Quantum transistors for heat flux in and out of working substance parts: harmonic vs transmon and Kerr environs

Abstract Quantum thermal transistors have been widely studied in the context of three-qubit systems, where each qubit interacts separately with a Markovian harmonic bath. In contrast, non-Markovianity is a general feature, inherent to a large fraction of realistic scenarios. Instead of Markovian environments, here we propose a transistor in which the interaction between the working substance and an environment comprising an infinite chain of qutrits is based on periodic collisions. We refer to the device as a working-substance thermal transistor, where the definition of the heat current is considered to be system-centric. We find that the transistor effect also prevails in this scenario. We consider the variation in amplification with respect to the temperature of the modulating bath, the system-environment coupling, and the interaction time. We also investigate how varying the interaction strengths between the terminals affects amplification. Additionally, the environment, comprising three-level systems, allows us to consider the effects of frail perturbations in the energy spacings of the qutrit, leading to non-linearity in the environment. We consider non-linearities that are either of transmon or of Kerr-type. We identify parameter regimes in which transmon and Kerr-type nonlinear environments provide a significant enhancement compared to linear environments.