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arXiv:2310.04347 · Physical Review A

Using non-Markovian dynamics in effective-negative-temperature-based transient quantum Otto engines

Arghya Maity, Ahana Ghoshal

Published Feb 8, 2024• 4 citations
arXivHTMLPDF

Abstract

Conventional quantum Otto engines based on effective-negative-temperature reservoirs rely on an assumption of perfect thermalization. In this study, the authors investigate the impact of non-Markovianity in these engines by terminating strokes before reaching thermal equilibrium, revealing that higher non-Markovianity enhances maximum efficiency but reduces overall performance over an extended period of functioning time. The authors also identify a class of effective-negative-temperature-based necessarily transient quantum Otto engines.

DOI
10.1103/physreva.109.022207

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Conventional quantum Otto engines based on effective-negative-temperature reservoirs rely on an assumption of perfect thermalization. In this study, the authors investigate the impact of non-Markovianity in these engines by terminating strokes before reaching thermal equilibrium, revealing that higher non-Markovianity enhances maximum efficiency but reduces overall performance over an extended period of functioning time. The authors also identify a class of effective-negative-temperature-based necessarily transient quantum Otto engines.
Cyclic classical and quantum thermal machines show higher efficiency when the strokes are carried out quasi-statically. Recent theoretical and experimental work on figures of merit for thermal machines show that they have an advantage when operating in environments with negative temperatures. In an experimental proof of concept [Phys. Rev. Lett. 122, 240602 (2019)], it was shown that quantum Otto engines operating at negative temperatures can exhibit a behavior in which the faster the cycle is carried out, the higher the efficiency. In this work, we make use of the concept of entropy production and friction work to explain this counterintuitive behavior, and we show that it only occurs when reservoirs have negative temperatures.
It is investigated whether non-Markovianity, i.e., the memory effects resulting from the coupling of the system to its environment, can be beneficial for the performance of quantum heat engines. Specifically, two physical models are considered. The first one is a well-known single-qubit Otto engine; the non-Markovian behavior is there implemented by replacing standard thermalization strokes with so-called extremal thermal operations which cannot be realized without the memory effects. The second one is a three-stroke engine in which the cycle consists of two extremal thermal operations and a single qubit rotation. It is shown that the non-Markovian Otto engine can generate more work-per-cycle for a given efficiency than its Markovian counterpart, whereas performance of both setups is superior to the three-stroke engine. Furthermore, both the non-Markovian Otto engine and the three-stroke engine can reduce the work fluctuations in comparison with the Markovian Otto engine, with their relative advantage depending on the performance target. This demonstrates the beneficial influence of non-Markovianity on both the average performance and the stability of operation of quantum heat engines.
Abstract Real quantum heat engines lack the separation of time and length scales that is characteristic for classical engines. They must be understood as open quantum systems in non-equilibrium with time-controlled coupling to thermal reservoirs as integral part. Here, we present a systematic approach to describe a broad class of engines and protocols beyond conventional weak coupling treatments starting from a microscopic modeling. For the four stroke Otto engine the full dynamical range down to low temperatures is explored and the crucial role of the work associated with the coupling/de-coupling to/from reservoirs as an integral part in the energy balance is revealed. Quantum correlations turn out to be instrumental to enhance the efficiency which opens new ways for optimal control techniques.
Abstract We study the performance of a quantum Otto cycle using a harmonic work medium and undergoing collisional dynamics with finite-size reservoirs. We span the dynamical regimes of the work strokes from strongly non-adiabatic to quasi-static conditions, and address the effects that non-Markovianity of the open-system dynamics of the work medium can have on the efficiency of the thermal machine. While such efficiency never surpasses the classical upper bound valid for finite-time stochastic engines, the behaviour of the engine shows clear-cut effects induced by both the finiteness of the evolution time, and the memory-bearing character of the system-environment evolution.
Enhancement of thermal efficiency of quantum heat engines has been discussed mainly in terms of quantumness of working substances. In the present study, we propose as another possibility to utilize a quantum-mechanical (reversible) feature of system-reservoir interaction, which reveals itself in the short-time regime as a non-Markovian effect on the reduced dynamics of the substance, before asymptotically approaching irreversible processes. For this purpose, we study a limit cycle of the quantum Otto engine comprising a working two-level system and two reservoirs, including the non-Markovian effect for the finite-time isochoric processes while the work-extracting processes are kept quantum adiabatic. Assuming that the system interacts weakly with the reservoirs consisting of infinite bosons, we find a parameter regime beyond the Carnot efficiency in which a positive work is extracted by including a non-Markovian effect called energy backflow. We also find that the interaction energy is finite and contributes to the positive work even for the weak interaction. The work diminishes if we include into the work the energy for detaching the working substance from reservoirs.
We use fast periodic control to realize finite-time Otto cycles exhibiting quantum advantage.Such periodic modulation of the working medium-bath interaction Hamiltonian during the thermalization strokes can give rise to non-Markovian anti-Zeno dynamics and corresponding reduction in the thermalization times.Faster thermalization can in turn significantly enhance the power output in engines or, equivalently, the rate of refrigeration in refrigerators.This improvement in performance of dynamically controlled Otto thermal machines arises due to the time-energy uncertainty relation of quantum mechanics.