Autonomous conversion of particle-exchange to quantum self-oscillations

Particle-exchange machines utilize electronic transport to continuously transfer heat between fermionic reservoirs. Here, we couple a quantum mechanical resonator to a particle-exchange machine hosted in a quantum dot and let the system run autonomously. This way, part of the energy exchanged between the reservoirs can be stored in the resonator in the form of self-oscillations. Our analysis goes well beyond previous works by exploring the slow transport regime and accessing arbitrarily strong dot--resonator coupling. First, we introduce a faithful measure of self-oscillations, and use it to certify that they can occur in the slow-transport regime. We furthermore show that the electrical current through the dot can be used to witness self-oscillations. Finally, we establish that, under realistic conditions, self-oscillations occur only when the machine operates as a heater. We define an experimentally measurable performance metric characterizing the efficiency of current--to--self-oscillations conversion. It reveals that, counterintuitively, strong dot--resonator coupling is detrimental to the conversion performance. The framework developed here can be readily implemented in a variety of nanoscale devices, such as a suspended carbon nanotube with an embedded quantum dot.