The role of local fields in quantum electrodynamics of isolated quantum dot (QD) has been analyzed. The system is modeled as a strongly confined in space two-level quantum oscillator illuminated by quantum light. Relation between local and acting fields in QD has been derived in the dipole approximation from the integral Maxwell equations for electromagnetic field operators. A formalism of the electromagnetic field quantization in electrically small scatterers has been developed. As a result, Hamiltonian of the system has been formulated in terms of the acting field with a separate term responsible for the effect of depolarization. Schr\"odinger equation with that Hamiltonian has been solved in linear approximation. Interaction of QD with different quantum states of light, such as Fock states, coherent states, Fock qubits, entangled states, has been analyzed. It has been shown that the local-fields induce a fine structure of the QD absorption (emission) spectrum: instead of a single line with the frequency corresponding to the exciton transition, a doublet appears with one component shifted to the blue (red). The value of the shift depends only on the geometrical and electronic properties of QD while the intensities of components are completely determined by the quantum light statistics. It has been demonstrated that in the limiting cases of classical light and single-photon state the doublet is reduced to a singlet shifted in the former case and unshifted in the latter one. A physical interpretation of the predicted effect has been proposed. Possible ways of experimental observation of the effect has been discussed together with the potentiality of its utilization in the quantum information processing.
The role of local fields in quantum electrodynamics of isolated quantum dot (QD) has been analyzed. The system is modeled as a strongly confined in space two-level quantum oscillator illuminated by quantum light. Relation between local and acting fields in QD has been derived in the dipole approximation from the integral Maxwell equations for electromagnetic field operators. A formalism of the electromagnetic field quantization in electrically small scatterers has been developed. As a result, Hamiltonian of the system has been formulated in terms of the acting field with a separate term responsible for the effect of depolarization. Schr"odinger equation with that Hamiltonian has been solved in linear approximation. Interaction of QD with different quantum states of light, such as Fock states, coherent states, Fock qubits, entangled states, has been analyzed. It has been shown that the local-fields induce a fine structure of the QD absorption (emission) spectrum: instead of a single line with the frequency corresponding to the exciton transition, a doublet appears with one component shifted to the blue (red). The value of the shift depends only on the geometrical and electronic properties of QD while the intensities of components are completely determined by the quantum light statistics. It has been demonstrated that in the limiting cases of classical light and single-photon state the doublet is reduced to a singlet shifted in the former case and unshifted in the latter one. A physical interpretation of the predicted effect has been proposed. Possible ways of experimental observation of the effect has been discussed together with the potentiality of its utilization in the quantum information processing.
A theory of both linear and nonlinear electromagnetic responses of a single quantum dot (QD) exposed to quantum light, accounting for depolarization induced local field has been developed. Based on the microscopic Hamiltonian accounting for the electron-hole exchange interaction, an effective two-body Hamiltonian has been derived and expressed in terms of the incident electric field, with a separate term describing the QD depolarization. The quantum equations of motion have been formulated and solved using the Hamiltonian for various types of the QD optical excitation, such as Fock qubit, coherent fields, vacuum state of electromagnetic field, and light with arbitrary photonic state distribution. For a QD exposed to coherent light, we predict the appearance of two oscillatory regimes in the Rabi effect separated by the bifurcation. In the first regime, the standard collapse-revival phenomenon does not reveal itself and the QD population inversion is found to be negative, while in the second one, the collapse-revival picture is found to be strongly distorted as compared to that predicted by the standard Jaynes-Cummings model. For the case of QD interaction with an arbitrary quantum light state in the linear regime, it has been shown that the local field induces a fine structure of the absorbtion spectrum. Instead of a single line with frequency corresponding to the exciton transition frequency, a duplet appears, with one component shifted by the amount of the local field coupling parameter. It has been demonstrated that the strong light--matter coupling regime arises in the weak-field limit. A physical interpretation of the predicted effects has been proposed.
The influence of local fields on the excitonic Rabi oscillations in isolated, arbitrary shaped quantum dot (QD) has been theoretically investigated. Hamiltonian of the system "QD+electromagnetic field" has been obtained. Both QD interaction with classical electromagnetic field and ultrashort optical pulse has been considered. As a result, the bifurcation and anharmonism in the Rabi oscillations in a QD exposed to the monochromatic field have been predicted. The dependence of Rabi oscillations period on the QD depolarization parameter, which characterize local field has been obtained. It has been shown, that for the Gaussian pulse the final state of inversion as a function of peak pulse strength demonstrates step-like transitions.
A theory of the nonlinear interaction between a single quantum dot (QD) and electromagnetic fields, accounting the QD-depolarization (local-field) has been developed. QD excitation by classical and quantum electromagnetic fields such as coherent state of light, Fock qubit and gaussian excitation has been considered. As a result, for the case of the QD illuminated by coherent states of light, we predict the appearance of two oscillatory regimes in the Rabi oscillations. In the first one, signatures of Rabi oscillations are found to be suppressed: the population inversion is negative and the conventional collapse-revivals phenomenon is absent, while in the second one the collapse and revivals are appeared, showing significant difference as compared to those predicted within the standard Jaynes-Cummins theory. Under the pulsed excitation, Rabi oscillation dynamics is found to be strongly depended on the input pulse area and duration.
The influence of electron-hole dipole-dipole interactions (local fields) on the excitonic Rabi oscillations in an isolated quantum dot (QD) has been theoretically investigated. An analysis for the QD interaction with monochromatic field and ultrashort Gaussian pulse has been performed. On the basis of optical Bloch equations the Rabi oscillation dynamics has been investigated. As a result, the bifurcation and essentially anharmonic regimes in the Rabi oscillations in a QD exposed to the monochromatic field have been predicted. The strong dependence of the period of Rabi oscillations on the QD depolarization has been revealed. For the Gaussian pulse it has been shown that the final state of inversion as a function of the pulse peak strength demonstrates step-like transitions.
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.