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Physical Review A

Feedback-driven quantum Otto-like engines

Dehua Liu, Yingying Hong, Shaolin Luo, Xian He, Zhaoqi Wu, Jianhui Wang

Published Jan 3, 2025• 6 citations
Publisher

Abstract

An analytical study of a feedback-driven quantum engine based on a two-level system is presented. This engine is similar to a quantum Otto engine but substitutes the quantum isochoric process with a feedback-driven operation based on a measured observable $A(\ensuremath{\theta})$, whose eigenstates are coherent superpositions of energy eigenstates. Projective measurements control the feedback operations, while work extraction or heat absorption occurs during driven operations. We derive the general time-dependent efficiency, power, and power fluctuations. Quantum coherence is examined through three mechanisms: (i) coherence associated with $\ensuremath{\theta}\ensuremath{\ne}0$, (ii) residual coherence after incomplete thermalization, and (iii) coherence generated by the interaction between the system and a coherent laser pulse on resonance. We investigate how the parameter $\ensuremath{\theta}$, quantum coherence, and timing of unitary and feedback-driven strokes influence engine performance. We demonstrate that quantum coherence can significantly enhance power output and efficiency while reducing fluctuations through optimal cycle parameter adjustments.

DOI
10.1103/physreva.111.012203

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An analytical study of a feedback-driven quantum engine based on a two-level system is presented. This engine is similar to a quantum Otto engine but substitutes the quantum isochoric process with a feedback-driven operation based on a measured observable A(\ensuremathθ)A(\ensuremath{\theta})A(\ensuremathθ), whose eigenstates are coherent superpositions of energy eigenstates. Projective measurements control the feedback operations, while work extraction or heat absorption occurs during driven operations. We derive the general time-dependent efficiency, power, and power fluctuations. Quantum coherence is examined through three mechanisms: (i) coherence associated with \ensuremathθ\ensuremath≠0\ensuremath{\theta}\ensuremath{\ne}0\ensuremathθ\ensuremath=0, (ii) residual coherence after incomplete thermalization, and (iii) coherence generated by the interaction between the system and a coherent laser pulse on resonance. We investigate how the parameter \ensuremathθ\ensuremath{\theta}\ensuremathθ, quantum coherence, and timing of unitary and feedback-driven strokes influence engine performance. We demonstrate that quantum coherence can significantly enhance power output and efficiency while reducing fluctuations through optimal cycle parameter adjustments.
We consider a finite-time quantum Otto heat engine that consists of two isochoric (thermal-contact) process, where the system is alternatively coupled to a hot squeezed and a cold thermal reservoir, and two unitary driven strokes, where the system is isolated from these two baths and its von Neumann entropy keeps constant. Both quantum inner friction and coherence are generated along the driven stroke and coherence cannot be fully erased after the finite-time hot isochore. Using full counting statistics, we present the probability distribution functions of heat injection and total work per cycle, which are dependent on the time duration along each process. With these, we derive the analytical expressions for the thermodynamic quantities of the two-level heat engine, such as total work, thermodynamic efficiency, entropy production, and work fluctuations, in which effects of coherence, squeezing, inner friction and finite-time heat exchange are included. We then numerically determine the thermodynamic quantities and the fluctuations using the parameters employed in the experimental implementation. Our results clarify the role of coherence and squeezing in the performance and fluctuations in the quantum Otto engines.
Abstract We propose a quantum Otto engine operating through a cycle of two isochoric processes, where the working substance interacts with a single-mode radiation field, and two unitary strokes, during which the working substance is decoupled from the field. We investigate the influence of quantum superposition and quantum internal friction on the engine’s power output and efficiency, demonstrating that these quantum effects enhance both performance metrics. While these enhancements are accompanied by increased power fluctuations, we show that such fluctuations can be effectively mitigated through careful selection of control parameters. Our results reveal that the proposed quantum Otto engine can achieve performance regimes that are thermally inconceivable in classical systems, including surpassing the Otto efficiency limit and attaining 100% efficiency with nonzero power output.
