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arXiv:1912.08689 · Physical Review Research

Many-body quantum heat engines with shortcuts to adiabaticity

Andreas Hartmann, Victor Mukherjee, Wolfgang Niedenzu, Wolfgang Lechner

Published May 8, 2020• 67 citations
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Abstract

The authors propose a many-body quantum heat engine (QHE) that efficiently operates at finite power. Due to the adiabatic theorem, efficient QHEs generally yield a vanishing power output. The method of shortcuts to adiabaticity is a promising candidate to overcome this bottleneck, but usually requires a-priori knowledge of the system's eigenstates at all times and is thus hard to implement for many-body systems. Here, the authors apply approximate local counter-diabatic protocols that are applicable in state-of-the-art experiments.

DOI
10.1103/physrevresearch.2.023145

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The authors propose a many-body quantum heat engine (QHE) that efficiently operates at finite power. Due to the adiabatic theorem, efficient QHEs generally yield a vanishing power output. The method of shortcuts to adiabaticity is a promising candidate to overcome this bottleneck, but usually requires a-priori knowledge of the system's eigenstates at all times and is thus hard to implement for many-body systems. Here, the authors apply approximate local counter-diabatic protocols that are applicable in state-of-the-art experiments.
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.
Finite-time quantum heat engines (QHEs) typically extract less work than their quasistatic counterparts because fast driving generates coherences and non-adiabatic transitions during the work strokes, a phenomenon commonly referred to as quantum friction. Quantum lubrication denotes a broad class of strategies that use auxiliary systems or controls to mitigate this loss. In this work, we introduce a lubrication protocol based on the quantum Zeno dynamics (QZD). By coupling the working medium to an auxiliary lubricant system and frequently monitoring the lubricant, we confine the joint evolution to a Zeno subspace and obtain an effective shortcut to adiabaticity during the work strokes of a QHE running an Otto cycle. In the ideal Zeno limit, the protocol reproduces the transitionless dynamics required to preserve populations in the instantaneous energy basis and recover the Otto efficiency at finite stroke duration. We also analyze several implementation-dependent thermodynamic costs, including switching, driving, monitoring, and imperfect thermalization, in order to assess how these costs constrain the practical gains in efficiency and power. Our results identify QZD as a conceptually distinct route to quantum lubrication and highlight quantum heat engines as a useful setting in which to study the interplay between strong coupling, measurement, and quantum thermodynamic control.
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 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.
The power and efficiency of many-body heat engines can be boosted by performing cooperative nonadiabatic operations in contrast to the commonly used adiabatic implementations. Here the key property relies on the fact that nonadiabaticity is required in order to allow for cooperative effects that can use the thermodynamic resources only present in the collective nonpassive state of a many-body system. In particular, we consider the efficiency of an Otto cycle, which increases with the number of copies used and reaches a many-body bound, which we discuss analytically.
We generalize the quantum heat engine (QHE) model which was first proposed by Bender et al. [J. Phys. A 33, 4427 (2000)] to the case in which an ideal Fermi gas with an arbitrary number N of particles in a box trap is used as the working substance. Besides two quantum adiabatic processes, the engine model contains two isoenergetic processes, during which the particles are coupled to energy baths at a high constant energy E(h) and a low constant energy E(c), respectively. Directly employing the finite-time thermodynamics, we find that the power output is enhanced by increasing particle number N (or decreasing minimum trap size L(A)) for given L(A) (or N), without reduction in the efficiency. By use of global optimization, the efficiency at possible maximum power output (EPMP) is found to be universal and independent of any parameter contained in the engine model. For an engine model with any particle-number N, the efficiency at maximum power output (EMP) can be determined under the condition that it should be closest to the EPMP. Moreover, we extend the heat engine to a more general multilevel engine model with an arbitrary 1D power-law potential. Comparison between our engine model and the Carnot cycle shows that, under the same conditions, the efficiency η = 1 - E(c)/E(h) of the engine cycle is bounded from above the Carnot value η(c) =1 - T(c)/T(h).