Multistage quantum absorption heat pumps

Collective effects on the performance and stability of quantum heat engines

Recent predictions for quantum-mechanical enhancements in the operation of small heat engines have raised renewed interest in their study both from a fundamental perspective and in view of applications. One essential question is whether collective effects may help to carry enhancements over larger scales, when increasing the number of systems composing the working substance of the engine. Such enhancements may consider not only power and efficiency, that is, its performance, but, additionally, its constancy, that is, the stability of the engine with respect to unavoidable environmental fluctuations. We explore this issue by introducing a many-body quantum heat engine model composed by spin pairs working in continuous operation. We study how power, efficiency, and constancy scale with the number of spins composing the engine and introduce a well-defined macroscopic limit where analytical expressions are obtained. Our results predict power enhancements, in both finite-size and macroscopic cases, for a broad range of system parameters and temperatures, without compromising the engine efficiency, accompanied by coherence-enhanced constancy for finite sizes. We discuss these quantities in connection to thermodynamic uncertainty relations.

Universal bounds on cooling power and cooling efficiency for autonomous absorption refrigerators

For steady-state autonomous absorption refrigerators operating in the linear response regime, we show that there exists a hierarchy between the relative fluctuation of currents for cold, hot, and work terminals. Our proof requires the Onsager reciprocity relation along with the refrigeration condition that sets the direction of the mean currents for each terminal. As a consequence, the universal bounds on the mean cooling power, obtained following the thermodynamic uncertainty relations, follow a hierarchy. Interestingly, within this hierarchy, the tightest bound is given in terms of the work current fluctuation. Furthermore, the relative uncertainty hierarchy introduces a bound on cooling efficiency that is tighter than the bound obtained from the thermodynamic uncertainty relations. Interestingly, all of these bounds saturate in the tight-coupling limit. We test the validity of our results for two paradigmatic absorption refrigerator models: (i) a four-level working fluid and (ii) a two-level working fluid, operating in the weak (additive) and strong (multiplicative) system-bath interaction regimes, respectively.

Three-qubit refrigerator with two-body interactions

We propose a three-qubit setup for the implementation of a variety of quantum thermal machines where all heat fluxes and work production can be controlled. An important configuration that can be designed is that of an absorption refrigerator, extracting heat from the coldest reservoir without the need of external work supply. Remarkably, we achieve this regime by using only two-body interactions instead of the widely employed three-body interactions. This configuration could be more easily realized in current experimental setups. We model the open-system dynamics with both a global and a local master equation thermodynamic-consistent approach. Finally, we show how this model can be employed as a heat valve, in which by varying the local field of one of the two qubits allows one to control and amplify the heat current between the other qubits.

Classical emulation of quantum-coherent thermal machines

The performance enhancements observed in various models of continuous quantum thermal machines have been linked to the buildup of coherences in a preferred basis. But is this connection always an evidence of "quantum-thermodynamic supremacy"? By force of example, we show that this is not the case. In particular, we compare a power-driven three-level continuous quantum refrigerator with a four-level combined cycle, partly driven by power and partly by heat. We focus on the weak driving regime and find the four-level model to be superior since it can operate in parameter regimes in which the three-level model cannot and it may exhibit a larger cooling rate and, simultaneously, a better coefficient of performance. Furthermore, we find that the improvement in the cooling rate matches the increase in the stationary quantum coherences exactly. Crucially, though, we also show that the thermodynamic variables for both models follow from a classical representation based on graph theory. This implies that we can build incoherent stochastic-thermodynamic models with the same steady-state operation or, equivalently, that both coherent refrigerators can be emulated classically. More generally, we prove this for any N-level weakly driven device with a "cyclic" pattern of transitions. Therefore, even if coherence is present in a specific quantum thermal machine, it is often not essential to replicate the underlying energy conversion process.

Quantum self-contained refrigerator in terms of the cavity quantum electrodynamics in the weak internal-coupling regime

We present two schemes to implement the self-contained refrigerator in the framework of the cavity quantum electrodynamics. The considered refrigerators are composed of three interacting microcavities (or two microcavities simultaneously interacting with one three-level atom) separately coupling to a thermal bath with a certain temperature. Despite the local master equation employed, the proposed analytic procedure shows the perfect thermodynamical consistency. It is also demonstrated that the heat is stably extracted from the lowest temperature bath with a fixed efficiency only determined by the intrinsic properties of the refrigerators, i.e., the frequency ratio of the two cavities in contact with the two higher temperature baths. These two schemes indicate that the system with the weak internal coupling in the infinite dimensional Hilbert space can be used to realize the quantum self-contained refrigerator on the principle completely the same as the original self-contained refrigerator.

Quantum coherence, many-body correlations, and non-thermal effects for autonomous thermal machines

One of the principal objectives of quantum thermodynamics is to explore quantum effects and their potential beneficial role in thermodynamic tasks like work extraction or refrigeration. So far, even though several papers have already shown that quantum effect could indeed bring quantum advantages, a global and deeper understanding is still lacking. Here, we extend previous models of autonomous machines to include quantum batteries made of arbitrary systems of discrete spectrum. We establish their actual efficiency, which allows us to derive an efficiency upper bound, called maximal achievable efficiency, shown to be always achievable, in contrast with previous upper bounds based only on the Second Law. Such maximal achievable efficiency can be expressed simply in term of the apparent temperature of the quantum battery. This important result appears to be a powerful tool to understand how quantum features like coherence but also many-body correlations and non-thermal population distribution can be harnessed to increase the efficiency of thermal machines.

