Theoretical modeling of quantum dots nanolasers and disordered coupled-cavity arrays

Ultrasmall semiconductor lasers have emerged as strong candidates for the implementation of quantum information processing devices. Manufacturing such nanophotonic light sources heavily relies on the use of cavity quantum electrodynamic effects to enhance spontaneous emission and enable the lasing threshold to be crossed with gain contributions from only a few solid-state emitters. In the cavity quantum electrodynamic regime, the emission dynamics of nanolasers
is governed by photonic and electronic correlation and fluctuations effects. This thesis accompanies some of the advancements in ultrasmall lasers by using microscopic quantum-opticalmodels to enable a better understanding of the underlying physical effects.

The frst main topic of this thesis draws on time-resolved photon-correlation spectroscopy
to investigate the build up of second-order coherence, associated with lasing, on a different timescale than the emission itself in a quantum-dot photonic-crystal nanolaser emitting in the telecom band. By combining measurements perfomed by Dr. Galan Moody at the National Institute of Standards and Technology, Colorado, USA, with a microscopic semiconductor laser theory, the non-Markovian behavior of the emission dynamics is attributed to carrier-photon correlations that are not amenable by using laser rate-equation formalism. The obtained insights have direct implications with respect to the modulation response, repetition rate, noise characteristics, and coherence properties of nanolasers for device applications.
The second main topic concerns a theoretical modeling of single-emitter lasing effects in a quantum dot (QD)-microlaser under controlled variation of background gain provided by off-resonant discrete gain centers. In the framework of a judicious two-color excitation scheme, recently put forward by the group of Prof. Stephan Reitzenstein in Berlin, the background gain contribution of off-resonant QDs can be continuously tuned by precisely balancing the relative excitation power of two lasers emitting at different wavelengths. In this thesis, a multicomponent gain medium semiconductor laser theory has been developed, which in conjunction with the measurements allows for identifying distinct single-QD signatures in the lasing characteristics, and for distinguishing between gain contributions of a single resonant emitter and acountable number of off-resonant background emitters to the optical output of the microlaser.

The upshot of the joint theoretical and experimental investigation is that in experimentally acicessible systems, and in the investigated micropillar in particular, the single-QD gain needs to be supported by the background gain contribution of off-resonant QDs to reach the transition to lasing. Theoretical calculations based on the developed model reveal that while a single QD cannot drive the investigated micropillar into lasing, its relative contribution to the emission can be as high as 70 % and it dominates the statistics of emitted photons in the intermediate excitation regime below threshold.

The last part of the dissertation deals with the analytical and numerical investigation of collective lasing in disordered coupled-cavity arrays. These systems are an interesting physical architectures, wherein the optical coupling between their building blocks allows for exploring some exotic states of photons including the Mott insulator and the fractional quantum Hall effect. The analysis focuses on the Jaynes-Cummings-Hubbard Hamiltonian, where each cavity contains a single two-level quantum dot interacting with the confined local mode and contiguous cavities are mutually coupled by photon hopping. By introducing a diagonal average approximation, it can be show that results for translation invariant coupled cavities, i.e. homogeneous coupled cavities, can be extended for weak photonic disordered array of cavities.