritons because of its strong anisotropic behavior in the eigenstates of the band structures. For the graphene system, we investigate the coupling of cyclotron transition and a multimode cavity described by a multimode Dicke model. This model exhibits a superradiant quantum phase transition, which we describe exactly in an effective Hamiltonian approach. The complete excitation spectrum in both the normal phase and superradiant phase regimes is given. At last, in contrast to the single mode case, multimode coupling of cavity photon and cyclotron transition can greatly reduce the critical vacuum Rabi frequency required for quantum phase transition, and dramatically enhance the superradiant emission by fast modulating the Hamiltonian. Our study provides new insights in cavity-controlled magneto-transport in these 2-D systems, which could lead to the development of polariton-based devices. The second part is a diversion from the main content of this thesis; readers who are not interested in foundational issues of physics can skip this part. For one charged quantum particle P moving in an electromagnetic vector potential Aˆµ = ( φˆ, - Aˆ ) created by some other charged particles, we can either use the framework of one particle quantum mechanics (OPQM) to calculate the evolutions of P, or we can treat this as an multi-particles problem in the framework of quantum field theory and calculate the evolution of P. These two methods need to be equivalent, i.e., they produce the same result for the evolution of P. One open question is how to describe the evolution of P within the framework of quantum field theory and show that these two methods yield the same result? In chapter 5, we are going to derive the OPQM from the quantum field theory, i.e., the quantum electrodynamics (QED) to be specific. We start with the discussions on the AB effect then raise a plausible interpretation within the QED framework. We provide a quantum treatment of the source of the electromagnetic potential and argue that the underlying mechanism in AB effect can be viewed as interactions between electrons described by QED theory where the interactions are mediated by virtual photons. On further analysis, we show that the framework of one particle quantum mechanics (OPQM) can be given, in general, as a mathematically approximated model which is reformulated from QED theory while the AB effect scheme provides a platform for our derivations. In addition, the classical Maxwell equations are derived from QED scattering process while both classical electromagnetic fields and potentials serve as mathematical tools that are constructed to approximate the interactions among elementary particles described by QED physics. This work opens up a new perspective on the nature of electromagnetic fields and potentials.
When in a quantum optical system the coupling between matter and cavity mode becomes comparable to the bare excitation frequency, we enter a non-perturbative coupling regime, as perturbation theory fails describing the system’s dynamics. While recent advances in Cavity Quantum Electrodynamics allowed to achieve very high values of the coupling strength, thanks to the resonators properties optimization and the employment of solid-state devices, an ever growing interest has been shown about the possibility of significantly modify materials’ properties. It has been demonstrated that the chemical structure of molecules strongly coupled to a photon mode can be altered, which opens the possibility to manipulate and control chemical reactions. The aim of this thesis is to explore non-perturbative regimes on several quantum systems, and to investigate the effects of the coupling upon their properties, such as internal degrees of freedom or electronic states structure. I first developed a novel theory to determine the polariton spectrum of a dipolar ensamble in which a Ising-like dipole-dipole interaction in the 2 non-perturbative regime is considered. A further important focus is the investigation of the saturation effects due to the inclusion of the inter-dipole interaction, and the interplay between the latter and light-matter coupling strength. I also explored specifically the influence of the coupling on the rotational degrees of freedom of an ensemble of two-dimensional freely rotating dipoles, all coupled to a single cavity mode, finding that they are driven by the collective light-matter coupling to undergo a crossover between an isotropic and an aligned phase. I then investigated the case of cavity-embedded doped quantum wells, demonstrating that not only it is possible to couple a discrete cavity mode and bound-to-continuum transitions, but also that a novel bound exciton state appears, induced by the coupling strength. This results shows how light–matter coupling can be used to tune both optical and electronic properties of semiconductor heterostructures beyond those permitted by mere crystal properties. Finally, I explored the physics of an array of THz metamaterial resonators coupled to cyclotron resonances of a two-dimensional electron gas, developing a multiple-mode theory that takes in account the interaction between multiple photon modes mediated by the electrons. My results show that this cross-interaction, due to the strong two-dimensional geometry of the optically active medium, leads to the hybridization of different uncoupled photon modes, and manifests as a visible change of the distribution of the coupled electromagnetic field.
Coupling between quantum emitters and modes of light is foundational to studies of quantum systems. Coherent interactions between matter and light have greatly advanced the development of quantum technologies. When an ensemble of atoms interacts with light that is confined within a cavity---a resonator for photons---light also mediates atom-atom interactions, leading to collective phenomena that cannot be extrapolated from microscopic behaviors. Understanding how interactions among quantum particles lead to macroscopic phenomena, such as phase transitions and breaking of symmetries, remains a challenge in modern physics. In this dissertation, I present results addressing this challenge in the context of mesoscopic arrays of optical-tweezer-trapped atoms interfaced with a high-finesse optical cavity. In particular, the physics we investigate arises from the collective scattering of light. Utilizing the ability to place atoms with nanometer-scale precision, we engineer superradiant and subradiant states, where control over interference of the emission from multiple atoms leads to collectively enhanced or suppressed amounts of scattered light. Building on this work, we investigate the emergence of optomechanical self-organization, mediated by superradiance in the cavity electromagnetic field. By coupling atoms to the same cavity mode, the atoms exert forces on one another through the exchange of photons, leading them to autonomously order themselves spatially. We characterize mesoscopic fluctuations and their effect on symmetry-breaking dynamics associated with self-organization. Finally, we extend this framework to theoretically investigate how the phase of the atom-cavity coupling can be altered to generate higher symmetries. Our analysis reveals first-order phase transitions and instabilities induced by non-reciprocal forces. Altogether, this work establishes a path towards realizing mesoscopic systems of complex phases of matter in cavity quantum electrodynamics with unprecedented programmability.
