A symmetry-based approach to dissipative many-body quantum optics in one-dimensional baths

We present a symmetry-based method to reduce the complexity of a class of dissipative many-body problems describing the dynamics of atoms coupled to one-dimensional baths. We draw inspiration from cavity QED, where permutational symmetry enables efficient computations. In one-dimensional environments, however, position-dependent atom-atom interactions prevent the invariance of the dynamics under exchange operation. Nevertheless, we identify scenarios where partial permutational symmetry is present. We leverage that symmetry to fold spatial degrees of freedom into internal ones, reducing subsets of atoms to collective multi-level spins. These resulting superspins each satisfy a generalized angular momentum algebra, thus reducing the (a priori) exponential complexity to polynomial. This framework can be used to efficiently compute many-body dynamics and to study the emergence of integrability in quantum systems.