Darlington pair of quantum thermal transistors

Abstract

Recent progress in manipulating individual quantum systems has led to the development of quantum thermal transistors, which control the thermal conductivity between two of its terminals according to an input signal on its third terminal. With several models for individual thermal transistors already developed, the next natural step is to investigate how multiple thermal transistors can interconnect to build useful composite devices. In electronics literature, the Darlington pair is a two-transistor configuration commonly used to construct electronic amplifiers with higher gain than is possible with a single transistor. We create the electronic Darlington pair's thermal equivalent using two individual thermal transistors in a similar configuration. Unlike previously studied models, multitransistor configurations like this contain internal transistor interconnections whose temperatures cannot be biased externally but are determined by the individual transistors' internal dynamics. We refine previous models to incorporate these transistor-transistor interactions and introduce an intermediate thermal bath to facilitate the thermal energy exchange between the Darlington pair transistors. We investigate temperature-based and optical field-based control strategies of the Darlington pair in terms of both steady-state and transient thermal flow characteristics through numerical simulations. Under both control strategies, the thermal Darlington pair's steady-state performance exhibits superior thermal amplification, sensitivity, and thermodynamic efficiency than an equivalent single thermal transistor. Our results closely mirror those expected from the corresponding electronic Darlington pair. Hence, we envision that we may readily adapt the intermediate bath formalism we developed in this work to translate a wide variety of useful electronic multitransistor configurations to their thermal equivalents.