Continuous-variable electromechanical quantum thermal transistors

We present a scheme to realize quantum thermal transistor effects in a continuous-variable electromechanical system including two microwave cavities and one mechanical oscillator. The thermal noise fluxes between the quantum system and its baths are evaluated by quantum master equation. It is shown that the thermal noise flux at one microwave cavity as an emitter can be dissipated into the other as a collector by combining the heating Stokes and cooling anti-Stokes processes. The indirect energy transfers between the two microwave modes can be significantly amplified by small energy changes at the mechanical oscillator as the base. The extremely high amplification depends sensitively on the detunings of the two microwave modes, which provides a new tool for precision measurements. This study opens the door for constructing quantum thermal transistors using various continuous-variable systems and is well accessible based on current experimental techniques.