Non-Markovian dynamics and steady-state entanglement of cavity arrays in finite-bandwidth squeezed reservoirs

When two chains of quantum systems are driven at their ends by a two-mode squeezed reservoir, they approach a steady state characterized by the formation of many entangled pairs. Each pair is made of one element of the first and one of the second chain. This effect has been already predicted under the assumption of broadband squeezing. Here we investigate the situation of finite-bandwidth reservoirs. This is done by modeling the driving bath as the output field of a non-degenerate parametric oscillator. The resulting non-Markovian dynamics is studied within the theoretical framework of cascade open quantum systems. It is shown that the formation of pair-entangled structures occurs as long as the normal-mode splitting of the arrays does not overcome the squeezing bandwidth of the reservoir.