Abstract
We demonstrate the existence of universal features in the finite-time thermodynamics of quantum machines by considering a many-body quantum Otto cycle in which the working medium is driven across quantum critical points during the unitary strokes. Specifically, we consider a quantum engine powered by dissipative energizing and relaxing baths. We show that under very generic conditions, the output work is governed by the Kibble-Zurek mechanism, i.e., it exhibits a universal power-law scaling with the driving speed through the critical points. We also optimize the finite-time thermodynamics as a function of the driving speed. The maximum power and the corresponding efficiency take a universal form, and are reached for an optimal speed that is governed by the critical exponents. We exemplify our results by considering a transverse-field Ising spin chain as the working medium. For this model, we also show how the efficiency and power vary as the engine becomes critical.
Highlights
Advances in quantum science and technology have made possible the laboratory implementation of minimal quantum devices such as heat engines and refrigerators using a variety of platforms that include trapped ions [1,2,3], nitrogen vacancy centers [4], and nuclear magnetic resonance experiments [5]
We have studied the effect of quantum criticality in quantum thermodynamics, by considering a many-body quantum machine operating close to a phase transition
As a working mediums (WMs) for the Otto cycle studied here, we have considered interacting Fermions coupled to local dissipative baths, which in the Fourier-transformed space, can be treated as noninteracting Fermions coupled to local noninteracting Fermionic dissipative baths
Summary
Advances in quantum science and technology have made possible the laboratory implementation of minimal quantum devices such as heat engines and refrigerators using a variety of platforms that include trapped ions [1,2,3], nitrogen vacancy centers [4], and nuclear magnetic resonance experiments [5]. The performance of quantum Otto cycles in both the adiabatic [25] and finite-time operation [7] can exhibit an enhancement due to bosonic quantum statistics, while a detrimental one has been predicted in the fermionic case. We show that the scaling of the work output of such QEs with the driving time follows a universal power law resulting from the Kibble-Zurek mechanism This result paves the way for the field of universal finite-time thermodynamics describing quantum machines driven through quantum critical points, which is the focus of our paper. We discuss Kibble-Zurek scaling and its connection to the output work and power of quantum Otto cycles in Sec. III A, while Sec. III B introduces an efficiency bound depending on dynamical critical exponent.
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