Quantum-enhanced absorption refrigerators

OPEN SUBJECT AREAS: QUANTUM MECHANICS Quantum-enhanced absorption refrigerators Luis A. Correa1,2,3, José P. Palao1,4, Daniel Alonso1,2 & Gerardo Adesso3 THERMODYNAMICS MOLECULAR MACHINES AND MOTORS QUBITS Received 15 January 2014 Accepted 16 January 2014 Published 4 February 2014 Correspondence and requests for materials should be addressed to L.A.C. (lacorrea@ull. es) 1 IUdEA Instituto Universitario de Estudios Avanzados, Universidad de La Laguna, La Laguna 38203, Spain, 2Dpto. Fı́sica Fundamental, Experimental, Electrónica y Sistemas, Universidad de La Laguna, La Laguna 38203, Spain, 3School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, UK, 4Departamento de Fı́sica Fundamental II, Universidad de La Laguna, La Laguna 38204, Spain. 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. A n absorption or heat-driven quantum refrigerator is a system capable of establishing a net steady-state transport of energy from a cold bath (c) to a hot bath (h), assisted only by the residual heat coming from an additional work reservoir (w)1–3. In this picture, the cold bath would play the role of the macroscopic or mesoscopic object to be cooled. In addition to their potential technological applications, these autonomous quantum-thermal devices are also appealing from the fundamental perspective, as they are naturally well suited for the study of thermodynamics at the level of individual open quantum systems1,4–6. In spite of the increasing interest that quantum absorption cooling has attracted over the last few years5,7–12, the field is far from new. A heat-driven quantum fridge is just one specific configuration of the more general quantum heat pump, that can function either as a heater, a chiller or even an engine. The use of three-level solid-state masers as physical support for heat pumps was already discussed in the late 1950s13,14, when spin refrigeration was also experimentally demonstrated15. The consistent quantum-thermodynamic description of these elementary threelevel prototypes was object of further study1,4 and, just recently, alternative finite-dimensional quantum systems realising autonomous heat pumps have been put forward in the literature2,3. The different designs of quantum heat pumps share limitations that can be understood from the assumptions on their interactions with the environments. Under the familiar conditions usually met in the quantum-optical regime, the dissipative processes may be assumed purely Markovian17–19, which severely restricts the performance of any heat-driven device, and confers a distinctive spectral structure to the environmental fluctuations16. In particular, once their steady state builds up, quantum heat pumps are governed by formal analogues of the laws of thermodynamics and, as a consequence, their absolute efficiency ideally saturates to the corresponding Carnot limits eC, albeit at vanishing ‘cooling power’14, i.e. in the reversible limit, the exchange of any finite amount of energy with the heat baths is performed in infinite time. For practical purposes, however, one needs to operate at nonvanishing power. In this case, the relevant issue to assess the functionality of these devices demands the optimisation of more practical figures of merit such as the efficiency at maximum cooling power e*. The natural question arises whether e* can approach eC arbitrarily closely even at finite cooling power, or if, on the contrary, it is upper bounded by some fundamental limit. The efficiency at maximum ‘mechanical’ power is extensively used to benchmark the operation of heat engines and a lot of effort has been devoted to establish a universal upper bound therefor20–22. Unfortunately, the general arguments used for engines do not provide simple bounds when the cycle is reversed into a refrigerator, and consequently, a different approach is needed to arrive to model-independent performance bounds. Here, we rigorously prove that the ‘smallest’ quantum absorption refrigerators, supported on ideal three-level masers, are SCIENTIFIC REPORTS | 4 : 3949 | DOI: 10.1038/srep03949 1 www.nature.com/scientificreports limited in their efficiency at maximum power by a fraction of eC, only related to the spectral properties of the environmental fluctuations at low frequencies. We show that this general performance bound applies as well to ‘larger’ and non-ideal designs2,3,8, as it is independent of the details of the working material of the refrigerator. Achieving a good understanding of the quantum-mechanical origin of the limitations of heat pumps can also provide key clues about how to surmount them. We show indeed that, by feeding an absorption fridge with engineered thermal resources, one can push its performance bounds considerably further, allowing for classically impossible superefficient quantum cooling. Namely, at given fixed environmental temperatures, the addition of squeezing to the work bath leads to efficiencies above eC and, most interestingly, to a systematic enhancement of the output harnessed power. This is achieved strictly within the framework of quantum thermodynamics and thus, in no violation of its laws6,23. Results Models of absorption refrigerator. As already advanced, a minimal model of autonomous heat pump13 consists of a three-level system with each of its transitions weakly coupled to one of the three independent heat baths [see Fig. 1(a)]. Essentially, as the steady state builds up, the ‘heat’ collected from the cold bath is dumped into the hot bath with the assistance of the extra energy provided by the work bath, which closes the cooling cycle. Of course, the opposite heating cycle also takes place in the steady-state, and it is the imbalance between these two stationary processes which renders the device either a refrigerator or a heater. As we shall see below, refrigeration occurs as long as the frequency of the transition coupled t (...truncated)