Semiconductor Bloch equations | EPFL Graph Search

The semiconductor Bloch equations (abbreviated as SBEs) describe the optical response of semiconductors excited by coherent classical light sources, such as lasers. They are based on a full quantum theory, and form a closed set of integro-differential equations for the quantum dynamics of microscopic polarization and charge carrier distribution. The SBEs are named after the structural analogy to the optical Bloch equations that describe the excitation dynamics in a two-level atom interacting with a classical electromagnetic field. As the major complication beyond the atomic approach, the SBEs must address the many-body interactions resulting from Coulomb force among charges and the coupling among lattice vibrations and electrons. Background The optical response of a semiconductor follows if one can determine its macroscopic polarization \mathbf{P} as a function of the electric field \mathbf{E} that excites it. The connection between \mathb

On the physics of multimode polaritons

Claudéric Ouellet-Plamondon

This thesis is devoted to the study of microcavity polariton systems, in which the strong coupling occurs between more than one exciton or photon modes i.e. multimode polaritons. The first part of this work states the theoretical background of light-matter interaction starting from quantum well excitons to the non-linear regime of interactions between polaritons. We apply this knowledge to the case of GaAs based microcavities with InGaAs/GaAs quantum wells which are experimentally tested. Sample characterization and optimization are also discussed. We first report on the observation of multiple polariton modes, originating from an electronic coupling between quantum wells inside a planar microcavity. When shallow quantum well stacks are placed at the antinodes of a microcavity, we measure a series of anticrossings when the cavity mode energy crosses that of the different excitonic levels. Comparing our experimental results with a coupled oscillator model that includes the electron and hole wave functions allows us to show that the exciton binding energy is affected by the interwell coupling. We then study the non-linear properties of these InGaAs based microcavities, in the search for polariton condensation. We study the effect of Indium content, number of quantum wells, types of quantum well stacks, number of pairs of Bragg mirrors and magnetic field on the non-linearity of the system. In all cases, we measure a single threshold, and a clear signature of the transition from strong to weak coupling regime. We discuss the limiting factors for condensation in our system, namely the cavity losses induced by optical disorder, the light-matter coupling strength, and the saturation of the quantum wells. In the second part of the thesis, we demonstrate the occurrence of spatial multistability using laterally confined polariton modes. We measure a multihysteresis curve of the transmitted intensity when we cycle the excitation power of a blue detuned laser with respect to the polariton modes. At each threshold of the hysteresis loop, we measure a switching of the spatial profile of the transmitted beam, and an energy jump of all the polariton modes. We reproduce all main characteristics of our experiment using a multimode generalization of the Gross-Pitaevskii equations in the exciton photon basis. The mechanism behind the spatial multistability is identified as a repulsive cross-interaction between polaritons in different modes. Following this experiment, we investigate the effect of decoherence on polariton bistability. We demonstrate how the polariton hysteresis loop collapses when increasing either the temperature or the power of a weak non-resonant laser. We explain this effect by the population of an incoherent reservoir that induces dephasing and repulsive interactions on the driven polaritons. All experimental findings are accurately simulated with the excitonic Bloch equations, and indicate that reservoir induced dephasing can be dominant over the reservoir induced energy blue shift. In the final chapter, we present ongoing work on polariton lattices, namely measurements of the band structure for a square, and an hexagonal lattice. We also present preliminary results on the effect of a magnetic field on the band structure of a polariton square lattice. We conclude by discussing a series of future experiments to continue the investigation of multimode polaritons.

EPFL2017

On the physics of polariton interactions

Naotomo Takemura

An exciton-polariton is a quasi-particle that emerges from the strong coupling between an exciton and a photon. Recently, the studies of the exciton-polariton have been receiving a great deal of attention in terms of both fundamental physics and potential applications. The very small polariton effective mass and the interactions brought respectively by the photon and excitonic content of polaritons enable a wide range of interesting physical phenomena including the realization of Bose-Einstein condensate, superfluidity, and quantum vortices. In addition to the interest in the basic physics, several device applications of semiconductor microcavities such as polariton switching, bistability, and stochastic resonance have also been proposed. In these researches, the interactions between exciton-polaritons, which is a source of nolinearity, are central. In this thesis, we explore the various aspects of the polariton interactions in semiconductor microcavities. We employ nonlinear spectroscopies as experimental techniques and compare our experimental results with different theoretical models. Firstly, we study lower-lower (upper-upper) polariton self-interactions and lower-upper polariton cross interactions. The self- and crossinteractions are identified in four-wave mixing two-dimensional Fourier spectra, which are followed by theoretical analyses based on a third-order perturbation theory and on a nonperturbative simulation of Gross-Pitaevskii equations. Secondly, using pump-probe spectroscopy, we measure the spin dependent nature of exciton-polariton interactions, which is called spinor interaction. The two spin projections of exciton-polaritons give rise to a spin anisotropy of the polariton interactions. In particular, we show that the polariton interactions with anti-parallel spins presents a scattering resonance behavior via an exciton molecule (biexciton), which we call polaritonic Feshbach resonance. The measurements of the spinor polariton interactions are compared with numerical simulations based on spinor Gross-Pitaevskii equations including the exciton-biexciton coupling. Finally, we explore the decoherence effect induced by the interaction of polaritons. Focusing on the delay dependence of the experimental pump-probe spectra, we find that the excitation induced dephasing (EID) plays an important role in the dynamics of exciton-polaritons. The delay dependence of the pump-probe spectra clearly probes that the coherent and incoherent parts of excitons temporally behave in a different way. These experimental features can be well reproduced only with the excitonic Bloch equations (EBE) approach, which is a theoretical framework that can include the incoherent population of excitons. In the last part of this thesis, a future perspective of the research is discussed while showing preliminary experimental results of pump-probe spectroscopy with a spectrally narrowband pump pulse.

EPFL2016

Dephasing effects on coherent exciton-polaritons and the breakdown of the strong coupling regime

Mitchell David Anderson, Souvik Biswas, Benoît Marie Joseph Deveaud, Daniel Oberli, Marcia Portella Oberli, Naotomo Takemura, Stéphane Trebaol

Using femtosecond pump-probe spectroscopy, we identify excitation-induced dephasing as a major mechanism responsible for the breakdown of the strong coupling between excitons and photons in a semiconductor microcavity. The effects of dephasing are observed on the transmitted probe-pulse spectrum as a density-dependent broadening of the exciton-polariton resonances and the emergence of a third resonance at high excitation density. A striking asymmetry in the energy shift between the upper and the lower polaritons is also evidenced. Using the excitonic Bloch equations, we quantify the respective contributions to the energy shift of many-body effects associated with Coulomb fermion exchange and photon assisted exchange processes and the contribution to collisional broadening.