Strong coupling between a quantum system and its many-body environment is becoming an increasingly important topic for many branches of physics. Numerous systems of experimental and technological relevance demonstrate strong system-environment coupling, leading to complex dynamical behaviour. This thesis is concerned with two particular examples of such systems, namely quantum dots (QDs) and excitonic energy transfer (EET) in molecular systems. Traditional quantum optics treatments are often insufficient to describe the transient, steady state, and optical properties of QDs due to system-environment correlations. In contrast, we present a modified theory of quantum optics capable of capturing the influence of a thermal environment on the behaviour of QDs. Using this framework we demonstrate a striking departure of the emission spectra and photon measurement statistics of a classically driven QD when compared to an analogous atomic system. Furthermore, in contradiction to accepted notions of decoherence and dissipation, we show that the interaction between a QD and its thermal environment induces non-classical light-matter correlations in an otherwise semi-classical regime of cavity quantum electrodynamics. Away from QDs, we develop the reaction coordinate (RC) formalism to describe the dynamics of a system coupled to a low frequency environment — a regime important to EET systems. We do so by identifying and incorporating important environmental degrees of freedom into an enlarged system Hamiltonian. Uniquely, this approach gives insight directly into the dynamical evolution of the environment and correlations accumulated between the system and environment. Furthermore, it is demonstrated that these corre- lations persist into the steady state, generating non-canonical equilibrium states of the system and environment. We then apply the RC model to describe EET in a molecular dimer, highlighting the effect that under- and over-damped environments have on the excitation dynamics. In doing so, we show interactions between the dimer and a structured environment can significantly enhance the energy transfer rate.
Strong coupling between a quantum system and its many-body environment is becoming an increasingly important topic for many branches of physics. Numerous systems of experimental and technological relevance demonstrate strong system-environment coupling, leading to complex dynamical behaviour. This thesis is concerned with two particular examples of such systems, namely quantum dots (QDs) and excitonic energy transfer (EET) in molecular systems. Traditional quantum optics treatments are often insufficient to describe the transient, steady state, and optical properties of QDs due to system-environment correlations. In contrast, we present a modified theory of quantum optics capable of capturing the influence of a thermal environment on the behaviour of QDs. Using this framework we demonstrate a striking departure of the emission spectra and photon measurement statistics of a classically driven QD when compared to an analogous atomic system. Furthermore, in contradiction to accepted notions of decoherence and dissipation, we show that the interaction between a QD and its thermal environment induces non-classical light-matter correlations in an otherwise semi-classical regime of cavity quantum electrodynamics. Away from QDs, we develop the reaction coordinate (RC) formalism to describe the dynamics of a system coupled to a low frequency environment — a regime important to EET systems. We do so by identifying and incorporating important environmental degrees of freedom into an enlarged system Hamiltonian. Uniquely, this approach gives insight directly into the dynamical evolution of the environment and correlations accumulated between the system and environment. Furthermore, it is demonstrated that these corre- lations persist into the steady state, generating non-canonical equilibrium states of the system and environment. We then apply the RC model to describe EET in a molecular dimer, highlighting the effect that under- and over-damped environments have on the excitation dynamics. In doing so, we show interactions between the dimer and a structured environment can significantly enhance the energy transfer rate.
Reduced abstract. This Thesis explores emergent cooperative phenomena in collective light-matter systems. We study ensembles of interacting quantum emitters coherently driven by a laser field and coupled to photonic structures, focusing on the hybrid description of emitters dressed by light. The interplay among quantum emitters, coherent driving, and photonic environments reveals a rich landscape of cooperative effects. While single-emitter dressing has been widely studied, we address collective phenomena in two non-identical emitters modelled as two-level systems. Strong interaction forms a dimer exhibiting superradiant and subradiant states, with two-photon resonances directly connecting ground and doubly excited states. This nonlinear process, central to the Thesis, enables new regimes of cooperative light-matter physics. Analytical studies show how interactions reshape observables such as emission intensity, photon statistics, and spectra, offering implications for quantum metrology. The sensitivity of two-photon processes to emitter distance and driving strength enables high-precision sensing and sub-wavelength imaging. Unexpectedly, we find that off-resonant virtual states may gain population through dissipation, redefining their role in open systems. To capture this, we develop a hierarchical adiabatic elimination method for metastable dynamics. We also analyze entanglement in emitters coupled to a lossy cavity, identifying five mechanisms, including the frequency-resolved Purcell effect introduced here. This selective enhancement stabilizes cooperative states and enables scalable entanglement. Our models, tailored to solid-state platforms such as quantum dots and molecular aggregates, address challenges like inhomogeneous broadening and decoherence, demonstrating the feasibility of harnessing cooperative light-matter effects for quantum technologies.
