Improving quantum thermal transistors through feedback-controlled baths

In recent years, integrating quantum feedback mechanisms into thermal machines has gained attention due to its benefits in manipulating the system states and energy flows. This is particularly advantageous for quantum thermal transistors in preserving their inherent quantum properties as they lose the purity of the system states due to decoherence and relaxation from interactions with thermal baths, within the subsystems, and monitoring. In the literature, studies have demonstrated that preserving quantum coherence can enhance the performance of quantum thermal machines, improving their efficiency. In our paper, we present a model that proposes engineering baths to be equipped with detectors and a controller to enable feedback in a quantum thermal transistor that emulates a role played by a feedback resistor in an electronic transistor. We use the framework of quantum feedback control via weak monitoring. We modify the system evolution trajectories by using a weak monitoring record from a detector. By taking the ensemble average of these trajectories, we unveil the evolution of the system density matrix that corresponds to the Markovian dynamics of the transistor. This type of feedback introduces minimal perturbation to the system and, once tuned, enhances the system coherence that would otherwise degrade due to bath interactions. Furthermore, there will be no change in the relaxation times. The probabilities of population terms remain unchanged. We treat this an enhancement in the operational characteristics of the quantum thermal transistor as it maintains its quantum features with an added benefit of improved amplification capabilities.