Dispersive readout with non-Markovian environments

Abstract

We study the non-Markovian dispersive readout of a single-mode bosonic (SMB) quantum system coupled to the open cavity with two non-Markovian environments. Assuming that the SMB quantum system is initially prepared in a thermal equilibrium state, the susceptibility of the measured SMB quantum system to the cavity can be obtained by the nonequilibrium linear response theory, which provides the dispersive frequency shift of the cavity. We analytically derive the transmission and reflection of the cavity in the non-Markovian regime and discuss the non-Markovian dispersive readout of the SMB quantum system, which is in good agreement with that obtained by the Markovian approximation. We show that the effect of non-Markovian dynamics on the system's behavior leads to the decrease of the transmission and shifts of the frequency corresponding to the peak of the transmission in the dispersive regime compared with the Markovian case and the increase of the sum of the transmission and reflection due to the excitation backflowing induced by the couplings of the cavity and two non-Markovian environments, which could be applied to quantum secure direct communication with quantum memory. Finally, we generalize the readout theory to the periodically driven SMB quantum system based on the Floquet theory and quantum network, which contain all influences from the non-Markovian environments. The formalism presented in this paper opens an alternative field of possible applications in quantum information and quantum communication with non-Markovianity by manipulating the spectral densities of the environments.