Fluctuations and optimal control in a floquet quantum thermal transistor

We use Full Counting Statistics to study fluctuations and optimal control in a three-terminal Floquet quantum thermal transistor. We model the setup using three qubits (termed as the emitter, collector, and base) coupled to three thermal baths. As shown in Phys. Rev. E 106, 024110 (2022), one can achieve a significant change in the emitter and collector currents through a small change in the base current, thereby achieving thermal transistor operation. We quantify fluctuations using variance, Fano factor and Thermodynamic Uncertainty Relation (TUR). We have proposed analytical lower bounds to the Fano factor and TUR ratios, and verified the same using examples of sinusoidal and π-flip modulations. We also use optimal control through the Chopped Random Basis optimization protocol in order to significantly enhance the amplification obtained in the transistor, or alternatively, to reduce the Fano factor. Importantly, we identify regime of ideal operation in the parameter space, characterized by high amplification and low Fano factor, as well as regime of worst performance, associated with large Fano factor, without a substantial enhancement in the amplification. Interestingly, optimization protocol allows us to reach the analytical lower bound of the Fano factor. We expect our results will be highly relevant for developing heat modulation devices in near-term quantum technologies.