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arXiv:2106.04164 · Physical Review Applied

Superradiant Many-Qubit Absorption Refrigerator

Michal Kloc, Kurt Meier, Kimon Hadjikiriakos, Gernot Schaller

Published Oct 29, 2021• 27 citations
arXivHTMLPDF

Abstract

Cooling fragile quantum systems requires quantum cooling technology. The smallest possible fridge employs a three-level system to autonomously cool the coldest of the three reservoirs. The authors suggest a setup with a quantum working fluid composed of $N$ collectively coupled qubits to effectively implement such a refrigerator. The collective couplings lead to a quadratic boost of the cooling current, $I\ensuremath{\propto}{N}^{2}$.

DOI
10.1103/physrevapplied.16.044061

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Cooling fragile quantum systems requires quantum cooling technology. The smallest possible fridge employs a three-level system to autonomously cool the coldest of the three reservoirs. The authors suggest a setup with a quantum working fluid composed of NNN collectively coupled qubits to effectively implement such a refrigerator. The collective couplings lead to a quadratic boost of the cooling current, I\ensuremath∝N2I\ensuremath{\propto}{N}^{2}I\ensuremath∝N2.
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.
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.
An implementation of a small quantum absorption refrigerator in a circuit QED architecture is proposed. The setup consists of three harmonic oscillators coupled to a Josephson junction. The refrigerator is autonomous in the sense that it does not require any external control for cooling, but only thermal contact between the oscillators and heat baths at different temperatures. In addition, the setup features a built-in switch, which allows the cooling to be turned on and off. If timing control is available, this enables the possibility for coherence-enhanced cooling. Finally, we show that significant cooling can be achieved with experimentally realistic parameters and that our setup should be within reach of current technology.
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.
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.