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. 2014 Feb 4:4:3949.
doi: 10.1038/srep03949.

Quantum-enhanced absorption refrigerators

Luis A Correa  1 , José P Palao  2 , Daniel Alonso  3 , Gerardo Adesso  4
Affiliations

Quantum-enhanced absorption refrigerators

Luis A Correa et al. Sci Rep. .

Abstract

Thermodynamics is a branch of science blessed by an unparalleled combination of generality of scope and formal simplicity. Based on few natural assumptions together with the four laws, it sets the boundaries between possible and impossible in macroscopic aggregates of matter. This triggered groundbreaking achievements in physics, chemistry and engineering over the last two centuries. Close analogues of those fundamental laws are now being established at the level of individual quantum systems, thus placing limits on the operation of quantum-mechanical devices. Here we study quantum absorption refrigerators, which are driven by heat rather than external work. We establish thermodynamic performance bounds for these machines and investigate their quantum origin. We also show how those bounds may be pushed beyond what is classically achievable, by suitably tailoring the environmental fluctuations via quantum reservoir engineering techniques. Such superefficient quantum-enhanced cooling realises a promising step towards the technological exploitation of autonomous quantum refrigerators.

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Figures

Figure 1
Figure 1
(a) Schematic representation of the three-level heat pump. The three independent baths are taken as infinite collections of uncoupled modes with Hamiltonian formula image. The dissipative interactions in each bath-transition pair are modeled by terms like e.g. formula image, with formula image. Here, the coupling constants gα,μ are proportional to formula image, which results in flat spectral densities, and the parameter γ controls the overall strength of the interaction. The three-stroke cooling and heating processes are depicted with blue and red arrows respectively. (b) Diagram of a two-qubit heat pump, where we shall always assume ωh > ωc. Energy transport between the two contacts is mediated by dissipation into the work bath thanks to a coupling term of the form formula image. (c) A design of heat pump with a contact qubit for each bath. In this case, the working material is provided with an explicit three-body interaction term to allow for energy exchanges formula image, with HI = g(|1w0h1c⟩ ⟨0w1h0c| + h.c.). The frequencies are constrained by ωh = ωc + ωw2.
Figure 2
Figure 2
Histograms of the efficiency at maximum power ε*/εC for ~105 random (a) three-level, (b) two-qubit and (c) three-qubit absorption fridges, as introduced in Figs. 1(a), 1(b), and 1(c), respectively. The temperatures {Tα}, the hot frequency ωh, the dissipation rates, and–-for the case (c)–the interaction strength g, were all chosen completely at random, but always respecting the conditions formula image and formula image, that guarantee the applicability of the master equation Eq. (1). In each case, we found the optimal pair {ωw, ωc} so that formula image was maximised, and computed the corresponding efficiency. This is equivalent to a global numerical optimisation of ε* over all free parameters of the models. In each of the panels above, we show three data sets that correspond to the same heat pump operating between 1d, 2d and 3d baths. In agreement with Eq. (9), ε* is bounded by formula image, formula image and formula image, respectively. It can also be seen that these bounds are tight, and that the majority of randomly sampled fridges cool very close to their corresponding bounds.
Figure 3
Figure 3
Parametric plot of power vs. efficiency of a three-level maser operating between three-dimensional bosonic reservoirs at temperatures Tw = 170, Th = 80 and Tc = 30 (formula image), for different values of the squeezing parameter of the work reservoir r = {0, 0.5, 1, 1.5, 2}. Both formula image, ε* and the maximum ε increase with r. In each curve, the hot frequency was fixed at ωh = 50, while ωc ranges from 0 up to ωc,max(r). The frontier between the white and the shaded region corresponds to the performance characteristic of an ideal reversed heat engine operating between the same hot and a cold baths. The general behaviour illustrated here is totally independent of the specific values of ωh and the set of temperatures {Tα}.</emph>
Figure 4
Figure 4
Level diagram of the two-qubit fridge of Fig. 1(b) with the transitions coupled to the work, hot and cold reservoirs depicted as red, orange and blue arrows respectively.
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