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arXiv:2107.11668 · Physical Review A

Designing robust quantum refrigerators in disordered spin models

Tanoy Kanti Konar, Srijon Ghosh, Amit Kumar Pal, Aditi Sen

Published Feb 22, 2022• 14 citations
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Abstract

We explore a small quantum refrigerator in which the working substance is made of paradigmatic nearest-neighbor quantum spin models, the $XYZ$ and the $XY$ model with Dzyaloshinskii-Moriya interactions, consisting of two and three spins, each of which is in contact with a bosonic bath. We identify a specific range of interaction strengths which can be tuned appropriately to ensure a cooling of the selected spin in terms of its local temperature in the weak-coupling limit. Moreover, we report that in this domain, when one of the interaction strengths is disordered, the performance of the thermal machine operating as a refrigerator remains almost unchanged instead of degrading, thereby establishing the flexibility of this device. However, to obtain a significant amount of cooling via ordered as well as disordered spin models, we observe that one has to go beyond the weak-coupling limit and compute the figures of merit by using global master equations.

DOI
10.1103/physreva.105.022214

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We explore a small quantum refrigerator in which the working substance is made of paradigmatic nearest-neighbor quantum spin models, the XYZXYZXYZ and the XYXYXY model with Dzyaloshinskii-Moriya interactions, consisting of two and three spins, each of which is in contact with a bosonic bath. We identify a specific range of interaction strengths which can be tuned appropriately to ensure a cooling of the selected spin in terms of its local temperature in the weak-coupling limit. Moreover, we report that in this domain, when one of the interaction strengths is disordered, the performance of the thermal machine operating as a refrigerator remains almost unchanged instead of degrading, thereby establishing the flexibility of this device. However, to obtain a significant amount of cooling via ordered as well as disordered spin models, we observe that one has to go beyond the weak-coupling limit and compute the figures of merit by using global master equations.
We design quantum refrigerators based on spin-jjj quantum XYZXYZXYZ and bilinear-biquadratic models with individual spins attached to bosonic thermal baths. By considering both local and global master equations, we illustrate an enhancement in the performance of the refrigerators with an increase in the spin dimension irrespective of the choice of the spin models. To assess the performance of the refrigerators, we introduce a distance-based measure to quantify the local temperature of a particle with arbitrary spin quantum number jjj. Interestingly, we find that the local temperature quantifier, defined via minimizing the distance between a spin-jjj thermal state and the evolved state of the spin-jjj particle in the steady state, coincides with the population-based definition of local temperature known in the literature for spin-12\frac{1}{2}21​ particles. Moreover, we demonstrate that the qualitative behavior of the distance-based local temperature is independent of the choice of the distance measure by comparing the trace distance, Uhlmann's fidelity, and relative entropy distance. We further observe by computing a local master equation that the quantum refrigerator consisting of a spin-1/21/21/2 and a spin-jjj particle can lead to a lower local temperature compared to a refrigerator with two identical spin-jjj particles following the XYZXYZXYZ interactions.
Abstract We propose a model of two identical autonomous quantum refrigerators that interact through their qubits coupled to cold thermal baths. We consider the same specific disposition for each refrigerator related to a three-level system coupled to different thermal baths and, in turn, to a qubit as the object to be cooled. By coupling the two systems, we show that under certain conditions on the model parameters, the devices can operate in the regime of an independent autonomous quantum refrigerator or be subject to an adjustment of the thermodynamic performances. We further investigate the correlations induced by the interaction between the two refrigerators, and illustrate their behavior with respect to their thermodynamic performances. We have found that adjusting the different interaction constants of the model can lead to an evolution of the quantum correlations of the two machines that is inversely related to the behavior of the thermodynamic quantities of both refrigerators. However, this is not necessarily the case when the temperatures of the model are considered as the reference parameters.
We investigate the performance of a three-spin quantum absorption refrigerator using a refined open quantum system model valid across all inter-spin coupling strengths. It describes the transition between previous approximate models for the weak and the ultrastrong coupling limit, and it predicts optimal refrigeration for moderately strong coupling, where both approximations are inaccurate. Two effects impede a more effective cooling: the coupling between the spins no longer reduces to a simple resonant energy exchange (the rotating wave approximation fails), and the interactions with the thermal baths become sensitive to the level splitting, thus opening additional heat channels between the reservoirs. We identify the modified conditions of refrigeration as a function of the inter-spin coupling strength, and we show that, contrary to intuition, a high-temperature work reservoir thwarts refrigeration in the strong coupling regime.
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 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.
The connection between quantum entanglement and quantum refrigerators is an active area in quantum thermodynamics. Ongoing investigations are exploring how entanglement in the working medium of a quantum refrigerator can impact its performance. The paper focuses on a two-qubit Heisenberg XXZ spin-[Formula: see text] system featuring Kaplan–Shekhtman–Entin-Wohlman–Aharony (KSEA) and Dzyaloshinsky–Moriya (DM) spin–orbit exchange interactions as the operational physical matter medium for a quantum refrigerator. We provide explicit formulations for relevant thermodynamic quantities of the quantum refrigerator, dependent on the magnetic field (B) and the strengths parameters of spin–orbit interactions. The study explores the relationship between entanglement and thermodynamic properties, using concurrence as a quantitative metric of thermal entanglement. The results emphasize the significant impact of fine-tuning the amplitudes of both DM and [Formula: see text] strengths on improving the quantum refrigerator’s performance. Finally, the findings suggest that entanglement between the qubits is superfluous for enhancing the quantum refrigerator’s efficiency.