| This thesis examines frustrated superradiant phase transitions in light-matter systems. We show that when a superradiant system faces conflicting constraints, it can become frustrated and fail to find its lowest-energy configuration. Using a Dicke trimer model, we demonstrate that a positive hopping energy across sites leads to a frustrated ground-state manifold with broken translational symmetry. The frustrated superradiant phase features two divergent time and fluctuation scales, which could be used as an experimental probe. We investigate how the interaction of broken time-reversal symmetry and frustration affects bosonic lattice systems, showing that varying the total flux of a synthetic magnetic field can transform the universality class of superradiant phase transition to one with anomalous critical exponents. Despite being a continuous phase transition, the anomalous superradiant phase transition shows distinct critical exponents on both sides of the transition and a discontinuity of correlations and fluctuation. The research also demonstrates that closest neighbor complex hopping produces effective long-range interactions, leading to a succession of first-order phase transitions between superradiant phases with different degrees of frustration. Overall, this thesis provides a comprehensive understanding of frustrated superradiant phase transitions in light-matter systems and highlights the emergence of unconventional critical phenomena in these systems. |
