Quantum Optics, Many Body Physics and Gaussian Free Field

Modern quantum technologies rely fundamentally on quantum optics, yet the most promising applications—quantum computation and quantum simulation—are inherently many-body phenomena. This thesis explores the interface between quantum optics and many-body physics, employing analytical techniques from statistical physics, condensed matter theory, and quantum field theory to study complex quantum optical systems.The unifying mathematical framework across all models studied is the Gaussian free field, which emerges as the underlying structure connecting three seemingly disparate research areas. First, we examine a bosonic impurity model where interactions with an environment simultaneously generate valuable non-Gaussian quantum resources while introducing dissipation. Our analysis reveals conditions under which constructive nonlinear effects can overcome destructive dissipative processes, illuminating alternative pathways for robust quantum resource generation.Second, we investigate measurement-altered criticality in both free boson conformal field theory and Dirac fermions, demonstrating how continuous measurements deform entanglement properties at criticality. This provides new insights into measurement-induced phase transitions relevant to quantum error correction and fault-tolerant computation.Third, we examine classical transport phenomena by studying the asymmetric simple inclusion process (ASIP) for bosons and the asymmetric simple exclusion process (ASEP) for fermions. Our analysis reveals that both systems, despite their fundamentally different particle statistics, exhibit universal Kardar-Parisi-Zhang behavior due to their underlying description as fluctuating interface dynamics.Throughout this work, the Gaussian free field serves as both computational tool and conceptual bridge, connecting three fundamentally different phenomena: the interplay between dissipation and quantum resource generation, the modification of criticality through continuous measurements, and unification of bosonic and fermionic transport beyond conventional bosonization.Our analytically tractable models reveal rich physical phenomena in prototypical quantum optical many-body systems.