Entanglement-preserving approach for reservoir-induced photonic dissipation in waveguide QED systems

Using an entanglement-preserving approach, we theoretically study the reservoir-induced photonic dissipations in waveguide quantum electrodynamic (wQED) systems coupled to an excitable reservoir consisting of oscillators. For the single-photon case, we show that the effects of dissipation can be described by a reduced Hamiltonian and a restricted eigenstate. For the multiphoton case, we show that the reduced Hamiltonian approach is, in general, not valid. Nonetheless, we identify a weak-reservoir condition for the reduced Hamiltonian approach to be approximately valid, which applies to the majority of current experiments. In addition, we apply the density matrix approach to investigate the same physical system and show that the Markovian density matrix approach can describe only the lowest-order dissipative effect. The deviations from the weak-reservoir scenario are suggested to be observable in an engineered excitable reservoir consisting of optical cavities.