Towards quantum thermal multi-transistor systems: Energy divider formalism

Abstract

A quantum thermal transistor controls the flow of thermal energy through two of its terminals in response to an external input signal on its third terminal. In recent years, several realizations of thermal transistors combining individual quantum systems have been proposed using temperatures or optical fields as the control signals. The success of the electronic transistor in modern technology partly lies in its ability to combine and make multi-transistor systems with enhanced flow control capability or even wholly different behaviors. Hence, as the next natural step, we investigate the intricacies of building composite systems combining multiple quantum thermal transistors. We identify that the interconnects of thermal transistors play a critical role in these systems by facilitating energy exchange from one transistor to another. By isolating the exact functionality of these interconnects, we develop a simple model that still captures all its essential characteristics. This model shows that directly coupling transistors allows a substantial energy transfer between them only under highly restrictive conditions. We then develop the energy divider formalism where a single properly tuned quantum harmonic oscillator acts as an intermediary between the transistors. We demonstrate that the oscillator mediates a substantial energy exchange under a considerably relaxed set of conditions and illustrate its operating principles through detailed quantum mechanical state analysis. We compare our energy divider based interconnect against the previously developed intermediate bath method and confirm that both ways achieve similar thermal energy flow rates between the transistors over a broad range of operating temperatures. At the same time, replacing an intermediate bath made up of a large number of harmonic oscillators with a single oscillator avoids many of the theoretical and practical limitations of the earlier method. For instance, time-domain simulations show that the energy divider based interconnect responds far faster to an external excitation than the corresponding intermediate bath based system. We believe the energy divider formalism provides valuable insights into the nature of thermal energy transfer within quantum thermal systems.