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arXiv:2204.14005 · Physical review. E

Precision bound and optimal control in periodically modulated continuous quantum thermal machines

Arpan Das, Shishira Mahunta, Bijay Kumar Agarwalla, Victor Mukherjee

Published Jul 31, 2023• 13 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreve.108.014137

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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.
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 investigate a two-qubit SWAP thermal machine -- a streamlined analogue of the four-stroke Otto cycle -- whose working medium comprises inertially moving Unruh-DeWitt qubit detectors, each coupled to a thermal quantum field bath prepared at a different temperature. In the presence of relative motion between the working medium and the thermal baths, we derive thermodynamic uncertainty relations (TURs) that quantify the trade-off between performance, entropy production, and power fluctuations. Our analysis identifies regimes where relativistic motion leads to stronger violation of classical TURs, previously observed in static quantum setups. In addition, we establish generalized performance bounds for the thermal machine operating as either a heat engine or a refrigerator, and discuss how relativistic motion can enhance their performances beyond the standard Carnot limits defined by rest-frame temperatures.
Abstract In the quest for high-performance quantum thermal machines, looking for an optimal thermodynamic efficiency is only part of the issue. Indeed, at the level of quantum devices, fluctuations become extremely relevant and need to be taken into account. In this paper we study the thermodynamic uncertainty relations for a quantum thermal machine with a quantum harmonic oscillator as a working medium, connected to two thermal baths, one of which is dynamically coupled. We show that parameters can be found such that the machine operates both as a quantum engine or refrigerator, with both sizeable efficiency and small fluctuations.
Precision in nonequilibrium processes comes at a thermodynamic cost: suppressing fluctuations generally requires increased dissipation. Thermodynamic uncertainty relations (TURs) make this trade-off quantitative by linking current fluctuations to entropy production in classical stochastic dynamics. In the decade since its discovery, the canonical steady-state TUR and its finite-time generalizations have become a cornerstone of non-equilibrium thermodynamics, constraining the performance of molecular machines and allowing heat dissipation to be inferred from observable fluctuations. Whether the canonical TUR can be violated in a controlled quantum device remains an outstanding experimental question, in part because doing so requires resolving extremely small steady-state currents as well as their fluctuations. Here we experimentally show that steady-state quantum transport can surpass the precision permitted by the canonical TUR. We observe this violation in a superconducting quantum thermal machine coupled to a microwave waveguide acting as a cold bath and to a classical noise source providing an effective infinite-temperature bath. We observe a TUR ratio Q=1.71±0.17Q = 1.71 \pm 0.17Q=1.71±0.17, in violation of the classical bound Q≥2Q \geq 2Q≥2. Our results demonstrate a fundamental distinction between classical and quantum thermodynamics, paving the way for quantum thermal devices that achieve enhanced precision at reduced energy cost.
We investigate a quantum thermal machine composed of two qubits coupled through a Raman-induced exchange interaction and driven by inhomogeneous transition frequencies. The system is analyzed within Carnot, Otto, and Stirling thermodynamic cycles, including the Stirling cycle with and without regeneration. We identify the conditions under which the device operates as a heat engine, refrigerator, thermal accelerator, or heater. Efficiency maps and operational-mode diagrams reveal well-defined boundaries in parameter space, governed by the frequency ratio r=ωˉ/ωr=\barω/ωr=ωˉ/ω, the coupling strength ggg, and the thermal gradient between reservoirs. The Carnot cycle exhibits sharp transitions between engine and refrigerator regimes, while the Otto cycle displays a richer structure with the coexistence of all operational modes. The Stirling cycle shows enhanced versatility and performance, particularly when assisted by a regenerator, where near-ideal efficiencies are achieved. Overall, the Raman-type interaction introduces a controllable left-right asymmetry that enables nontrivial manipulation of thermodynamic behavior through frequency tuning.
We combine the formalisms of Floquet theory and full counting statistics with a Markovian embedding strategy to access the dynamics and thermodynamics of a periodically driven thermal machine beyond the conventional Born–Markov approximation. The working medium is a two-level system and we drive the tunneling as well as the coupling to one bath with the same period. We identify four different operating regimes of our machine which include a heat engine and a refrigerator. As the coupling strength with one bath is increased, the refrigerator regime disappears, the heat engine regime narrows and their efficiency and coefficient of performance decrease. Furthermore, our model can reproduce the setup of laser cooling of trapped ions in a specific parameter limit.