Transport and dynamics in the frustrated two-bath spin-boson model

We study the strong coupling dynamics as well as transport properties of photons in the two-bath spin-boson model, in which a spin-1/2 particle is frustratingly coupled to two independent Ohmic bosonic baths. Using a combination of numerical and analytical methods, we show that the frustration in this model gives rise to rich physics in a very wide range of energies. This is in contrast to the one-bath spin-boson model, where the non-trivial physics occurs at an energy scale close to the renormalized spin frequency. The renormalized spin frequency in the two-bath spin-boson model is still important, featuring in different observables, including the non-equiblirum dynamics of both the spin and the baths along with the elastic transport properties of a photon. The latter however reveals a much more complex structure. The elastic scattering displays non-monotonic behavior at high frequencies, and is very different in the two channels: intra- and inter-bath scattering. The photon can also be inelastically scattered, a process in which it is split into several photons of smaller energies. We show that such inelastic processes are highly anisotropic, with the outgoing particles being preferentially emitted into only one of the baths. Moreover, the inelastic scattering rate is parameterically larger than in the one-bath case, and can even exceed the total elastic rate. Our results can be verified with state-of-the-art circuit and cavity quantum electrodynamics experiments.