Master Equations for Computing Gauge-Invariant Observables in the Ultrastrong Coupling Regime of Cavity-QED
physics , quantum optics , cavity quantum electrodynamics (QED)
The revolutionary discoveries made in quantum theory have caused a surge of technological innovation --- from the laser to the modern computer. As we gain a deeper understanding of the quantum world, we are beginning to enable the control of quantum systems and the use of their innate properties to our advantage. We now have the possibility to achieve quantum computing, quantum simulation, and quantum cryptography among many other novel technologies. To help drive this innovation, it is imperative to have accurate and reliable theoretical models. One key system of interest is a simple two-level atom interacting with a quantized single-mode cavity. The currently accepted models for this system make approximations that can break down when the atom-cavity coupling becomes sufficiently large. Namely, in the ultrastrong coupling (USC) regime, we can see ambiguous, gauge-dependent predictions. In this thesis, we develop and utilize gauge-invariant master equation techniques to properly simulate this coupled system in arbitrary coupling regimes. We first introduce the necessary theoretical background, followed by an analysis of the effects of the ``gauge-correction'' on the cavity emitted spectra, along with a few other observables of interest in cavity quantum electrodynamics. We then extend our model to include a second atom as a weakly-coupled detector (sensor). Finally, we make this second atom ultrastrongly coupled as well, and analyze the effects of changing the properties of the second atom relative to the first. We see that, in the USC regime, the gauge-correction causes profound and qualitative changes to all the observables studied. These results provide important ramifications for our theoretical understanding of these systems and show that many previously reported results in the USC regime are incorrect and ambiguous, as they do not satisfy gauge invariance.