Experimental Demonstration of Quantum Effects in the Operation of Microscopic Heat Engines

Abstract

The heat engine, a machine that extracts useful work from thermal sources, is one of the basic theoretical constructs and fundamental applications of classical thermodynamics. The classical description of a heat engine does not include coherence in its microscopic degrees of freedom. By contrast, a quantum heat engine might possess coherence between its internal states. Although the Carnot efficiency cannot be surpassed 1-3 , and coherence can be performance degrading in certain conditions 4-9 , it was recently predicted that even when using only thermal resources, internal coherence can enable a quantum heat engine to produce more power than any classical heat engine using the same resources 10,11 . Such a power boost therefore constitutes a quantum thermodynamic signature. It has also been shown that the presence of coherence results in the thermodynamic equivalence of different quantum heat engine types 10,12 , an effect with no classical counterpart. Microscopic heat machines have been recently implemented with trapped ions 13,14 , and proposals for heat machines using superconducting circuits 15,16 and optomechanics 17,18 have been made. When operated with standard thermal baths, however, the machines implemented so far have not demonstrated any inherently quantum feature in their thermodynamic quantities. Here we implement two types of quantum heat engines by use of an ensemble of nitrogen-vacancy centres in diamond, and experimentally demonstrate both the coherence power boost and the equivalence of different heat-engine types. This constitutes the first observation of quantum thermodynamic signatures in heat machines. 2A quantum heat engine consists of a microscopic system, or an ensemble of such systems, whose internal state can be a coherent superposition of energy states. The engine cycle consists of a sequence of operations (strokes), which include the interaction of the system (or part thereof) either with a thermal bath (cold or hot), or with an external classical/semi-classical field responsible for work extraction. Interactions with the thermal baths act to change the populations of the energy states of the heat engine incoherently, in contrast to the field, which changes the populations coherently. Fig. 1 schematically presents three basic quantum heat-engine types: continuous, two-stroke and four-stroke, which differ by the ordering of the different strokes. Of these types, the four-stroke engine bears the strongest resemblance to macroscopic classical engines such as the Otto engine. It can be described (classically) by a two level system undergoing a four part cycle, illustrated in the top panel of Fig. 1a, consisting of alternating couplings to the hot and cold baths, interspersed with couplings to the work reservoir, whose effect is to change the spacing between the levels. It can be shown that this dynamics is equivalent to classical swap operations in a multilevel system 10 (multilevel embedding), as shown in the middle panel of Fig. 1a (taking U = swap). In a quantum heat engine, the oper...

Quantum signatures in the quantum Carnot cycle

“…Conversely, for short cycle-times the engine operation requires coherence and the strong dephasing nulls the power output ( <  0). Similar behaviour has been observed in the sudden Otto cycle and the two-stroke NV engines [27,44,62].…”

“…Global coherence enables engine operation at short cycle-times, where the Endo-Shortcut and Carnot-Shorcut become dissipators. This indicates a quantum signature [44]. In the presence of pure-dephasing, the coherence vanishes, reducing power and efficiency.…”

“…Moreover, for very short cycle-times global coherence becomes crucial to obtain non-vanishing power. This phenomena is a quantum signature [43][44][45], which can be unraveled from thermodynamics observables. We consider a thermodynamic quantum signature as a measurable thermodynamic quantity, such as work or efficiency, which indicates a unique quantum behaviour.…”

Quantum magnetometry using two-stroke thermal machines

“…These systems can be extremely well controlled experimentally [70,71] and have been used in recent experimental implementations of quantum heat engines [3,72]. An alternative route may be spin systems based on nuclear-magnetic resonances or nitrogen-vacancy setups as in the QHE experiments from [73,74]. For future work we envisage to adapt our protocol to autonomous quantum heat engines that do not require external control.…”

Coherence and catalysis in the Jaynes–Cummings model

“…The phase of the superposition is determined by the phase of the coherent state of the cavity mode. Such interactions are of central importance in quantum information [36,37] and also in quantum thermodynamics, as it is these which may be used to extract maximal work from coherence [29,38,39,19,40,41]. We evaluate how the fidelity of the final state changes with subsequent interactions, and analyse the results in the light of [29].…”