Remarkable experimental progress and theoretical advancements in the study of strongly corre- lated systems have opened up new doors towards a better understanding of interesting states of matter. Such states could possibly be used to develop novel technological applications based on the principles of quantum mechanics. In recent years, the investigation of both complex solid state and ultracold atom systems has lead to a number of fascinating discoveries with regards to their non-equilibrium properties. One route to probe non-equilibrium physics is to consider the evolution of open systems defined by the coupling to an external environment introducing dissipation. Engineering the environment according to predefined requirements can then be used to dynamically prepare states which are difficult to access otherwise. This thesis explores the dynamics of many-body open quantum systems aiming at under- standing the effects resulting from the interplay of kinetic motion, interactions and dissipation in different physical settings. First, we build upon recent developments concerning the coupling of ultracold atoms to optical resonators which are subject to photon losses. We show how the dissipation can trigger an attractor dynamics towards a topologically non-trivial steady state that is robust against perturbations. The numerically obtained full open system evolution en- ables us to not only characterize in detail the steady state but also to analyze the features of the approaching dynamics. Second, we study the propagation of two-time correlation functions in interacting quantum spin-1/2 chains in contact with an environment causing dephasing. Pro- vided with the numerically exact full time-evolution, we identify an algebraic scaling regime where time-translation invariance breaks down and uncover the emergence of aging dynam- ics. Finally, we study a system of interacting fermionic atoms in a one-dimensional lattice with particle loss at the central site. There we report on the dissipation-induced deceleration of the non-equilibrium dynamics known as the quantum Zeno effect. As in the majority of cases quantum many-body systems are not solvable analytically, another central aspect of this thesis deals with adapting numerical methods based on matrix product state algorithms to investigate open quantum systems dynamics.
Recent advances in theoretical physics have increasingly focused on the dynamics of quantum systems with many interacting degrees of freedom, while ultracold atom platforms now enable the realization of diverse theoretical models with precise control over system parameters and advanced monitoring techniques. A prominent example is cavity quantum electrodynamics (CQED), where large atomic or molecular ensembles are coupled to high-finesse optical cavities, enabling strong interaction with confined electromagnetic modes and leading to phenomena such as the superradiant phase transition, in which atoms and photons form a coherent state. Most theoretical studies of CQED have concentrated on regimes of spatially uniform atom–cavity coupling, where collective behavior allows a description in terms of the classical dynamics of a few macroscopic variables. However, experimental capabilities now permit exploration beyond this limit, though theoretical progress is hindered by the exponential computational complexity of simulating large quantum systems, particularly when environmental coupling is included. This thesis addresses such challenges by developing efficient approaches, within the Keldysh formalism of non-equilibrium quantum field theory, to study systems with strongly disordered interactions coupled to external reservoirs. Two representative models are considered: a disordered spin–boson model describing light–matter interactions with quenched disorder, relevant to recent CQED experiments in confocal cavities, and a fermion–phonon system governed by the Yukawa–Sachdev–Ye–Kitaev (Yukawa-SYK) model. Both systems are quantum critical, exhibiting a continuum of low-energy modes above their stationary states, yet disorder produces qualitatively distinct dynamical behaviors: in the spin–boson system it induces slow, glassy relaxation, whereas in the Yukawa-SYK model it leads to rapid thermalization. These contrasting outcomes reveal the non-trivial role of disorder in quantum many-body systems and motivate further investigation into its effects on non-equilibrium quantum dynamics.
