Decoherence and excitation-transfer mechanisms in semiconductor quantum dots

The aim of this thesis is to supply a theoretical study of the interaction mechanisms between quantum dots beyond the simple picture of macroatoms. Coulomb interaction between excitons, exciton-phonon interaction as well as radiative interaction are, in particular, considered. These mechanisms can be exploited to coherently couple quantum dots, thus being the physical tool enabling quantum information processing using quantum-dot-based logic gates. On the other hand, the same mechanisms are responsible for the decoherence of the quantum-state that prevent the storing of the quantum information. Already if considered as simple two-level systems, quantum dots are subject to mutual interaction. Quantum dots in the excited state can be considered as dipoles, and are thus coupled with each other via the dipole-dipole electrostatic interaction. This results in excitation transfer between dots over distances of a few tens of nanometers. In Chapter 2 we show that taking into account the retarded nature of the electromagnetic field results in a correction to this effect, that become a leading contribution at large distances, effectively coupling quantum dots over distances of a few hundreds of nanometers. Strong exciton-phonon-coupling in quantum dots results in a very efficient decoherence mechanism. The strongly localized polarization in an excited quantum dot can induce virtual phonon emission and reabsorption processes which act as a phase-destroying mechanism. In quantum dot molecules the decay rate of the interband polarization is almost one order of magnitude larger than in the single quantum dot case, and depends on the interdot distance. The description of this coupling mechanism is possible only beyond the marcoatom picture. In Chapter 3 we develop a model that describes the phonon-mediated interaction between quantum dots in a dot molecule, explaining the strong distance dependence of the exciton dephasing rates in terms of a matching condition between the phonon wavelength and the interdot distance, which enhances the phonon-assisted scattering from bright to dark states. The heterodyne spectral interferometry is a novel implementation of transient nonlinear spectroscopy that enables to study the transient nonlinear polarization emitted from individual localized electronic transitions, in both intensity and phase. Two-dimensional spectra obtained by means of this technique display signals that can be associated to the coherent coupling between different resonances of the system under study. This technique is theoretically modeled for the first time in Chapter 4, where a very satisfactory description of the measured spectra is provided, showing that coherent coupling between different optical transitions of a quantum system result in off-diagonal peaks of the two-dimensional excitation spectrum. Furthermore, we show that in the low intensity regime, each spectral signal can be associated to a specific pair of coupled resonances as long as the level structure of the system under study is known.

Long-range radiative interaction between semiconductor quantum dots

Gaetano Parascandolo, Vincenzo Savona

We develop a Maxwell-Schrodinger formalism in order to describe the radiative interaction mechanism between semiconductor quantum dots. We solve the Maxwell equations for the electromagnetic field coupled to the polarization field of a quantum dot ensemble through a linear nonlocal susceptibility and compute the polariton resonances of the system. The radiative coupling, mediated by both radiative and surface photon modes, causes the emergence of collective modes whose lifetimes are longer or shorter compared to the ones of noninteracting dots. The magnitude of the coupling and the collective-mode energies depend on the detuning and on the mutual quantum dot distance. The spatial range of this coupling mechanism is of the order of the wavelength. This coupling should therefore be accounted for when considering quantum dots as building blocks of integrated systems for quantum information processing.

2005

Electronic and Optical Properties of Semiconductor Quantum Dots

Guillaume Jean Tarel

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.

EPFL2011

Cavity-Optomechanics with Silica Microtoroids

Stefan Alexander Weis

Here, I report on a cryogenic cavity optomechanics experiment that has been set up with the goal to cool a mechanical degree of freedom of a fused silica microtoroidal resonator into the quantum regime by means of a combination of cryogenic and laser cooling. Based on the experience with a Helium-4 exchange gas cryostat obtained during a previous cryogenic optomechanics experiment, a novel setup with a Helium-3 cryostat at its heart has been set up. Cooling of a mechanical degree of freedom of a microtoroid close to its motional quantum ground state could be achieved and a regime, where full quantum control becomes possible, has come into reach. Silica microtoroids sustain at the same time ultra-high finesse optical whispering gallery modes (WGM) as well as radial mechanical modes ("radial breathing modes", RBM). The two degrees of freedom are mutually coupled, since mechanical motion changes the optical resonance frequency, and the mechanical motion is affected by the radiation pressure forces of an optical field contained in the optical mode. As the optical cavity lifetime is finite, the intracavity optical field amplitude is not adjusting instantaneously to the changed boundary conditions as induced by a mechanical displacement, but in a retarded manner, which gives rise to an effect known as dynamical backaction, that for example can be used to laser cool a mechanical mode. Using a 1550 nm laser important insight has been gained on the dependency of mechanical decay rate and frequency as a function of temperature, which is dominated by two level systems within amorphous fused silica. The different temperature regimes have been explored, including experiments at the lowest accessible temperatures, where evidence of resonant saturable absorption of TLS has been found. Using 780 nm light instead, cooling below ten quanta could be achieved and "optomechanically induced transparency", the optomechanical equivalent of electromagnetically induced transparency as found in atomic vapors, could be demonstrated, enabling all-optical switching of a laser beam and storage of pulses. Novel, optimized spokes-supported toroids then enabled us to push up the optomechanical coupling sufficiently, such that cooling to below two thermal quanta could be achieved and —for the first time in the optical domain— the quantum-coherent coupling regime could be accessed. Here, the optomechanical coupling rate exceeds the optical and mechanical decay rates (i.e. "strong coupling"), but also the mechanical decoherence rate, such that quantum-state transfer between optics and mechanics comes into reach. In addition, this thesis contains the technological steps taken and experimental hurdles overcome towards these experiments.