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arXiv:1611.09045 · Europhysics Letters (EPL)

Energy efficient quantum machines

Obinna Abah, Eric Lutz

Published May 1, 2017• 101 citations
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Abstract

We investigate the performance of a quantum thermal machine operating in finite time based on shortcut-to-adiabaticity techniques. We compute efficiency and power for a paradigmatic harmonic quantum Otto engine by taking the energetic cost of the shortcut driving explicitly into account. We demonstrate that shortcut-to-adiabaticity machines outperform conventional ones for fast cycles. We further derive generic upper bounds on both quantities, valid for any heat engine cycle, using the notion of quantum speed limit for driven systems. We establish that these quantum bounds are tighter than those stemming from the second law of thermodynamics.

DOI
10.1209/0295-5075/118/40005

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We investigate the performance of a quantum thermal machine operating in finite time based on shortcut-to-adiabaticity techniques. We compute efficiency and power for a paradigmatic harmonic quantum Otto engine by taking the energetic cost of the shortcut driving explicitly into account. We demonstrate that shortcut-to-adiabaticity machines outperform conventional ones for fast cycles. We further derive generic upper bounds on both quantities, valid for any heat engine cycle, using the notion of quantum speed limit for driven systems. We establish that these quantum bounds are tighter than those stemming from the second law of thermodynamics.
We consider a paradigmatic quantum harmonic Otto engine operating in finite time. We investigate its performance when shortcut-to-adiabaticity techniques are used to speed up its cycle. We compute efficiency and power by taking the energetic cost of the shortcut driving explicitly into account. We analyze in detail three different shortcut methods: counterdiabatic driving, local counterdiabatic driving, and inverse engineering. We demonstrate that all three lead to a simultaneous increase of efficiency and power for fast cycles, thus outperforming traditional heat engines.
We investigate the performance of a quantum Otto refrigerator operating in finite time and exploiting local counterdiabatic techniques. We evaluate its coefficient of performance and cooling power when the working medium consists of a quantum harmonic oscillator with a time-dependent frequency. We find that the quantum refrigerator outperforms its conventional counterpart, except for very short cycle times, even when the driving cost of the local counterdiabatic driving is included. We moreover derive upper bounds on the performance of the thermal machine based on quantum speed limits and show that they are tighter than the second law of thermodynamics.
The finite time operation of a quantum Otto heat engine leads to a trade-off between efficiency and output power, which is due to the deviation of the system from the adiabatic path. This trade-off caveat can be bypassed by using the shortcut-to-adiabaticity protocol. We experimentally implemented a quantum Otto heat engine using spin-1/2 nuclei on a nuclear magnetic resonance (NMR) quantum processor. We investigated its performance using the shortcut-to-adiabaticity technique via counter-adiabatic driving with the inclusion of the cost to perform the shortcut. We use two different metrics that incorporate the cost of shortcut-to-adiabaticity to define engine efficiency and experimentally analyze which one is more appropriate for the NMR platform. We found a significant improvement in the performance of the quantum Otto heat engine driven by shortcut-to-adiabaticity, as compared to the non-adiabatic heat engine.
Thermodynamic constraints impose a trade-off between power and efficiency in heat engines, preventing the simultaneous achievement of high power and high efficiency. For classical microscopic engines, explicit inequalities have been discovered, demonstrating the inherent inevitability of this power-efficiency trade-off. However, extensions of these results to quantum engines have so far been limited to cases of slow operation. In this study, we derive a power-efficiency trade-off relation for a paradigmatic quantum engine operating within a finite time, specifically the Otto cycle of a quantum harmonic oscillator. By utilizing a phase-space approach based on quasiprobability representations, we establish a universal trade-off relation applicable to arbitrary time-dependent protocols during the adiabatic processes. Our results reveal that the power of the quantum engine vanishes as the efficiency approaches the quantum-mechanical efficiency bound, which is stricter than the Carnot bound. Furthermore, we identify the conditions under which the upper bound is attained, which indicate maximum power is achieved when the generation of quantum coherence is reduced, and the difference in time durations of the isochoric processes increases. These findings are validated through numerical calculations, which confirm their applicability across various types of protocols for heat engine cycles.
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.
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.