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arXiv:1812.08728 · Physical Review A

Coherence effects in the performance of the quantum Otto heat engine

Patrice A. Camati, Jonas F. G. Santos, Roberto M. Serra

Published Jun 10, 2019• 162 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.99.062103

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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.
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.
The concept of inner friction, by which a quantum heat engine is unable to follow adiabatically its strokes and thus dissipates useful energy, is illustrated in an exact physical model where the working substance consists of an ensemble of misaligned spins interacting with a magnetic field and performing the Otto cycle. The effect of this static disorder under a finite-time cycle gives a new perspective of the concept of inner friction under realistic settings. We investigate the efficiency and power of this engine and relate its performance to the amount of friction from misalignment and to the temperature difference between heat baths. Finally we propose an alternative experimental implementation of the cycle where the spin is encoded in the degree of polarization of photons.
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.
Abstract In this work, we investigate the impact of energetic coherence in nonthermal reservoirs on the performance of the Otto cycle. We first focus on the situation where the working substance is a qubit. Due to the existence of coherence of nonthermal reservoir, various anomalous operating regimes such as the engine and refrigerator with efficiencies exceeding Carnot limits, as well as the hybrid refrigerator that can simultaneously achieve cooling and supplying work to an external agent, can occur. We demonstrate that the energetic coherence of the system’s steady state plays a significant role in determining the cycle’s functions by adding an additional stroke implementing dephasing and phase modulation operations in the cycle. The energetic coherence of the system is necessary to trigger the reservoir’s coherence to exert influences on the cycle. We decompose the thermodynamic quantities to the components arising from the populations and coherence of the system, and find that the reservoir’s coherence impacts the cycle from two aspects: one is the modification of the system’s steady-state populations or temperatures, and the other is the direct contributions to the heat in the interaction between the system and reservoirs. We then explore the scenario where the working substance is two identical qubits, and the reservoirs are common to them. We show that the degenerate coherence of the system in the steady state can enhance the performances of the cycle as different machines. Additionally, the energetic coherence of the reservoir modifies the functions of the cycle still through the energetic coherence of the system rather than their degenerate coherence.
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.