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 Gupt et al (2022 Phys. Rev. E 106 024110), 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.

In this article, we analytically explore the quantum phenomena of scattering by harmonically trapped 2D quantum gases. We show the temperature’s dependence on the differential scattering cross-section (DSC) near and around the critical transition regime for both particle and light scattering cases separately. For the particle scattering case, we consider scatterers with quantized bound motion in a harmonic trap. Our findings on the structure factor for light scattering give phase transition phenomena for 2D bosonic atoms and the thermal behavior of the system. This result has practical significance for recent experimental setups such as in situ image analysis and bosonic simulations. Finally, we show the temperature-dependent refractive index for a 2D harmonically trapped bosonic medium. This parameter is important in neutron scattering experiments.

In this article, we study the particle scattering that occurs by harmonically trapped quantum gases in an artificial magnetic field with the short-ranged Fermi-Huang interactions among the incident particle and the scatterers. Both elastic and inelastic differential scattering cross-sections are obtained in analogy with the potential scattering. We have shown that the differential scattering cross-sections which depend on finite temperature and the magnetic field strength. Coherent scattering by harmonically trapped Bose and Fermi scatterers in an artificial magnetic field gives rise to a tool for probing their quantum statistical properties. We have shown that the scattered particle intensity can exhibit oscillatory behaviours at zero Kelvin temperature which depends on the strength of the magnetic field and the geometric shapes of the atomic cloud. At the limit of zero magnetic field strength, we have investigated the importance of the shell structure on the cross-section of scattering.