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Thermal Science

Work output and efficiency of a reversible quantum Otto cycle

Feng Wu, Zhichun Yang, Lingen Chen, Xiaowei Liu, Shuang Wu

Published Jan 1, 2010• 22 citations
Publisher

Abstract

An idealized reversible Otto cycle working with a single quantum mechanical particle contained in a potential well is investigated based on the Schrödinger equation in this paper. The model of a reversible quantum Otto cycle, which consists of two reversible adiabatic and two constant-well widen branches, is established. As an example, we calculate a particularly simple case in which only two of the eigenstates of the potential well contribute to the wave-function in the well. The relationship between the optimal dimensionless work output W

DOI
10.2298/tsci1004879w

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•Jun 24, 2020•0 citations
An idealized reversible Otto cycle working with a single quantum mechanical particle contained in a potential well is investigated based on the Schrödinger equation in this paper. The model of a reversible quantum Otto cycle, which consists of two reversible adiabatic and two constant-well widen branches, is established. As an example, we calculate a particularly simple case in which only two of the eigenstates of the potential well contribute to the wave-function in the well. The relationship between the optimal dimensionless work output W
Abstract The efficiency of a quantum heat engine is maximum when the unitary strokes of the quantum Otto cycle are adiabatic. On the other hand, this may not be always possible due to small energy gaps in the system, especially at the critical point (CP) where the gap between the ground state and the first excited state vanishes and the system gets excited. With the aim to regain this lost adiabaticity, we modify one of the unitary strokes of the Otto cycle by allowing the system to first evolve with a time dependent Hamiltonian as in the case of a usual Otto cycle, followed by an additional evolution with a different time independent Hamiltonian so that the system reaches a less excited state. This will help in increasing the magnitude of the heat absorbed from the hot bath so that the work output and efficiency of the engine can be increased. We demonstrate this method using an integrable model and a non-integrable model as the working medium and discuss the generality and limitations of this method. In the case of a two spin system, the optimal value for the time till which the system needs to be freely evolved is calculated analytically in the adiabatic limit. The results show that implementing this modified unitary stroke significantly improves the work output and efficiency of the engine, especially when it crosses the CP.
We study the performance of a quantum Otto cycle operating in trapping potentials of different shapes. We show that, while both the mean work output and the efficiency of two Otto cycles in different trapping potentials can be made equal, the work probability distribution will still be strongly affected by the difference in structure of the energy levels. To exemplify our results, we study the family of potentials of the form V(t)(x) ∼ x(2q). This family of potentials possesses a simple scaling property that allows for analytical insights into the efficiency and work output of the cycle. We perform a comparison of quantum Otto cycles in various physically relevant scenarios and find that in certain instances, the efficiency of the cycle is greater when using potentials with larger values of q, while in other cases, the efficiency is greater with harmonic traps.
In this paper, we analyze the total work extracted and the efficiency of the magnetic Otto cycle in its classic and quantum versions. As a general result, we found that the work and efficiency of the classical engine is always greater than or equal to its quantum counterpart, independent of the working substance. In the classical case, this is due to the fact that the working substance is always in thermodynamic equilibrium at each point of the cycle, maximizing the energy extracted in the adiabatic paths. We apply this analysis to the case of a two-level system, finding that the work and efficiency in both the Otto's quantum and classical cycles are identical, regardless of the working substance, and we obtain similar results for a multilevel system where a linear relationship between the spectrum of energies of the working substance and the external magnetic field is fulfilled. Finally, we show an example of a three-level system in which we compare two zones in the entropy diagram as a function of temperature and magnetic field to find which is the most efficient region when performing a thermodynamic cycle. This work provides a practical way to look for temperature and magnetic field zones in the entropy diagram that can maximize the power extracted from an Otto magnetic engine.
The quantum heat engines have drawn much attention due to miniaturization of devices recently. We study the dynamics of the quantum Otto heat engine using the driven-dissipative Schrödinger equation. Starting from different initial states, we simulate the time evolutions of the internal energy, power and heat-work conversion efficiency. The initial state impacts on these thermodynamic quantities before the Otto cycle reaches stable. In the transition period, the efficiency and power may be higher or lower than the corresponding values in the cyclostationary state. Remarkably, the efficiency could surpass the Otto limit and even the Carnot limit and the power could be much higher than the rated power. The efficiency anomaly is due to the energy in the initial state. Thus, we suggest that periodically pumping could take the similar role of a hot bath but could be manipulated flexibly. Furthermore, we propose a new quantum engine working in a single reservoir to convert the pump energy into mechanical work. This manipulative engine could potentially be applied to working in the microenvironments without a large temperature difference, such as the biological tissues in vivo. Our protocol is expected to model a new quantum engine with the advantage of applicability and controllability.
Abstract For an Otto cycle there always exists a trade-off between the cycle efficiency and the output power due to the requirement of cycle length. The shortcut to adiabatic (STA) technology provides an effective way to deal with the difficulty of zero-output power in conventional Otto cycle. In this paper, the Otto cycle of three-qubit system as the working substance with counterdiabatic driving has been investigated. It is demonstrated that the tripartite Otto cycle as a universal machine, in the suitable regimes of external control parameter, could work as a quantum heat engine (QHE), refrigerator or heat pump. And, the performances of QHE and refrigerator with and without STA, such as the power and efficiency of QHE and the coefficient of performance (COP) and figure of merit (FOM) of refrigerator, have been investigated. It shows the application of STA scheme can lead to an effective enhancement in the performances of Otto cycle, including achievements of a high QHE’s/refrigerator’s power associated with a moderate QHE’s efficiency/COP of refrigerator. Especially, it is interesting that even in a short-time cycle the optimization of control parameters could arise a remarkable improvement in the efficiency (or COP) of STA QHE (refrigerator), approaching the ideal efficiency or COP of conventional Otto cycle with quasi-static process. Finally, with the aid of parameter optimization the trade-off regions between the efficiency and the power (the COP and the FOM) of STA Otto engine (refrigerator) have been advised.
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.