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Science

A (theoretical) quantum refrigerator

Jelena Stajic

Published Mar 7, 2019• 0 citations
Publisher

Abstract

Physics How thermodynamics works at a scale where quantum rules apply has fascinated many physicists. Buffoni et al. propose an intriguing scheme for making a tiny refrigerator that exploits the laws of quantum mechanics. Their refrigerator consists of two qubits that were initially in contact with reservoirs at different temperatures. In a refrigeration cycle, the qubits first underwent a quantum measurement, which changed their state and caused them to exchange energy with the measurement apparatus; the cycle was closed by putting the qubits back in contact with their respective reservoirs, giving away more heat than they received. The researchers predict that the procedure is robust with respect to experimental noise and may be realizable with superconducting qubits. Phys. Rev. Lett. 122 , 070603 (2019).

DOI
10.1126/science.363.6431.1053-e

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Physics
How thermodynamics works at a scale where quantum rules apply has fascinated many physicists. Buffoni et al. propose an intriguing scheme for making a tiny refrigerator that exploits the laws of quantum mechanics. Their refrigerator consists of two qubits that were initially in contact with reservoirs at different temperatures. In a refrigeration cycle, the qubits first underwent a quantum measurement, which changed their state and caused them to exchange energy with the measurement apparatus; the cycle was closed by putting the qubits back in contact with their respective reservoirs, giving away more heat than they received. The researchers predict that the procedure is robust with respect to experimental noise and may be realizable with superconducting qubits.
Phys. Rev. Lett. 122 , 070603 (2019).
The emergence of the laws of thermodynamics from the laws of quantum mechanics is an unresolved issue. The generation of the third law of thermodynamics from quantum dynamics is analysed. The scaling of the optimal cooling power of a reciprocating quantum refrigerator is sought as a function of the cold bath temperature as T c →0. The working medium consists of noninteracting particles in a harmonic potential. Two closed-form solutions of the refrigeration cycle are analyzed, and compared to a numerical optimization scheme, focusing on cooling toward zero temperature. The optimal cycle is characterized by linear relations between the heat extracted from the cold bath, the energy level spacing of the working medium and the temperature. The scaling of the optimal cooling rate is found to be proportional to T c 3/2 giving a dynamical interpretation to the third law of thermodynamics.
One of the formulations of the third laws of thermodynamics is that a processes become more isentropic as one approaches the absolute zero temperatures. We examine this prediction by studying an operating model of a quantum refrigerator pumping heat from a cold to a hot reservoir. The working medium consists of a gas of noninteracting harmonic oscillators. The model can be solved in closed form in the quasi-static limit or numerically for general conditions. It is found that the isentropic limit for Tc → 0 is approached only on the expansion segment of the refrigeration cycle. The scaling of the cooling rate with temperature is shown to be consistent with the second law of thermodynamics. This scaling is also consistent with the unattainability principle which is an alternative formulation of the third law of thermodynamics.
The study of nanoscopic thermal devices attracts an increasing attention, not only because of their key role in understanding the emergence of thermodynamics from quantum theory, but also for the potential use of quantum-mechanical thermal cycles, especially refrigerators, in quantum technologies. This thesis, is devoted to the performance optimization of autonomous (heat-driven) refrigerators. For a quantum refrigerator, one has a full microscopic description of the simple system serving as a working medium, and of its interaction with the external heat baths. This enables a consistent `finite-time? thermodynamic analysis, not relying on any phenomenological assumptions about the leading sources of irreversibility, and allows to establish arguably general performance bounds, essential to benchmark the operation of realistic devices. In particular, tight and model-independent upper bounds for the coefficient of performance at maximum power, are derived here for a class of strongly coupled refrigerators, and seen to hold more generally for other types of heat and power-driven cycles. Remarkably, these ultimate limitations only depend on the particulars of the system-baths interaction at the interface with the object to be cooled. Strategies might be then defined so as to saturate those limits: It is shown how the working medium of the refrigerator may be, for instance, scaled up into a parallel multi-stage configuration, resembling that of macroscopic multi-effect absorption chillers, as a means to increase its cooling power. Similarly, by applying reservoir engineering techniques on selected transitions between the energy states of the working medium, one can mimic exploitable non-equilibrium fluctuations in the baths, capable of boosting the overall power and COP beyond what would be otherwise allowed by the second law of thermodynamics. In this way, heat-driven chillers could be set to compete on a equal footing with the best power-driven refrigerators.
The authors theoretically investigate a cyclic superconducting quantum refrigerator for on-chip cooling. This work predicts substantial cooling of the cold reservoir (Cu) through repeated cycles of adiabatic magnetization and demagnetization of the working substance (Ta), with the excess heat moving to a hot reservoir of superconductor (Nb) having a large gap. The proposed refrigerator is particularly well suited for additional cooling from the base temperature of a dilution refrigerator, about 10 mK, down to about 1 mK. This device could be very effective for cooling superconducting circuits, single-photon detectors, or on-chip sensors.
Experimental demonstration of a truly quantum mechanical solid-state heat engine or refrigerator remains elusive up to now. Here, a four-stroke quantum refrigerator that can be realized using a superconducting qubit coupled alternately to two resonators with embedded reservoirs is analyzed theoretically. Besides being a practically feasible thermal machine, this concept presents a number of fundamentally interesting features. At high frequencies, the system exhibits nearly coherent dynamics, leading to quantum oscillations in cooling power versus operation frequency. At intermediate frequencies, an ideal Otto cycle can be realized. In the nearly adiabatic regime, the cooling power is quadratic in frequency and can be separated to classical and quantum contributions. Interestingly, it is shown here that quantum coherence leads always to performance that is inferior as compared to that arising from purely classical dynamics. Furthermore, in the nearly adiabatic regime the efficiency of the refrigerator exceeds clearly that of the standard Otto cycle.
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.