This thesis is devoted to theoretically study the systems of single quantum dots (QDs) embedded in various photonic nanostructures, in close relation with experimental data. The word single is essential: due to their nanometer size, QDs have mainly been studied as ensembles. It is only recently that the experimental progress, in particular in the domain of QDs growth, has allowed to address single QDs. This helped to observe that the confined states in a QD resemble those of an atom, leading in turn to the macro-atom picture for QDs. It opened the path to the study of cavity quantum electrodynamics (CQED) in the solid state, as the analogous of a system of an atom in an electromagnetic cavity. However, already at the level of the QD (i.e. without a solid state cavity), the macro-atom picture has been proven to be oversimplified. Various effects related to the solid state environment of the QD have been experimentally and theoretically evidenced, like the influence of acoustic and optical phonons. These are channels of decoherence for the otherwise well isolated and confined QD levels. When adding the cavity, these effects are possibly enhanced, which can lead to very large deviations from the CQED ideal picture. Therefore the clear understanding of these effects is of essential importance, especially in view of the application of solid state systems to quantum information science. In Chapter 2, we address the radiation-matter coupling between two QDs in a nanocavity. This field of research combines the high quality of light resonators to the nonlinearities of the semiconductor material. It is promising in view of manipulating and transferring single long-lived excitations, an essential goal for quantum information science. Then, we study the deviations of a QD from the idealized macroatom picture. First, in Chapter 3, we include the influence of acoustic phonons on the light emitted by a QD-cavity system. We show that the QD modified susceptibility leads to the qualitative explanation of the cavity feeding effects, which is one of the most striking deviations of the QD-cavity system from the ideal CQED picture. In addition to phonons are extended two-dimensional states populated by the non resonant pumping laser in the QD's wetting layer (WL). In Chapters 4 and 5 we build a Monte-Carlo model of the excitation-decay mechanism in a QD-cavity system. We use it to describe the influence of WL states on the dynamics of the QD, leading in turn to a non-CQED behavior. This approach is particularly successful in the case of large QD-cavity detuning, where it predicts both time-dependent and spectral characteristics of the emitted light. Finally, in Chapter 6, we discuss our conclusions, emphasizing in particular that the knowledge of the actual solid state environment of the QD leads to a better control over the parameters allowing to reach the CQED regime. We also discuss the possible extensions of this work, in particular in relation to the analysis of the stimulated emission regime.
Open quantum systems have drawn attention over decades due to its applicability in the foundation of theoretical physics, e.g. statistical mechanics, quantum mechanics and condensed matter physics. The dynamics of open quantum systems has been described as separate entities from their surrounding environment that consists of a very large number of modes, somehow coupled to the mode of the system. Even though the exact solution of the dynamical behavior of the system is impossible to calculate, we obtain a tentative solution using the crucial Markov approximation. The input-output formalism of the quantum Langevin equation (QLE) has been considered as a useful tool which provides a semi-classical description of the dynamics of the system, whereas the master equation provides a complete picture of the dynamics of the system expressed in terms of density matrix. While studying the dynamics of nonlinear system/environment coupling using QLE, we see, for a small value of external field, that the steady state system field does not change much from the steady state field obtained in the absence of nonlinear dissipation. However, in a case where a stronger external field is applied, we see that the deviation becomes substantial from the solution of linear system. We also see that the nonlinear coupling introduces significant difference in the cavity fluctuation spectrum. The description, therefore, provides a potential explanation of parametric effects in terms of nonlinear dissipation phenomena associated with the nonlinear coupling. Even though the theories developed in the context of open quantum systems have proven to be powerful tools, they do not provide a satisfactory platform to be implemented on non-linear Hamiltonians. We often approximate it by linearizing over nonlinear steady state field amplitude, and therefore, the interesting effects are often overlooked. The limitation of the analytics provokes us to simulate open quantum dynamics numerically. The numerical method consists of transformation of the environmental degrees of freedom to a one-dimensional many-body chain, and the computational technique includes numerical diagonalization and renormalization process. The time-adaptive density matrix renormalisation group (t-DMRG) is known as one of the most powerful techniques for the simulation of strongly-correlated many-body quantum systems. In this thesis, along with the theoretical modeling, we implement DMRG numerical scheme for the simulation of canonical S/B model by mapping it to one-dimensional harmonic chain with nearest neighbor interactions, and use the method to investigate the dynamics of the free dissipative system. The thermalization of open quantum systems is also studied by generating minimally entangled typical thermal states (METTS) through imaginary time evolution, and real-time evolving an empty system in the presence of the thermal bath. Further, we simulate coherently driven free dissipative Kerr nonlinear system numerically using Euler's method by solving Heisenberg equation of motion and t-DMRG algorithm, and demonstrate how the numerical results are analogous to classical bistability. By comparing with analytics, we see that the DMRG numerics is analogous to the quantum-mechanical exact solution obtained by mapping the equation of motion of the density matrix of the system to a Fokker-Plank equation. The comparison between two different numerical techniques shows that the semi-classical Euler's method determines the dynamics of the system field of one among two coherent branches, whereas DMRG numerics gives the superposition of both of them. Hence, DMRG-determined time dynamics undergoes generating non-classical states. Our approach of dealing with nonlinearity represents an important contribution in the developments of technique to study the dynamical and steady-state behavior of open quantum systems, which is a fundamental aspect of quantum physics.
