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arXiv:1910.01600 · Physical review. E

Three-qubit refrigerator with two-body interactions

Adam Hewgill, J. Onam González, José P. Palao, Daniel Alonso, Alessandro Ferraro, Gabriele De Chiara

Published Jan 7, 2020• 41 citations
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Abstract

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.

DOI
10.1103/physreve.101.012109

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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.
Quantum mechanics has given us a new playground in which to experiment that boasts several unique features. In this thesis, we explore it in the context of thermodynamics: looking at what kind of thermal devices can be constructed and how quantum behaviour affects them. We consider three research strands. In the first part we formulate a selection of heat engines with two-qubit systems, utilising environments that induce quantum correlations into the system. We see that these correlations can have some effects on the work of the engine, but this effect is system dependent. Describing the dynamics of a quantum system in contact with an external environment is often achieved with a master equation. When considering systems comprised of multiple subsystems, the description becomes more complicated and some of the master equations that have been used previously produce unphysical results. In the second part of this thesis we show that if one does the proper analysis of the microscopic derivation of these master equations, then no thermodynamical inconsistencies occur. When one considers a system connected to three or more environments, a whole new set of possible thermodynamical machines becomes available. One notable case of these is the absorption refrigerator, which performs refrigeration without the need for an external work source. For the third part, we show how one can construct an absorption refrigerator using a three-qubit system with two-body interactions and describe its operation. We also show some thermal control properties of the three-qubit system.
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.
Quantum thermal machines, a sub-field of quantum thermodynamics, are actively studied with the aim to understand the connection between quantum mechanics and thermodynamics. In this work, qubits are used as the active medium in an absorption driven heat pump. The dynamics of this thermal machine are computationally simulated by treating the qubits as an open quantum system interacting with three bosonic heat baths. Some thermodynamic bounds for the system parameters are derived and used in order to define a refrigerating regime for the system.
We show that quantum absorption refrigerators, which have traditionally been studied as of three qubits, each of which is connected to a thermal reservoir, can also be constructed by using three qubits and two thermal baths, where two of the qubits, including the qubit to be locally cooled, are connected to a common bath. With a careful choice of the system, bath, and qubit-bath interaction parameters within the Born-Markov and rotating-wave approximations, one of the qubits attached to the common bath achieves a cooling in the steady state. We observe that the proposed refrigerator may also operate in a parameter regime where no or negligible steady-state cooling is achieved, but there is considerable transient cooling. The steady-state temperature can be lowered significantly by an increase in the strength of the few-body interaction terms existing due to the use of the common bath in the refrigerator setup. The proposed refrigerator built with three qubits and two baths is shown to provide steady-state cooling for both Markovian qubit-bath interactions between the qubits and canonical bosonic thermal reservoirs, and a simpler reset model for the qubit-bath interactions.
Quantum thermodynamics supplies a consistent description of quantum heat engines and refrigerators up to a single few-level system coupled to the environment. Once the environment is split into three (a hot, cold, and work reservoir), a heat engine can operate. The device converts the positive gain into power, with the gain obtained from population inversion between the components of the device. Reversing the operation transforms the device into a quantum refrigerator. The quantum tricycle, a device connected by three external leads to three heat reservoirs, is used as a template for engines and refrigerators. The equation of motion for the heat currents and power can be derived from first principles. Only a global description of the coupling of the device to the reservoirs is consistent with the first and second laws of thermodynamics. Optimization of the devices leads to a balanced set of parameters in which the couplings to the three reservoirs are of the same order and the external driving field is in resonance. When analyzing refrigerators, one needs to devote special attention to a dynamical version of the third law of thermodynamics. Bounds on the rate of cooling when Tc→0 are obtained by optimizing the cooling current. All refrigerators as Tc→0 show universal behavior. The dynamical version of the third law imposes restrictions on the scaling as Tc→0 of the relaxation rate γc and heat capacity cV of the cold bath.
We study the phenomenon of absorption refrigeration, where refrigeration is achieved by heating instead of work, in two different setups: a minimal set up based on coupled qubits and two nonlinearly coupled resonators. Considering ZZZZZZ interaction between the two qubits, we outline the basic ingredients required to achieve cooling. Using local as well as global master equations, we observe that inclusion of an XXXXXX type term in the qubit-qubit coupling is detrimental to cooling. We compare the cooling effect obtained in the qubit case with that of nonlinearly coupled resonators (multilevel system) where the ZZZZZZ interaction translates to a Kerr-type nonlinearity. For small to intermediate strengths of nonlinearity, we observe that multilevel quantum systems, for example qutrits, give better cooling effect compared to the qubits. Using Keldysh nonequilibrium Green's function formalism, we go beyond first order sequential tunneling processes and study the effect of higher order processes on refrigeration. We find a reduced cooling effect compared to the master equation calculations.