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arXiv:2002.02225 · Physical review. B./Physical review. B

Geometric properties of adiabatic quantum thermal machines

Bibek Bhandari, Pablo Terrén Alonso, Fabio Taddei, Felix von Oppen, Rosario Fazio, Liliana Arrachea

Published Oct 8, 2020• 66 citations
arXivHTMLPDF

Abstract

A quantum thermal machine can be controlled by time-periodic perturbations that define a cycle, as in conventional macroscopic thermal machines. This paper presents a general and unified approach to the study of quantum thermal machines, including both heat engines and refrigerators, which operate under periodic adiabatic driving and are in contact with thermal reservoirs kept at different temperatures. Importantly, many observables characterizing the operation and the performance of these machines are geometric in nature.

DOI
10.1103/physrevb.102.155407

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A quantum thermal machine can be controlled by time-periodic perturbations that define a cycle, as in conventional macroscopic thermal machines. This paper presents a general and unified approach to the study of quantum thermal machines, including both heat engines and refrigerators, which operate under periodic adiabatic driving and are in contact with thermal reservoirs kept at different temperatures. Importantly, many observables characterizing the operation and the performance of these machines are geometric in nature.
We adopt a geometric approach to describe the performance of adiabatic quantum machines, operating under slow time-dependent driving and in contact with two reservoirs with a temperature bias during all the cycle.We show that the problem of optimizing the power generation of a heat engine and the efficiency of both the heat engine and refrigerator operational modes is reduced to an isoperimetric problem with nontrivial underlying metrics and curvature.This corresponds to the maximization of the ratio between the area enclosed by a closed curve and its corresponding length.We illustrate this procedure in a qubit coupled to two reservoirs operating as a thermal machine by means of an adiabatic protocol.
We study the performance of quantum thermal machines in which the working fluid of the model is represented by a many-body quantum system that is periodically connected with external baths via local couplings. A formal characterization of the limit cycles of the set-up is presented in terms of the mixing properties of the quantum channel that describes the evolution of the fluid over a thermodynamic cycle. For the special case in which the system is a collection of spin 1/2 1 / 2 particles coupled via magnetization preserving Hamiltonians, a full characterization of the possible operational regimes (i.e., thermal engine, refrigerator, heater and thermal accelerator) is provided: in this context we show in fact that the different regimes only depend upon a limited number of parameters (essentially the ratios of the energy gaps associated with the local Hamiltonians of the parts of the network which are in direct thermal contact with the baths).
We identify and interpret the possible quantum thermal machine regimes with a transverse-field Ising model as the working substance. In general, understanding the emergence of such regimes in a many-body quantum system is challenging due to the dependence on the many energy levels in the system. By considering infinitesimal work strokes, we can understand the operation from equilibrium properties of the system. We find that infinitesimal work strokes enable both heat engine and accelerator operation, with the output and boundaries of operation described by macroscopic properties of the system, in particular the net transverse magnetization. At low temperatures, the regimes of operation and performance can be understood from quasiparticles in the system, while at high temperatures an expansion of the free energy in powers of inverse temperature describes the operation. The understanding generalises to larger work strokes when the temperature difference between the hot and cold reservoirs is large. For hot and cold reservoirs close in temperature, a sufficiently large work stroke can enable refrigerator and heater regimes. Our results and method of analysis will prove useful in understanding the possible regimes of operation of quantum many-body thermal machines more generally.
Abstract Based on a recently developed non-perturbative platform designed to simulate the full quantum dynamics of quantum thermal machines, the situation of a quantum refrigerator operating according to an Otto cycle is studied. The periodic steady-state dynamics is discussed in detail as well as the key thermodynamic quantities work, heat, and entropy. A particular benefit of the formulation is that it allows to access explicitly the work required for switching on and off the interaction with the respective thermal reservoirs in a consistent way. The domains in which the device operates in refrigerator mode are characterized.
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 present a unified approach to study continuous measurement-based quantum thermal machines in static as well as adiabatically driven systems. We investigate both steady-state and transient dynamics for the time-independent case. In the adiabatically driven case, we show how measurement-based thermodynamic quantities can be attributed geometric characteristics. We also provide the appropriate definition for heat transfer and dissipation owing to continuous measurement in the presence and absence of adiabatic driving. We illustrate the aforementioned ideas and study the phenomenon of refrigeration in two different paradigmatic examples: a coupled quantum dot and a coupled qubit system, both undergoing continuous measurement and slow driving. In the time-independent case, we show that quantum coherence can improve the cooling power of measurement-based quantum refrigerators. Exclusively for the case of coupled qubits, we consider linear as well as nonlinear system-bath couplings. We observe that nonlinear coupling produces cooling effects in certain regimes where otherwise heating is expected. In the adiabatically driven case, we observe that quantum measurement can provide significant boost to the power of adiabatic quantum refrigerators. We also observe that the obtained boost can be larger than the sum of power due to individual effects. The measurement-based refrigerators can have similar or better coefficient of performance in the driven case compared to the static one in the regime where heat extraction is maximum. Our results have potential significance for future application in devices ranging from measurement-based quantum thermal machines to refrigeration in quantum processing networks.