The object of this PhD Thesis is light and matter quantum interaction including studies on cavity and circuit quantum electrodynamics (CQED and cQED), quantum information theory and entanglement dynamics in open systems. In recent years both theoretical and experimental efforts have been devoted to study problems regarding the transfer of quantum correlations, quantum memories, entanglement protection against decoherence and new regimes accessible in cQED. One of the fundamental model underlying these topics is the well known Jaynes-Cummings (JC) one for light-matter interaction, introduced in quantum optics already in 1963. This paradigmatic model describes the coherent exchange of a single excitation between a qubit (a two-level system) and a mode of a quantized harmonic oscillator. The JC model describes a lot of purely quantum effects such as Rabi oscillations and generation of entangled quantum states, which were confirmed by several sophisticated experiments in CQED. This model has been then applied in many other frameworks. Analytical results can be derived only under the so-called rotating wave approximation (RWA), which allows to neglect the energy contributions coming from the counter-rotating terms, which describe the simultaneous excitation (or de-excitation) of the qubit and the field mode. In this Thesis a first interesting investigation, based on the JC model, is related to the realization of quantum memories. The main aspect is the transfer of generic quantum entangled states of a propagating radiation to some qubits, such as two-level atoms placed in separated optical cavities. Generalizing previous results for bipartite entangled systems, I investigated the more complex case of tripartite systems, where the very quantification of entanglement is still an open problem. This issue is broadened to open systems in contact with a common environment which induces decoherence effects unavoidable in realistic implementations. The main result of this analysis is that it is possible to map in an optimal way a quantum state from radiation to qubits in the unitary dynamics, and even in the presence of a dissipative environment a significative amount of entanglement can be transferred. This study has been carried on with either theoretical calculations or numerical simulations performed adopting the powerful Monte Carlo wave function method. A second important problem for quantum memories faced in this PhD Thesis, regards the protection of qubits entanglement for long enough times in order to implement quantum information tasks. A possible way to obtain this goal is to add an external coherent field driving two or more two-level atoms interacting with a common mode of a cavity electromagnetic field. In fact it is possible to demonstrate that, under certain conditions, an effective Hamiltonian of the whole system involves, together with the familiar JC terms, also the counter-rotating ones. The main feature that comes out from this analysis is the possibility to freeze, during system dynamics, peculiar quantum entangled states of the atomic qubits in so called decoherence-free subspaces. This important property allows to store the entanglement in matter qubits, isolating the quantum state from environment induced decoherence. Though the system includes dissipation, analytical results have been obtained for multipartite entanglement and decoherence by solving the master equation through a projection on a suitable basis and using the method of characteristics. In particular it is possible to monitor the rate of decoherence via measurements of joint atomic probabilities, shading light on the fascinating border between the quantum and the classical world. A last topic investigated in this Thesis concerns the recently developed and quite promising implementation of the JC model well outside CQED, that is cQED. Here superconductive circuits, which play the role of artificial atoms, interact on-chip with transmission line resonators, instead of the usual electromagnetic cavities. These systems have the advantage of being quite easily engineered exploiting the most advanced available technologies. Moreover they allow a great flexibility in handling the relevant parameters, since the inter-system coupling is here of capacitive or inductive nature, instead of the usual electric dipole interaction in CQED. In this way a strong and ultrastrong coupling regime have become available, giving a direct access to the physics beyond the JC model and its possible applications. I first performed a detailed characterization of system dynamics in order to test the main approximations usually introduced to describe superconductive circuits as qubits. Then I described, both analytically and numerically, the dissipative dynamics of a superconductive qubit coupled to a resonator mode in the deep strong regime.