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arXiv:2006.00725 · Quantum Science and Technology

A many-body heat engine at criticality

Thomás Fogarty, Thomas Busch

Published Sep 28, 2020• 48 citations
arXivHTMLPDF

Abstract

Abstract We show that a quantum Otto cycle in which the medium, an interacting ultracold gas, is driven between a superfluid and an insulating phase can outperform similar single particle cycles. The presence of an energy gap between the two phases can be used to improve performance, while the interplay between lattice forces and the particle distribution can lead to a many-body cooperative effect. Since finite time driving of this cycle can create unwanted non-equilibrium dynamics which can significantly impair the performance of the engine cycle, we also design an approximate shortcut to adiabaticity for the many-body state that can be used to achieve an efficient Otto cycle around a critical point.

DOI
10.1088/2058-9565/abbc63

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Abstract We show that a quantum Otto cycle in which the medium, an interacting ultracold gas, is driven between a superfluid and an insulating phase can outperform similar single particle cycles. The presence of an energy gap between the two phases can be used to improve performance, while the interplay between lattice forces and the particle distribution can lead to a many-body cooperative effect. Since finite time driving of this cycle can create unwanted non-equilibrium dynamics which can significantly impair the performance of the engine cycle, we also design an approximate shortcut to adiabaticity for the many-body state that can be used to achieve an efficient Otto cycle around a critical point.
We show that a quantum Otto cycle in which the medium, an interacting ultracold gas, is driven between a superfluid and an insulating phase can outperform similar single particle cycles. The presence of an energy gap between the two phases can be used to improve performance, while the interplay between lattice forces and the particle distribution can lead to a many-body cooperative effect. Since finite time driving of this cycle can create unwanted non-equilibrium dynamics which can significantly impair the performance of the engine cycle, we also design an approximate shortcut to adiabaticity for the many-body state that can be used to achieve an efficient Otto cycle around a critical point.
The finite-time operation of a quantum heat engine that uses a single particle as a working medium generally increases the output power at the expense of inducing friction that lowers the cycle efficiency. We propose to scale up a quantum heat engine utilizing a many-particle working medium in combination with the use of shortcuts to adiabaticity to boost the nonadiabatic performance by eliminating quantum friction and reducing the cycle time. To this end, we first analyze the finite-time thermodynamics of a quantum Otto cycle implemented with a quantum fluid confined in a time-dependent harmonic trap. We show that nonadiabatic effects can be controlled and tailored to match the adiabatic performance using a variety of shortcuts to adiabaticity. As a result, the nonadiabatic dynamics of the scaled-up many-particle quantum heat engine exhibits no friction, and the cycle can be run at maximum efficiency with a tunable output power. We demonstrate our results with a working medium consisting of particles with inverse-square pairwise interactions that includes non-interacting and hard-core bosons as limiting cases.
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 consider a finite-time quantum Otto cycle with single- and two spin-1/2 systems as its working medium. To mimic adiabatic dynamics at a finite time, we employ a shortcut-to-adiabaticity technique and evaluate the performance of the engine including the cost of the shortcut. We compare our results with the true adiabatic and nonadiabatic performances of the same cycle. Our findings indicate that the use of the shortcut-to-adiabaticity scheme significantly enhances the performance of the quantum Otto engine as compared to its adiabatic and nonadiabatic counterparts for different figures of merit.
While the emergent field of quantum thermodynamics has the potential to impact energy science, the performance of thermal machines is often classical. We ask whether quantum effects can boost the performance of a thermal machine to reach quantum supremacy, i.e., surpassing both the efficiency and power achieved in classical thermodynamics. To this end, we introduce a nonadiabatic quantum heat engine operating an Otto cycle with a many-particle working medium, consisting of an interacting Bose gas confined in a time-dependent harmonic trap. It is shown that thanks to the interplay of nonadiabatic and many-particle quantum effects, this thermal machine can outperform an ensemble of single-particle heat engines with same resources, demonstrating the quantum supremacy of many-particle thermal machines.
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.