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arXiv:2210.02681

Quantum Thermodynamics applied for Quantum Refrigerators cooling down a qubit

Hideaki Okane, Shunsuke Kamimura, Shingo Kukita, Yasushi Kondo, Yuichiro Matsuzaki

Published Jan 4, 2023• 2 citations
arXivHTMLPDF

Abstract

Abstract We discuss a quantum refrigerator to increase the ground state probability of a target qubit whose energy difference between the ground and excited states is less than the thermal energyof its environment. We consider two types of quantum refrigerators: (1) one extra qubit with frequent pulse operations and(2) two extra qubits without them. These two types of refrigerators are evaluated from the viewpoint of quantum thermodynamics. More specifically,we calculate the heat removed from the target qubit, the work done for the system, and the coefficient of performance (COP), the ratio between the heat ant work.We show that the COP of the second type outperforms that of the first one.Our results are useful to design a high-performance quantum refrigerator cooling down a qubit.

DOI
10.21203/rs.3.rs-2421810/v1

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Abstract We discuss a quantum refrigerator to increase the ground state probability of a target qubit whose energy difference between the ground and excited states is less than the thermal energyof its environment. We consider two types of quantum refrigerators: (1) one extra qubit with frequent pulse operations and(2) two extra qubits without them. These two types of refrigerators are evaluated from the viewpoint of quantum thermodynamics. More specifically,we calculate the heat removed from the target qubit, the work done for the system, and the coefficient of performance (COP), the ratio between the heat ant work.We show that the COP of the second type outperforms that of the first one.Our results are useful to design a high-performance quantum refrigerator cooling down a qubit.
We study a quantum absorption refrigerator, in which a target qubit is cooled by two machine qubits in a nonequilibrium steady-state. It is realized by a strong internal coupling in the two-qubit fridge and a vanishing tripartite interaction among the whole system. The coherence of a machine virtual qubit is investigated as quantumness of the fridge. A necessary condition for cooling shows that the quantum coherence is beneficial to the nonequilibrium fridge, while it is detrimental as far as the maximum coefficient of performance (COP) and the COP at maximum power are concerned. Here, the COP is defined only in terms of heat currents caused by the tripartite interaction, with the one maintaining the two-qubit nonequilibrium state being excluded. The later can be considered to have no direct involvement in extracting heat from the target, as it is not affected by the tripartite interaction.
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Abstract We study several optimal working regimes of one-qubit quantum refrigerators having one qubit at their cold side. We demonstrate that they can be optimized using the techniques of finite-time thermodynamics on the solutions of the Lindblad equation. Our results show that differently to what happens in classic refrigerators, in our quantum ones the optimization of the cooling power does not lead to an optimal working regime but that using the Ω\OmegaΩ Ω function we can find it. Then, we generalize the study using a family of target functions defined by powers of the coefficient of performance times the cooling power to carry out a more general optimization. These last optimizations reveal the importance that every parameter defining the refrigerator has on the performance of the refrigerators when they work optimally.
The derivation of general performance benchmarks is important in the design of highly optimized heat engines and refrigerators. To obtain them, one may model phenomenologically the leading sources of irreversibility ending up with results that are model independent, but limited in scope. Alternatively, one can take a simple physical system realizing a thermodynamic cycle and assess its optimal operation from a complete microscopic description. We follow this approach in order to derive the coefficient of performance at maximum cooling rate for any endoreversible quantum refrigerator. At striking variance with the universality of the optimal efficiency of heat engines, we find that the cooling performance at maximum power is crucially determined by the details of the specific system-bath interaction mechanism. A closed analytical benchmark is found for endoreversible refrigerators weakly coupled to unstructured bosonic heat baths: an ubiquitous case study in quantum thermodynamics.
A four-level entangled quantum refrigeration cycle working with a two-qubit entangled system is proposed in this paper. Based on the first law of quantum thermodynamics and the concept of thermal entanglement, the relation between the quantum entanglement and the several thermodynamic quantities such as the heat transfer, the input work and the coefficient of performance is analyzed. It is found that the isoline of the coefficient of performance is the loop line and it no longer monotonically changes with the ratio of entanglement; in a small exchange constant J the operation region of the refrigerator is c1>c2 and in a larger exchange constant J the operation region of the refrigerator may be c1>c2 or c1c2; the maximal coefficient of performance increases as the exchange constant increases.
We investigate, theoretically and experimentally, the thermodynamic performance of a minimal three-qubit heat-bath algorithmic cooling refrigerator. We analytically compute the coefficient of performance, the cooling power, and the polarization of the target qubit for an arbitrary number of cycles, taking realistic experimental imperfections into account. We determine their fundamental upper bounds in the ideal reversible limit and show that these values may be experimentally approached using a system of three qubits in a nitrogen-vacancy center in diamond.