Nanowire Defined Double Quantum Dot Maser

Abstract

Motivated by ongoing experiments in the group of Jason Petta (Princeton University), we investigate a system of double-quantum dot coupled to a cavity and also coupled to a lead of conducting electrons. These experiments provide a platform to investigate several aspects of non-equilibrium physics studied in condensed matter physics, quantum optics and lasers, thus bringing these different fields under a common umbrella. The double-quantum dot coupled to a cavity is well calibrated and a tunable setup helping to probe the rich physics of Jaynes Cummings Hamiltonian and its various extensions. It captures the physics of conventional lasers (in some parameter regimes) and even goes beyond it providing an example of a non-conventional maser. The aim of the thesis is broadly three-fold in nature. Firstly, we will arrive at an effective Hamiltonian and accompanying Liouvillians from first principles by studying the role of phonons and conducting electrons. We show that phonons provide a systematic path to understand the origin of the relaxation and dephasing Lindblad operators which are usually phenomenologically added. The role of conduction electron bath as a source of incoherent pump (to the gain medium) has been established and quantified. Secondly, we compute analytically and numerically the various experimentally measured quantities of interest such as the transmission amplitude, phase-response and the electron current across the double dot. The analytics (largely based using analogy with lasers) and exact numerics have been compared thereby helping us to put-forward the various regimes of validity of several systematic approximations in various parameter regimes. We believe that such an involved quantitative understanding of validity regimes is central to exploring the physics coming out of these recent experiments. Thirdly, we make an extensive comparison between our theory and recent experimental data (Yinyu Liu et al, Private Communication, 2013). We show that our theoretical results stemming largely from first principles agree with most of the experimental data highlighting the role of phonons. However, some open questions remain due to discrepancy between theory and experiment in some regimes of parameters.