Enabling the self-contained refrigerator to work beyond its limits by filtering the reservoirs

In this paper, we study the quantum self-contained refrigerator [Linden et al., Phys. Rev. Lett. 105, 130401 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.130401] in the strong internal coupling regime with engineered reservoirs. We find that if some modes of the three thermal reservoirs can be properly filtered out, the efficiency and the working domain of the refrigerator can be improved in contrast to the those in the weak internal coupling regime, which indicates one advantage of the strong internal coupling. In addition, we find that the background natural vacuum reservoir could cause the filtered refrigerator to stop working and the background natural thermal reservoir could greatly reduce the cooling efficiency.

Performance of autonomous quantum thermal machines: Hilbert space dimension as a thermodynamical resource

Multilevel autonomous quantum thermal machines are discussed. In particular, we explore the relationship between the size of the machine (captured by Hilbert space dimension) and the performance of the machine. Using the concepts of virtual qubits and virtual temperatures, we show that higher dimensional machines can outperform smaller ones. For instance, by considering refrigerators with more levels, lower temperatures can be achieved, as well as higher power. We discuss the optimal design for refrigerators of a given dimension. As a consequence we obtain a statement of the third law in terms of Hilbert space dimension: Reaching absolute zero temperature requires infinite dimension. These results demonstrate that Hilbert space dimension should be considered a thermodynamic resource.

Quantum thermal machine acting on a many-body quantum system: Role of correlations in thermodynamic tasks

We study the functioning of a three-level thermal machine when acting on a many-qubit system, the entire system being placed in an electromagnetic field in a stationary out-of-thermal-equilibrium configuration. This realistic setup stands between the two so-far-explored cases of single-qubit and macroscopic object targets, providing information on the scaling with system size of purely quantum properties in thermodynamic contexts. We show that, thanks to the presence of robust correlations among the qubits induced by the field, thermodynamic tasks can be delivered by the machine both locally to each qubit and collectively to the many-qubit system: This allows a task to be delivered also on systems much bigger than the machine size.

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

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.

Internal dissipation and heat leaks in quantum thermodynamic cycles

The direction of the steady-state heat currents across a generic quantum system connected to multiple baths may be engineered to realize virtually any thermodynamic cycle. In spite of their versatility, such continuous energy-conversion systems are generally unable to operate at maximum efficiency due to non-negligible sources of irreversible entropy production. In this paper we introduce a minimal model of irreversible absorption chiller. We identify and characterize the different mechanisms responsible for its irreversibility, namely heat leaks and internal dissipation, and gauge their relative impact in the overall cooling performance. We also propose reservoir engineering techniques to minimize these detrimental effects. Finally, by looking into a known three-qubit embodiment of the absorption cooling cycle, we illustrate how our simple model may help to pinpoint the different sources of irreversibility naturally arising in more complex practical heat devices.

Small quantum absorption refrigerator with reversed couplings

Small quantum absorption refrigerators have recently attracted renewed attention. Here we present a missing design of a two-qubit fridge, the main feature of which is that one of the two machine qubits is itself maintained at a temperature colder than the cold bath. This is achieved by "reversing" the couplings to the baths compared to previous designs, where only a transition is maintained cold. We characterize the working regime and the efficiency of the fridge. We demonstrate the soundness of the model by deriving and solving a master equation. Finally, we discuss the performance of the fridge, in particular the heat current extracted from the cold bath. We show that our model performs comparably to the standard three-level quantum fridge and thus appears appealing for possible implementations of nanoscale thermal machines.

Four-level refrigerator driven by photons

We propose a quantum absorption refrigerator driven by photons. The model uses a four-level system as its working substance and couples simultaneously to hot, cold, and solar heat reservoirs. Explicit expressions for the cooling power Q̇(c) and coefficient of performance (COP) η(COP) are derived, with the purpose of revealing and optimizing the performance of the device. Our model runs most efficiently under the tight coupling condition, and it is consistent with the third law of thermodynamics in the limit T→0.

Optimal performance of endoreversible quantum refrigerators

The derivation of general performance benchmarks is important in the design of highly optimized heat engines and refrigerators. To obtain them, one may model phenomenologically the leading sources of irreversibility ending up with results that are model independent, but limited in scope. Alternatively, one can take a simple physical system realizing a thermodynamic cycle and assess its optimal operation from a complete microscopic description. We follow this approach in order to derive the coefficient of performance at maximum cooling rate for any endoreversible quantum refrigerator. At striking variance with the universality of the optimal efficiency of heat engines, we find that the cooling performance at maximum power is crucially determined by the details of the specific system-bath interaction mechanism. A closed analytical benchmark is found for endoreversible refrigerators weakly coupled to unstructured bosonic heat baths: an ubiquitous case study in quantum thermodynamics.