We consider theoretically a semiconductor nanostructure embedded in one-dimensional microcavity and study the modification of its electron energy spectrum by the vacuum fluctuations of the electromagnetic field. To solve the problem, a nonperturbative diagrammatic approach based on the Green's function formalism is developed. It is shown that the interaction of the system with the vacuum fluctuations of the optical cavity opens gaps within the valence band of the semiconductor. The approach is verified for the case of large photon occupation numbers, proving the validity of the model by comparing to previous studies of the semiconductor system excited by a classical electromagnetic field. The developed theory is of general character and allows for unification of quantum and classical descriptions of the strong light-matter interaction in semiconductor structures.
Cavity quantum electrodynamic (cQED) systems have attracted extensive research interest in the past decades as the main driving force of quantum optics. First experimental demonstrations focused on the enhancement of spontaneous emission and optical nonlinearities related to a single quantum emitter confined in a microcavity. Major technological effort was needed to enter the strong coupling regime of single emitter cQED to study for instance the non-harmonicity of resulting Jaynes-Cummings ladder and to perform quantum non-demolition measurements at the heart of quantum optics. Corresponding milestone experiments paved the way towards the realization of a wide variety of non-classical light sources bringing the concept of photonic quantum networks to a practical level. cQED systems can be realized using atomic, superconducting and semiconductor platforms. In view of future applications in the quantum information technology, the solid state platform of microcavities with embedded quantum emitters is the most attractive one as it promises low-cost mass production as well as interoperability with the integrated electronic circuit technology of today. Therefore, quantum dot (QD)-microcavity systems are very attractive for further investigations in this field. Indeed, even though cQED effects have been studied for many years now, there are still fundamental aspects remaining to be explored. One example is the exploration of a strongly coupled cQED system under coherent optical excitation which is one of the primary goals of this work. The work presented in this thesis aims at a deeper understanding of cQED effects in semiconductor based implementations of this central topic of quantum optics. It includes comprehensive spatially-resolved studies of the QD-micropillar system in the both weak and strong coupling regime. For this purpose an advanced 90 degree excitation and detection scheme, suitable for efficient wavelength-independent driving of the coupled exciton (X) and cavity mode (C) system, was implemented. This flexible and powerful technique enables access to the three-dimensional emission characteristics of QD-micropillars providing important new insight into cQED effects which is the central aspect of the first part of this thesis. The performed studies show for instance a pronounced anticorrelation (correlation) of the directional emission characteristics down to the single emitter level in the weak (strong) coupling regime demonstrating directly their fundamentally different nature. Related investigations of the lasing regime present a straightforward characterization method to demonstrate lasing action in high-Beta microlasers without the need for time consuming studies employing photon statistics. The second part of the thesis addresses another very important yet unexplored fundamental aspect of cQED. The main focus is on coherently-driven strongly-coupled QD-microcavity systems. Of particular interest is the regime where the coherent excitation dresses the X-C polariton at high excitation powers. This regime is found at the crossover from a quantum (Jaynes Cummings) to a semi-classical (Mollow Triplet-like) system and can be observed between the limiting cases of an anharmonic and a harmonic ladder solely by varying the excitation strength. An indispensable condition for the first observation of this transitory regime is driving the system through the matter (X) component, which distinguishes this work from previous studies. Counterintuitively, significant cavity losses with respect to the coupling strength are required to create the highly coherent state of the laser-dressed polariton. Moreover, this work pioneers in resonance fluorescence (RF) studies of strongly-coupled QD-microcavity systems and reveals that strong X-C coupling suppresses the RF substantially. Additionally, injection pulling of a single polariton is observed for the first time in the QD-microcavity system, which links this classical effect of injection locking, which is also found in macroscopic lasers, to the quantum regime. Complementary studies on long range off-resonant X-C coupling, mutual coupling of two QD Xs as well as temperature stability of the coherent coupling regime deepen the fundamental understanding of the strong light-matter interaction in semiconductor systems.
Cavity qed is the domain of quantum optics which studies the behaviour of single atoms and photons coupled together in an electromagnetic resonator. During the last ten years, various spectacular effects have been observed on such systems, either on the atom’s or on the field’s properties. The presence of a cavity around an atom can produce an alteration of the atomic radiative rates which has been observed in several experiments. Ideally, cavity qed deals with two-level atoms coupled resonantly or nearly resonantly to a single cavity mode. This is of course a simplification of real situations, in which atoms have many levels and the cavity sustains more than one mode. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect.