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arXiv:1508.02025 · Physical Review E

Small quantum absorption refrigerator in the transient regime: Time scales, enhanced cooling, and entanglement

Jonatan Bohr Brask, Nicolas Brunner

Published Dec 1, 2015• 100 citations
arXivHTMLPDF

Abstract

A small quantum absorption refrigerator, consisting of three qubits, is discussed in the transient regime. We discuss time scales for coherent dynamics, damping, and approach to the steady state, and we study cooling and entanglement. We observe that cooling can be enhanced in the transient regime, in the sense that lower temperatures can be achieved compared to the steady-state regime. This is a consequence of coherent dynamics but can occur even when this dynamics is strongly damped by the dissipative thermal environment, and we note that precise control over couplings or timing is not needed to achieve enhanced cooling. We also show that the amount of entanglement present in the refrigerator can be much larger in the transient regime compared to the steady state. These results are of relevance to future implementations of quantum thermal machines.

DOI
10.1103/physreve.92.062101

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A small quantum absorption refrigerator, consisting of three qubits, is discussed in the transient regime. We discuss time scales for coherent dynamics, damping, and approach to the steady state, and we study cooling and entanglement. We observe that cooling can be enhanced in the transient regime, in the sense that lower temperatures can be achieved compared to the steady-state regime. This is a consequence of coherent dynamics but can occur even when this dynamics is strongly damped by the dissipative thermal environment, and we note that precise control over couplings or timing is not needed to achieve enhanced cooling. We also show that the amount of entanglement present in the refrigerator can be much larger in the transient regime compared to the steady state. These results are of relevance to future implementations of quantum thermal machines.
We examine a quantum absorption refrigerator that comprises three qubits, each of which is connected with a separate spin-star environment, with the three qubit-bath units coupled through an effective six-body interaction. The refrigerator exhibits the feature of transient cooling, i.e., lowering of the temperature of the first qubit in sufficiently small timescales, rather than steady-state refrigeration. A key advantage of our model is that the symmetries of the Hamiltonian enable a semi-analytic solution of the reduced density matrices of the refrigerator qubits, even in the presence of a large number of environmental spins. We derive the condition for autonomous refrigeration and analyze how the optimal cold-qubit temperature scales with the number of bath spins. We find a power-law scaling towards a constant asymptotic value. We also find the scaling of the minimum time required for optimal cooling as a function of the number of bath spins. Furthermore, we quantify the non-Markovianity of the cold-qubit dynamics using a restricted Breuer-Laine-Piilo information-backflow measure and observe that stronger backflow correlates with lower transient minimum temperatures across the sampled parameter regime. The transient-cooling performance is found to be robust under broad parameter variations. Compared to a conventional Markovian three-qubit refrigerator, the CSQAR achieves lower cold-qubit temperatures on shorter timescales. We further analyze the heat currents associated with the three qubits and their respective baths.
We show that it is possible to construct a quantum absorption refrigerator that provides refrigeration only in the transient regime, by using three interacting qubits, each of which is also interacting with a local heat bath. Though the machine does not provide any effective cooling in the steady state, significant cooling of a qubit can be achieved much before the system reaches its steady state. We also demonstrate a scenario where the temperature of the qubit that has to be cooled, decreases monotonically to its minimum steady-state temperature. This facilitates bypassing of precise time control in cooling. We study the behaviour of the ratio of the heat currents of the machine for both the scenarios. The results remain qualitatively unchanged for different models of thermal baths. We also comment on the temporal behaviour of bipartite and multipartite quantum correlations present in the system, when transient cooling without steady-state cooling takes place.
The extension of thermodynamics into the quantum regime has received much attention in recent years. A primary objective of current research is to find thermodynamic tasks which can be enhanced by quantum mechanical effects. With this goal in mind, we explore the finite-time dynamics of absorption refrigerators composed of three quantum bits (qubits). The aim of this finite-time cooling is to reach low temperatures as fast as possible and subsequently extract the cold particle to exploit it for information processing purposes. We show that the coherent oscillations inherent to quantum dynamics can be harnessed to reach temperatures that are colder than the steady state in orders of magnitude less time, thereby providing a fast source of low-entropy qubits. This effect demonstrates that quantum thermal machines can surpass classical ones, reminiscent of quantum advantages in other fields, and is applicable to a broad range of technologically important scenarios.
We explore a small quantum refrigerator consisting of three qubits, each of which is kept in contact with an environment. We consider two settings: one is when there is necessarily transient cooling and the other is when both steady-state and transient coolings prevail. Our primary focus, however, is on the transient cooling phenomena. We show that in the transient regime, the temperature of the cold qubit can decrease further compared to the case where all qubits are connected to Markovian environments, by replacing the environment attached to the cold qubit with a finite-size spin environment, modeled by a few quantum spins interacting with the cold qubit. We also consider refrigeration with more than one finite-size spin environment of the three-qubit refrigerating device. As expected, a steady temperature is reached only if there are at least two Markovian baths, regardless of whether the cold qubit is attached to an environment. However, distinct envelopes of temperature oscillations are observed in all cases. We investigate the effects of the finite-size environments on the cooling of the cold qubit when one, two, or all Markovian baths are replaced by finite-size environments. Additionally, we examine this effect in two- and single-qubit self-sustained devices connected to one or more finite-size environments. In deriving the dynamical equations for the qubits connected to finite-size environments, we made no assumptions about the Markovian nature of the environment. As a result, these finite-size environments inherently exhibit information backflow from the environment to the system, a hallmark of non-Markovianity. Hence, we propose a witness to detect non-Markovianity in such systems. Finally, the cooling processes are studied in presence of Markovian noise, and we analyze the response on the refrigeration of the noise strength. In particular, we find the noise strength until which refrigeration remains possible.
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.
Small self-contained quantum thermal machines function without external source of work or control but using only incoherent interactions with thermal baths. Here we investigate the role of entanglement in a small self-contained quantum refrigerator. We first show that entanglement is detrimental as far as efficiency is concerned-fridges operating at efficiencies close to the Carnot limit do not feature any entanglement. Moving away from the Carnot regime, we show that entanglement can enhance cooling and energy transport. Hence, a truly quantum refrigerator can outperform a classical one. Furthermore, the amount of entanglement alone quantifies the enhancement in cooling.