Nonperturbative cavity/waveguide quantum electrodynamics and dissipative quantum phase transition

Strong coupling between matter and quantized electromagnetic modes in cavity or waveguide may offer yet another approach of controlling equilibrium phases or dynamics of many-body systems. Recent developments have realized such strong light-matter interaction in genuinely quantum and nonperturbative regimes, where conventional approximate theoretical methods cannot be applied in general. I will talk about how one can analyze strongly coupled quantum light-matter systems at arbitrary interaction strengths on the basis of an asymptotically disentangling unitary transformation [1,2]. I discuss its application to construction of tight-binding Hamiltonians, dynamics of bound states in the continuum, and revisiting dissipative quantum phase transition in resistively shunted Josephson junctions [3].