A lot of experimental and theoretical studies of a system in cavity quantum electrodynamics (cavity QED), which consists of two spatially separated quantum emitters strongly coupled to a single optical cavity mode, have recently attracted much interest in the quantum optics community for various quantum information applications. Here, we propose a method for high-order harmonic generation in a photonic crystal microcavity coupled to single semiconductor quantum dots (QDs). The system is coherently driven by a bichromatic laser consisting of the control and signal fields at low input power (a few nanowatts) and the cavity output power via the cavity loss channel is monitored. Via numerical simulations, we thoroughly explore the difference of the generated high-order harmonic spectra between two QDs, one QD, and zero QDs in microcavity. The results clearly indicate that harmonic generation can be significantly enhanced via collective coherent coupling in the case of two spatially separated QDs coupled to the same photonic crystal microcavity mode. In addition, we present a study of the carrier-envelope phase (CEP) effect on high-order harmonic spectra, which may provide the insight of CEP effect in a new regime. Beyond this, our obtained results also apply to other classes of single-mode cavity-QED setup incorporating two-level atoms or comparable solid-state emitters.
A lot of experimental and theoretical studies of a system in cavity quantum electrodynamics (cavity QED), which consists of two spatially separated quantum emitters strongly coupled to a single optical cavity mode, have recently attracted much interest in the quantum optics community for various quantum information applications. Here, we propose a method for high-order harmonic generation in a photonic crystal microcavity coupled to single semiconductor quantum dots (QDs). The system is coherently driven by a bichromatic laser consisting of the control and signal fields at low input power (a few nanowatts) and the cavity output power via the cavity loss channel is monitored. Via numerical simulations, we thoroughly explore the difference of the generated high-order harmonic spectra between two QDs, one QD, and zero QDs in microcavity. The results clearly indicate that harmonic generation can be significantly enhanced via collective coherent coupling in the case of two spatially separated QDs coupled to the same photonic crystal microcavity mode. In addition, we present a study of the carrier-envelope phase (CEP) effect on high-order harmonic spectra, which may provide the insight of CEP effect in a new regime. Beyond this, our obtained results also apply to other classes of single-mode cavity-QED setup incorporating two-level atoms or comparable solid-state emitters.
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.
Carrier-envelope-phase-dependent effects of high-harmonic generation for two-level atoms interacting with Gaussian shape few-cycle pulses (with $\ensuremath{\phi}=0$ and $\ensuremath{\phi}=\ensuremath{\pi}/2$) have been investigated theoretically by using a time-frequency analysis. The differences in energies and populations of the two adiabatic states and the harmonic spectra in the cutoff region are illustrated. We find that, by tuning the carrier-envelope phase, the high-harmonic generation in the cutoff region can be controlled. Our results also show that the model of two-level atoms driven by few-cycle pulses can be used to study carrier-envelope phase effects.
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.
A single atom in a cavity is the model system of cavity quantum electrodynamics (CQED). The strong coupling regime between the atom and cavity-confined photon corresponds to the reversible exchange of energy between the two modes, and underpins a wide range of CQED phenomena with applications in quantum information science, including for example as quantum logic gates and as sources of entangled states. An important advance was achieved recently when strong coupling between excitons and cavity photons was reported for the first time for localized quantum dots (QDs) in micron-size solid state cavities. This has significance in terms of scalability and integration with other optical devices, and could lead to the emergence of "quantum optics on a chip" technology. However the results presented so far for quantum dots are in the linear regime, corresponding to coupling to the vacuum field (vacuum Rabi splitting); they are not a true QED effect and can equally well be described by classical physics as the coupling between two oscillators. In this paper, we present evidence for a purely quantum phenomenon for the QD/cavity photon system, namely the increase in splitting of the levels when the mean number of photons in the cavity is increased. This corresponds to non-linearities on the single-photon scale: the presence of a single excitation in the cavity changes the level structure, affecting the emission energies for a second photon. Such results are a first step in demonstrating the promise of quantum dots for CQED applications.
The ability to engineer and convert photons between different modes in a solid-state approach has extensive technological implications not only for classical communication systems but also for future quantum networks. In this paper, we put forward a scheme for coherent mode conversion of optical photons by utilizing the intermediate coupling between a single quantum dot and a bimodal photonic crystal microcavity via a waveguide. Here, one mode of the photonic crystal microcavity is coherently driven by an external single-frequency continuous-wave laser field and the two cavity modes are not coupled to each other due to their orthogonal polarizations. The undriven cavity mode is thus not directly coupled to the input driving laser and the only way it can get light is via the quantum dot. The influences of the system parameters on the photon-conversion efficiency are analyzed in detail in the limit of weak probe field and it is found that high photon-conversion efficiency can be achieved under appropriate conditions. It is shown that the cavity dark mode, which is a superposition of the two optical modes and is decoupled from the quantum dot, can appear in such a hybrid optical system. We discuss the properties of the dark mode and indicate that the formation of the dark mode enables the efficient transfer of optical fields between the two cavity modes.
Multi-photon lasing has been realized in systems with strong nonlinear interactions between emitters and cavity modes, where single-photon processes are suppressed. Coherence between the internal states of a quantum emitter, or among multiple emitters, plays a key role. Such continuous nonclassical sources of light can find applications in quantum computation, quantum sensing, quantum metrology, and quantum communication.
This thesis explores the multi-photon lasing phenomena in various quantum dot-photonic crystal cavity quantum electrodynamic (QED) setups. Exciton-phonon interactions are inevitable in such systems and are incorporated using the polaron-transformed master equation. The Born-Markov approximation is employed to obtain the reduced density matrix rate equation. Using quantum laser theory, we derived the Scully-Lamb laser rate equations and evaluated the single- and multi-photon excess emission rates defined as the difference between emission and absorption rates into the cavity mode without mean-field approximations. We investigated cooperative two-photon lasing, correlated emission lasing, hyperradiant lasing, non-degenerate two-mode two-photon lasing, and continuous variable entanglement in open quantum systems with single or multiple semiconductor quantum dots (two-level, three-level, and four-level) driven coherently/incoherently and coupled to single/ bimodal cavities.