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arXiv:2412.16920 · Physica Scripta

Fluctuations and optimal control in a Floquet quantum thermal transistor

Samir Kumar Das, Shishira Mahunta, Nikhil Gupt, Victor Mukherjee, Arnab Ghosh

Published Jul 30, 2026• 0 citations
arXivHTMLPDF

Abstract

Abstract 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.

DOI
10.1088/1402-4896/ae92ba

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Abstract 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.
We use Floquet formalism to study fluctuations in periodically modulated continuous quantum thermal machines. We present a generic theory for such machines, followed by specific examples of sinusoidal, optimal, and circular modulations, respectively. The thermodynamic uncertainty relations (TUR) hold for all modulations considered. Interestingly, in the case of sinusoidal modulation, the TUR ratio assumes a minimum at the heat engine to refrigerator transition point, while the chopped random basis optimization protocol allows us to keep the ratio small for a wide range of modulation frequencies. Furthermore, our numerical analysis suggests that TUR can show signatures of heat engine to refrigerator transition, for more generic modulation schemes. We also study bounds in fluctuations in the efficiencies of such machines; our results indicate that fluctuations in efficiencies are bounded from above for a refrigerator and from below for an engine. Overall, this study emphasizes the crucial role played by different modulation schemes in designing practical quantum thermal machines.
A quantum thermal transistor is designed by the strong coupling between one qubit and one qutrit which are in contact with three heat baths with different temperatures. The thermal behavior is analyzed based on the master equation by both the numerical and the approximately analytic methods. It is shown that the thermal transistor, as a three-terminal device, allows a weak modulation heat current (at the modulation terminal) to switch on and off and effectively modulate the heat current between the other two terminals. In particular, the weak modulation heat current can induce the strong heat current between the other two terminals with the multiple-region amplification of heat current. Furthermore, the heat currents are quite robust to the temperature (current) fluctuation at the lower-temperature terminal within a certain range of temperature, and so it can behave as a heat current stabilizer.
Quantum thermal field effect transistor (qtFET) composed of left-qubit, middle-qutrit, and right-qubit subsystems has been proposed and extensively analysed. In this architecture, the left qubit is coupled to the middle qutrit, which in turn interacts with the right qubit. Each subsystem interacts independently with its respective baths. The middle subsystem serves as a modulator. We have shown that the qtFET exhibits functionality analogous to that of a conventional electronic field effect transistor (eFET). The left, right, and middle subsystems of the qtFET correspond to the drain, source, and gate of an eFET in a common gate configuration, respectively. Our results show that the qtFET can precisely modulate thermal currents, highlighting its potential as a fundamental building block for quantum thermal devices and amplifiers in emerging quantum technologies. This qtFET can be used as a modulator in quantum systems with remarkable precision and can be used as a vital component in amplifiers to develop quantum devices. The integration of Bayesian optimization into the parameter optimization of quantum thermal devices has been demonstrated in this thesis. Bayesian optimization has been performed and used for parameter optimization of qtFET. qtFET has been developed to function as amplifier using optimized parameters in an analogous way to an eFET behaves as amplifier. The transconductance of qtFET has been achieved in order of ten thousands using extended search space range, while performing parameter optimization using Bayesian optimization. The amplification factor is taken as the ratio of gate transconductance and differential conductance. Then the amplification factor is optimized using extended upper bound of search space range of coupling strengths, dissipation rates, and energy levels of subsystem of qtFET which resulted in amplification factor in order of ten millions. This qtFET has been developed to detect variations in temperature at the nanoscale (10−910^{-9}10−9) using optimized parameters. In this work, a heatmap depicting the variation of the thermal current as function of middle bath temperature and interaction strength between middle and right subsystem of qtFET has been verified using first law of thermodynamics. Finally, the negative differential thermal resistance (NDTR) has been found to verify the optimized amplification factor results of qtFET in this work.
Quantum thermal field effect transistor (qtFET) composed of left-qubit, middle-qutrit, and right-qubit subsystems has been proposed and extensively analysed. In this architecture, the left qubit is coupled to the middle qutrit, which in turn interacts with the right qubit. Each subsystem interacts independently with its respective baths. The middle subsystem serves as a modulator. We have shown that the qtFET exhibits functionality analogous to that of a conventional electronic field effect transistor (eFET). The left, right, and middle subsystems of the qtFET correspond to the drain, source, and gate of an eFET in a common gate configuration, respectively. Our results show that the qtFET can precisely modulate thermal currents, highlighting its potential as a fundamental building block for quantum thermal devices and amplifiers in emerging quantum technologies. This qtFET can be used as a modulator in quantum systems with remarkable precision and can be used as a vital component in amplifiers to develop quantum devices. The integration of Bayesian optimization into the parameter optimization of quantum thermal devices has been demonstrated in this thesis. Bayesian optimization has been performed and used for parameter optimization of qtFET. qtFET has been developed to function as amplifier using optimized parameters in an analogous way to an eFET behaves as amplifier. The transconductance of qtFET has been achieved in order of ten thousands using extended search space range, while performing parameter optimization using Bayesian optimization. The amplification factor is taken as the ratio of gate transconductance and differential conductance. Then the amplification factor is optimized using extended upper bound of search space range of coupling strengths, dissipation rates, and energy levels of subsystem of qtFET which resulted in amplification factor in order of ten millions. This qtFET has been developed to detect variations in temperature at the nanoscale (10−910^{-9}10−9) using optimized parameters. In this work, a heatmap depicting the variation of the thermal current as function of middle bath temperature and interaction strength between middle and right subsystem of qtFET has been verified using first law of thermodynamics. Finally, the negative differential thermal resistance (NDTR) has been found to verify the optimized amplification factor results of qtFET in this work.
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.
Abstract We investigate the performance of a three-qubits quantum thermal transistor using coarse-graining, global, and local master equations, respectively. Special attention is paid to the validity of the three methods in different internal coupling strengths. The effects of system and bath parameters on the amplification effect are studied. It is found that small middle qubit frequency, weak internal coupling, and symmetric configuration of system-bath coupling lead to large amplification factor. The heat current amplification mechanism is discussed and quantum coherence does not contribute to amplification. Besides, the thermal transistor is realized by tuning the temperature of the middle bath, the temperature of the left bath, or the internal coupling strength.