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arXiv:1812.00927 · Physical review. E

Critical-point behavior of a measurement-based quantum heat engine

Suman Chand, Asoka Biswas

Published Nov 29, 2018• 33 citations
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Abstract

We study how a quantum heat engine performs across the critical value of an external parameter, pertaining to the quantum phase transition. Considering a two-ion system subjected to a magnetic field, we show that the system performs in a quantum Otto cycle above a critical value of the magnetic field, while below such critical point, it does not operate in a heat cycle at all. Moreover, at the critical point, its interaction with an ancillary ion deteriorates the performance of the system as a heat engine. We further show that a strong interaction between the constituent ions of an ion-based system is crucial for it to work in a heat-work cycle, while the coupling to the ancillary system must be minimized.

DOI
10.1103/physreve.98.052147

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We study how a quantum heat engine performs across the critical value of an external parameter, pertaining to the quantum phase transition. Considering a two-ion system subjected to a magnetic field, we show that the system performs in a quantum Otto cycle above a critical value of the magnetic field, while below such critical point, it does not operate in a heat cycle at all. Moreover, at the critical point, its interaction with an ancillary ion deteriorates the performance of the system as a heat engine. We further show that a strong interaction between the constituent ions of an ion-based system is crucial for it to work in a heat-work cycle, while the coupling to the ancillary system must be minimized.
We show how one can implement a quantum heat machine by using two interacting trapped ions, in presence of a thermal bath. The electronic states of the ions act like a working substance, while the vibrational mode is modelled as the cold bath. The heat exchange with the cold bath is mimicked by the projective measurement of the electronic states. We show how such measurement in a suitable basis can lead to either a quantum heat engine or a refrigerator, which undergoes a quantum Otto cycle. The local magnetic field is adiabatically changed during the heat cycle. The performance of the heat machine depends upon the interaction strength between the ions, the magnetic fields, and the measurement cost. In our model, the coupling to the hot and the cold baths is never switched off in an alternative fashion during the heat cycle, unlike other existing proposals of quantum heat engines. This makes our proposal experimentally realizable using current tapped-ion technology.
Quantum heat machines, encompassing heat engines, refrigerators, heaters, and accelerators, represent the forefront of quantum thermodynamics, offering a novel paradigm for converting heat energy into useful mechanical work. Leveraging quantum mechanical principles, these machines promise superior efficiency and performance compared to classical counterparts, with potential applications in renewable energy and quantum computing. This paper investigates a quantum Otto engine operating in both ideal and finite-time scenarios, employing a two-level system interacting with a harmonic oscillator within the framework of the anisotropic quantum Rabi-Stark model (AQRSM) as the working medium. This model is notable for exhibiting both first-order and continuous quantum phase transitions. By focusing on quantum heat engines, our study reveals that these phase transitions critically modulate the efficiency and power of AQRSM-based engines, outperforming quantum engines fueled by working medium with harmonic spectrum. Additionally, we explore the impacts of quantum friction and conduct limit cycle analysis in finite-time operations, providing insights into optimizing quantum heat engines for practical implementation.
A properly selected quantum heat engine consumes resources efficiently. Also, there are many parameters to determine the right option. In this study, we construct and compare the quantum mechanical counterparts of Stirling and Otto cycles for an experimentally achievable quantum working medium where two spins 1/2 interact through isotropic Heisenberg interaction in the tunable external magnetic field. We consider two comparison cases that operate heat cycles with the same system parameters or equal efficiencies. The quantum Stirling cycle produces more work than that of the Otto cycle under the same parameters or equal efficiency conditions. The quantum Stirling engine operates a wider range of coupling strengths. The work performed in the cycles is enhanced by coupling strength. On the other hand, we investigate the role of coupling strength on the performance of the non-regenerative quantum Stirling heat cycle under various magnitudes of the magnetic field. The distance between the applied magnetic fields at the initial and final points of the isothermal stage is found to be an enhancer for the work output and efficiency of the quantum Stirling cycle.
Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance.