Quantum thermal transistor is a microscopic thermodynamical device that can modulate and amplify heat current through two terminals by the weak heat current at the third terminal. Here we study the common environmental effects on a quantum thermal transistor made up of three strong-coupling qubits. It is shown that the functions of the thermal transistor can be maintained and the amplification rate can be modestly enhanced by the skillfully designed common environments. In particular, the presence of a dark state in the case of the completely correlated transitions can provide an additional external channel to control the heat currents without any disturbance of the amplification rate. These results show that common environmental effects can offer new insights into improving the performance of quantum thermal devices.

This paper systematically studied heat transfer through two transversely coupled qubits in contact with two types of heat reservoirs. One is the independent heat reservoir which essentially interacts with only a single qubit, the other is the common heat reservoir which is allowed to simultaneously interact with two qubits. Compared to independent heat reservoirs, common reservoirs always suppress heat current in most cases. However, the common environment could enhance heat current, if the dissipation rate corresponding to the higher eigenfrequency is significantly higher than that corresponding to the lower eigenfrequency. In particular, in the case of resonant coupling of two qubits and the proper dissipations, the steady state can be decomposed into a stationary dark state which doesn't evolve and contributes zero heat current, and a residual steady state which corresponds to the maximal heat current. This dark state enables us to control steady-state heat current with an external control field and design a thermal modulator. In addition, we find that inverse heat currents could be present in the dissipative subchannels between the system and reservoirs, which interprets the suppression roles of common heat reservoirs. We also calculate the concurrence of assistance (COA) of the system and find that heat current and COA have the same trend with temperature, which further indicates that entanglement can be regarded as a resource to regulate heat transport.