Exploring thermodynamics at the quantum level opens up intriguing possibilities, including testing information theory in the quantum regime, the development of quantum fluctuation theorems, and the realization of microscopic quantum heat engines (QHE). In particular, microscopic QHE may operate more efficiently for work extraction than its classical counterpart by exploring the quantum effect. Over the years, enthusiastic interests have been devoted to implementing QHE by controlling l nonequilibrium dynamics in various microscopic systems, such as atomic systems, trapped ions, solid-state spin systems, photonic systems, single-electron transistors, nuclear magnetic resonance, superconducting qubits, among others. As quantum coherence is an intrinsic property for quantum systems, previous studies have intensively investigated the role of quantum coherence by using single particles or few-level quantum systems as the working medium. Recently, some researches show this potential high efficiency, while the other investigations show that quantum coherence effects are generally detrimental to reaching bounds on the maximum efficiency and power of these efficient thermal engines. Hence understanding the advantage of quantumness in QHE qualitatively and quantitatively remains a central issue from both a fundamental and practical perspective of quantum thermodynamics. In this work, we report an experimental demonstration of a quantum heat engine that can truly exhibit quantum advantage. By building a quantum Szilard engine, where quantum correlation exists between the working medium and the thermal bath, we have conclusively identified quantum correlation as a source of quantum advantage for QHE, since the reduced state of its working medium is a Gibbs state that naturally excludes the intrinsic coherence feature. By quantifying the correlation with quantum steering, we clearly show that an optimized steering-type inequality, which is expressed by the average work over different ways of work extraction on the working medium, can distinguish quantum Szilard engines from classical heat engines. The more the quantum steering inequality is violated, the more average work the quantum Szilard engine can output than its classical counterpart.
Following the rising interest in quantum information science, the extension of a heat engine to the quantum regime by exploring microscopic quantum systems has seen a boom of interest in the last decade. Although quantum coherence in the quantum system of the working medium has been investigated to play a nontrivial role, a complete understanding of the intrinsic quantum advantage of quantum heat engines remains elusive. We experimentally demonstrate that the quantum correlation between the working medium and the thermal bath is critical for the quantum advantage of a quantum Szilard engine, where quantum coherence in the working medium is naturally excluded. By quantifying the non-classical correlation through quantum steering, we reveal that the heat engine is quantum when the demon can truly steer the working medium. The average work obtained by taking different ways of work extraction on the working medium can be used to verify the real quantum Szilard engine.
FIG. 1. Conventional and modified Szilard engine. (a) For the conventional Szilard engine, the working medium is a single atom that initially stayed in a thermal equilibrium state. A demon measures which half of the box the atom is in. If the atom is in the right half of the box, a movable shutter is put down in the middle. Then the shutter is hung to a load and extracts work from the atom. (b) For the modified Szilard engine, both the working medium and the bath are resembled by a single spin qubit respectively. Alice (the demon) prepares the initial state of the whole system, performs measurement Mˆi on the bath qubit, and tells Bob the operations Uˆ±i depending on the measurement outcomes ±1. Bob implements the operations Uˆ±i on the working medium qubit to extract work from its internal energy.
FIG. 3. Difference between work extracted from classical and quantum global states. The quantum (classical) global state is a pure entangled state ρ1 (separable state ρ2). The blue (red) data points are the work difference of measurement Mˆ1 = σz (Mˆ2 = σy), with errorbars representing one standard deviation. The solid lines are the theoretical predictions. For the Mˆ1 measurement, work extraction from both the classical and quantum global states are optimal, yielding the same extracted work. While for the Mˆ2 measurement, work extraction from the classical state is no longer optimal, and can extract less work than from the quantum global state.
Conclusions
We have experimentally demonstrated a truly quantum Szilard engine in diamond when the demon can "steer” the working medium where an optimized steering-type inequality that we derived can be violated. Our theoretical and experimental results show that a quantum heat engine which excludes intrinsic coherence feature in working medium, can truly exhibit quantum advantage. We hope our work triggers further studies to generalize our results to the other kind of quantum heat engines. Our work can be naturally extended to the case of the working medium with higher dimensions. In the future, it will be interesting to study these heat engines where the working medium is a higher dimensional system. The investigation of quantifying genuine high dimensional quantum steering can benefit to it. As well, our research can stimulate the bloom of high-dimensional quantum steering.