The working substance fueling a quantum heat engine may contain coherence in its energy basis, depending on the dynamics of the engine cycle. In some models of quantum Otto heat engines, energy coherence has been associated with entropy production and quantum friction. We considered a quantum Otto heat engine operating at finite time. Coherence is generated and the working substance does not reach thermal equilibrium after interacting with the hot heat reservoir, leaving the working substance in a state with residual energy coherence. We observe an interferencelike effect between the residual coherence (after the incomplete thermalization) and the coherence generated in the subsequent finite-time stroke. We introduce analytical expressions highlighting the role of coherence and examine how this dynamical interference effect influences the engine performance. Additionally, in this scenario in which coherence is present along the cycle, we argue that the careful tuning of the cycle parameters may exploit this interference effect and make coherence acts like a dynamical quantum lubricant. To illustrate this, we numerically consider an experimentally feasible example and compare the engine performance to the performance of a similar engine where the residual coherence is completely erased, ruling out the dynamical interference effect.
The working substance fueling a quantum heat engine may contain prominent quantum properties such as coherence and nonclassical correlations. In particular, coherence has been somewhat related to quantum friction, whose origin has been mostly associated with the noncommutativity of a driven Hamiltonian at different times. Here, we consider a quantum Otto heat engine operated at finite time and undergoing incomplete thermalization with a heat source. We introduce analytical expressions relating the engine efficiency and extractable power to the coherence measured in the energy basis of the working substance during the engine cycle. We show that coherence, which has been related to an increase in entropy production and irreversibility, can in also be employed to improve the quantum engine performance, mitigating quantum friction. Such an improvement may be achieved by carefully tuning cycle parameters. To illustrate this coherent improvement we performed a numerical analysis in an experimentally feasible example.
Measurement-based quantum heat engines have attracted significant interest as alternatives to conventional thermal engines, as they replace the hot thermal reservoir with quantum measurements, thereby offering greater controllability and simpler implementation. Motivated by these advantages, we investigate a measurement-driven quantum Otto engine with a qubit working substance and study the optimal work extractable from such engines, including whether their performance can surpass that of conventional quantum Otto cycles. We analyze the engine in both the infinite-time (adiabatic) and finite-time (non-adiabatic) regimes, considering two distinct implementations obtained through optimization over all projection-valued measurements (PVMs) and over all two-outcome positive operator-valued measurements (POVMs). We show that measurement-based engines can outperform conventional quantum Otto engines within specific parameter regimes and that POVM-based engines can yield higher optimal work extraction than PVM-based ones. Furthermore, by incorporating the thermodynamic cost associated with resetting the auxiliary system required for POVM implementation, we demonstrate that the resulting net work output can still exceed that of PVM-based engines under suitable conditions on the spectral gaps and cold bath temperature. We also identify regimes in which non-adiabatic implementations can yield higher work output and efficiency than their adiabatic counterparts. Our study provides operational guidelines for designing improved measurement-driven quantum Otto engines.
In this work we investigate a finite-time quantum Otto-like heat engine with a single-qubit working substance, distinguished from the standard Otto cycle by introducing a unitary operation before the cold isochore. This operation suppresses the slowest decaying mode of the open-system dynamics and broadens the spectral gap, thereby inducing an exponential to accelerate the subsequent thermalization process toward stationarity. We derive analytic expressions for the work, heat, and efficiency, and perform numerical simulations comparing the standard Otto engine, the shortcut to adiabatic engine, and our proposed Otto-like engine. Our analysis demonstrates that with an appropriate parameter selection, the additional unitary operation can significantly boost the system's power and efficiency. Finally, using the unified optimization criterion Φ, we further show that the modified cycle consistently outperforms both the conventional cycle and the shortcut to adiabatic protocol.