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Physical review. E

Smallest quantum thermal machine: The effect of strong coupling and distributed thermal tasks

Zhong‐Xiao Man, Yun‐Jie Xia

Published Jul 12, 2017• 30 citations
Publisher

Abstract

The functions of the smallest self-contained thermal machine consisting of a single qutrit are studied when the weak internal coupling assumption is relaxed. It is shown that in the presence of one target to be cooled the strong coupling is not beneficial to the refrigeration. The reason is explained by examining the effect of the strong coupling on the contributions of all eigenstates transitions to the heat current of the related thermal reservoir. When acting simultaneously on two targets, the machine can be manipulated to implement distributed tasks on them, such as cooling one target and meanwhile heating another one, by adjusting the coupling strengths between the machine with the two targets. In particular, we show that the machine can realize temperature reversal for the two qubits, namely, the qubit that is coupled to the high temperature reservoir is refrigerated to a temperature below that of the qubit contacting with the low temperature reservoir.

DOI
10.1103/physreve.96.012122

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The functions of the smallest self-contained thermal machine consisting of a single qutrit are studied when the weak internal coupling assumption is relaxed. It is shown that in the presence of one target to be cooled the strong coupling is not beneficial to the refrigeration. The reason is explained by examining the effect of the strong coupling on the contributions of all eigenstates transitions to the heat current of the related thermal reservoir. When acting simultaneously on two targets, the machine can be manipulated to implement distributed tasks on them, such as cooling one target and meanwhile heating another one, by adjusting the coupling strengths between the machine with the two targets. In particular, we show that the machine can realize temperature reversal for the two qubits, namely, the qubit that is coupled to the high temperature reservoir is refrigerated to a temperature below that of the qubit contacting with the low temperature reservoir.
We investigate the fundamental dimensional limits to thermodynamic machines. In particular, we show that it is possible to construct self-contained refrigerators (i.e., not requiring external sources of work) consisting of only a small number of qubits and/or qutrits. We present three different models, consisting of two qubits, a qubit and a qutrit with nearest-neighbor interactions, and a single qutrit, respectively. We then investigate the fundamental limits to their performance; in particular, we show that it is possible to cool towards absolute zero.
A quantum thermal transistor is designed by the strong coupling between one qubit and one qutrit which are in contact with three heat baths with different temperatures. The thermal behavior is analyzed based on the master equation by both the numerical and the approximately analytic methods. It is shown that the thermal transistor, as a three-terminal device, allows a weak modulation heat current (at the modulation terminal) to switch on and off and effectively modulate the heat current between the other two terminals. In particular, the weak modulation heat current can induce the strong heat current between the other two terminals with the multiple-region amplification of heat current. Furthermore, the heat currents are quite robust to the temperature (current) fluctuation at the lower-temperature terminal within a certain range of temperature, and so it can behave as a heat current stabilizer.
We study the performance of three-level quantum absorption refrigerators, paradigmatic autonomous quantum thermal machines, and reveal central impacts of strong couplings between the working system and the thermal baths. Using the reaction coordinate quantum master equation method, which treats system-bath interactions beyond weak coupling, we demonstrate that in a broad range of parameters the cooling window at strong coupling can be captured by a weak-coupling theory, albeit with parameters renormalized by the system-bath coupling energy. As a result, at strong system-bath couplings the window of cooling is significantly reshaped compared to predictions of weak-coupling treatments. We further show that strong coupling admits direct transport pathways between the thermal reservoirs. Such beyond-second-order transport mechanisms are typically detrimental to the performance of quantum thermal machines. Our study reveals that it is inadequate to claim for either a suppression or an enhancement of the cooling performance as one increases system-bath coupling-when analyzed against a single parameter and in a limited domain. Rather, a comprehensive approach should be adopted so as to uncover the reshaping of the operational window.
Small quantum absorption refrigerators have recently attracted renewed attention. Here we present a missing design of a two-qubit fridge, the main feature of which is that one of the two machine qubits is itself maintained at a temperature colder than the cold bath. This is achieved by "reversing" the couplings to the baths compared to previous designs, where only a transition is maintained cold. We characterize the working regime and the efficiency of the fridge. We demonstrate the soundness of the model by deriving and solving a master equation. Finally, we discuss the performance of the fridge, in particular the heat current extracted from the cold bath. We show that our model performs comparably to the standard three-level quantum fridge and thus appears appealing for possible implementations of nanoscale thermal machines.
Few-level systems coupled to thermal baths provide useful models for quantum thermodynamics and to understand the role of heat currents in quantum information settings. Useful operations such as cooling or thermal masers have been proposed in autonomous three-level systems. In this work, we propose the coherent coupling of two qutrits as a simultaneous refrigerator and heat pump of two reservoirs forming a system. This occurs thanks to the coupling to two other reservoirs which are out of equilibrium but do not inject heat in the system. We explore the thermodynamic performance of such operation and discuss whether it can be distinguished from the action of a Maxwell demon via measurements of current fluctuations limited to the working substance.
We propose a three-qubit setup for the implementation of a variety of quantum thermal machines where all heat fluxes and work production can be controlled. An important configuration that can be designed is that of an absorption refrigerator, extracting heat from the coldest reservoir without the need of external work supply. Remarkably, we achieve this regime by using only two-body interactions instead of the widely employed three-body interactions. This configuration could be more easily realized in current experimental setups. We model the open-system dynamics with both a global and a local master equation thermodynamic-consistent approach. Finally, we show how this model can be employed as a heat valve, in which by varying the local field of one of the two qubits allows one to control and amplify the heat current between the other qubits.