The ability to control and measure electron motion in quantum conductors has incredibly advanced in the last years. Experimentalists have developed single-electron sources, which generate elementary single electron excitations above the Fermi sea of electrons remarkably in an on-demand fashion. The impact of this tool spans across broad subjects such as metrology (redefining the unit of electric current), quantum information (realizing qubits with itinerant electrons), and electron optics (probing the wave nature of electrons).
These outstanding breakthroughs are possible by carefully driving quantum conductors with voltages oscillating in time. Modern high-frequency AC experiments can induce nonadiabatic excitation of electrons which can not be explained by equilibrium properties at each fixed time instance.
In our paper Beating Carnot efficiency with periodically driven chiral conductors [DOI: 10.1038/s41467-022-30039-7], we wonder if such nonequilibrium effect can be used within the context of quantum thermodynamics. More specifically, is it possible to enhance the efficiency of a quantum conductor heat engine with AC voltage driving? The question strongly catches our attention because it is directly related to a hot issue in quantum thermodynamics, namely, how does the quantum and/or nonequilibrium status of thermal machines affect their efficiency?
To answer the question, it is first necessary to clarify the flow of energy, heat and entropy in the quantum regime. Previous studies focused on the adiabatic regime. In our paper, we go beyond the adiabatic regime to explore unforseen consequences of both nonequilibriumness and quantumness.
Motivated by the classic works of Carnot, Kelvin, and Planck, we search for the optimal working protocol of the heat engine. We consider various shapes of the voltage signal. We find that the electric current enchances when the AC voltage induces electron-hole asymmetry, as expected. Such asymmetry appears when the probability of photon absorption differs from that of emission. Now, the heat engine efficiency is determined by the work output divided by the heat input. A crucial point is to realize that most AC voltage sources inject net energy into the engine, thus reducing the developed power more than the increase by the dynamic electron-hole asymmetry. Our key contribution to cancel this detrimental effect relies on chiral conductors.
In condensed matter one can arrange conductors where electrons propagating in opposite directions become spatially separated, such as quantum Hall systems or topological insulators. In such chiral conductors, one can even apply the AC voltage only to those electrons propagating in a given direction, as is the case with Levitons, a type of elementary excitation in single-electron sources built over quantum Hall systems. It is precisely the combination of chiral quantum conductors and selective AC voltage driving that lies behind the surprising enhancement of the thermodynamic efficiency found in our paper. In short, the energy injection from the AC voltage completely vanishes and the engine performance is boosted above the Carnot limit! However, this joyful finding also makes alarm bells ring. In classical thermodynamics, the Carnot bound is intimately related to the second law of thermodynamics and this law should be valid for both classical and quantum regimes. Interestingly, we show that when the entropy is calculated with the Shannon formula the entropy production rate is always nonnegative, in full agreement with the second law.
This exciting journey has also left us with more questions. What is the optimal protocol for a quantum heat engine when the upper bound of the efficiency is no longer universal as found in our paper? Moreover, we only considered the time-averaged power output. How does it fluctuate and how is it connected to thermodynamic uncertainty relations? Finally, how do unique quantum effects such as coherence and entanglement affect the functionality of AC driven chiral engines?