Collective Light-Matter Interactions and Superradiance: A Tensor-Network Approach

Abstract

In this thesis, we investigate the driven-dissipative dynamics of an array of atoms addressed by an external field using Matrix Product Density Operators. Using the Time-Dependent Variational Principle, we overcome the exponential scaling of the Lindblad master equation. We validate the method against the exact Dicke limit, capturing the cooperative superradiant cascade, and demonstrate that spatial separation between emitters rapidly suppresses this collective emission. Under continuous laser driving, we characterize the competition between coherent pumping and superradiant dissipation, showing that global detuning acts as an energy penalty that restricts population transfer and lowers the steady-state excitation fraction. This establishes a robust computational approach for studying complex light-matter interactions in extended many-body arrays