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

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.Recently, the study of small self-contained quantum thermal machines has received growing interest; see [1][2][3][4] for recent reviews. Such machines typically consist of only a few quantum levels, hence can be considered 'small' quantum systems (in terms of Hilbert space dimension). Moreover, these machines are termed selfcontained (or autonomous) as they function without any source of work or external control, but use only heat baths at different temperatures. The simplicity of these models makes them an ideal testbed for investigating quantum thermodynamics [3].First works in this area go back to the study of the thermodynamics features of lasers [5]. Since then, many designs have been proposed and studied (see e.g. [6][7][8][9]), among these a quantum absorption refrigerator consisting of three qubits [10]. The efficiency of this machine [11] and more general performance bounds [12,13] were discussed. The basic functioning and fundamental limits of the fridge can be captured via the concept of virtual qubits [14]. Moreover, quantum entanglement was shown to appear in this model, and to enhance cooling in certain regimes [15]. Possibilities for experimental implementations [16][17][18] were also discussed.So far, most works have discussed quantum absorption refrigerators in the steady-state regime, giving a detailed characterization of its physical properties. On the other hand, the transient regime remains basically unexplored so far. The latter is however of interest. First, from a conceptual point of view, it is relevant to understand the approach to equilibrium. Second, from a more applied point of view, it is natural to ask how fast cooling can be achieved, and what the timescale for reaching equilibrium is. The study of quantum effects, such as entanglement and coherence in the transient regime is also an interesting issue.Here we investigate the physics of a quantum absorption refrigerator in the transient regime. We focus on the three-qubit quantum fridge model of Ref.[10], characterizing time scales, cooling properties and entanglement. First, the time scales for coherent dynamics, damping, and decay to the steady state in terms of the bath coupling and...

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