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arXiv:2301.04323 · Physical Review A

Deriving lower bounds on the efficiency of near-degenerate thermal machines via synchronization

Taufiq Murtadho, Juzar Thingna, Sai Vinjanampathy

Published Jul 17, 2023• 6 citations
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Abstract

We study the relationship between quantum synchronization and the thermodynamic performance of a four-level near-degenerate extension of the Scovil--Schulz-DuBois thermal maser. We show how the existence of interacting coherences can potentially modify the relationship between synchronization and the coherent power output of such a maser. In particular, the cooperation and competition between interacting coherences cause the coherent heat and efficiency to be bounded by the synchronization measure in addition to the well-studied power synchronization bound. Overall, our results highlight the role of quantum synchronization in the working of a thermal machine.

DOI
10.1103/physreva.108.012205

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We study the relationship between quantum synchronization and the thermodynamic performance of a four-level near-degenerate extension of the Scovil--Schulz-DuBois thermal maser. We show how the existence of interacting coherences can potentially modify the relationship between synchronization and the coherent power output of such a maser. In particular, the cooperation and competition between interacting coherences cause the coherent heat and efficiency to be bounded by the synchronization measure in addition to the well-studied power synchronization bound. Overall, our results highlight the role of quantum synchronization in the working of a thermal machine.
Quantum coherence has been demonstrated in various systems including organic solar cells and solid state devices. In this article, we report the lower and upper bounds for the performance of quantum heat engines determined by the efficiency at maximum power. Our prediction based on the canonical three-level Scovil and Schulz-Dubois maser model strongly depends on the ratio of system-bath couplings for the hot and cold baths and recovers the theoretical bounds established previously for the Carnot engine. Further, introducing a fourth level to the maser model can enhance the maximal power and its efficiency, thus demonstrating the importance of quantum coherence in the thermodynamics and operation of the heat engines beyond the classical limit.
Thermodynamics of a three-level maser was studied in the pioneering work of Scovil and Schulz-DuBois [Phys. Rev. Lett. 2, 262 (1959)]. In this work we consider the same three-level model, but treat both the matter and the light quantum mechanically. Specifically, we analyze an extended (three-level) dissipative (ED) Jaynes-Cummings model (JCM) within the framework of a quantum heat engine, using formulas for heat flux and power in bipartite systems introduced in our previous work [E. Boukobza and D. J. Tannor Phys. Rev. A 74, 063823 (2006)] Amplification of the selected cavity mode occurs even in this simple model, as seen by a positive steady state power. However, initial field coherence is lost, as seen by the decaying off-diagonal field density matrix elements, and by the Husimi-Kano QQQ function. We show that after an initial transient time the field's entropy rises linearly during the operation of the engine, which we attribute to the dissipative nature of the evolution and not to matter-field entanglement. We show that the second law of thermodynamics is satisfied in two formulations (Clausius, Carnot) and that the efficiency of the ED JCM heat engine agrees with that defined intuitively by Scovil and Schulz-DuBois. Finally, we compare the steady state heat flux and power of the fully quantum model with the semiclassical counterpart of the ED JCM, and derive the engine efficiency formula of Scovil and Schulz-DuBois analytically from fundamental thermodynamic fluxes.
Synchronization in quantum systems has been largely driven by specific examples of frequency entrainment as well as mutual synchronization. Here we study quantum synchronization as a Liouville space perturbation theory. We begin by clarifying the role of centers, symmetries, and oscillating coherences in the context of quantum synchronization. We then analyze the eigenspectrum of the Liouville superoperator generating the dynamics of the quantum system and determine the conditions under which synchronization arises. We apply our framework to derive a powerful relationship between energy conservation, degeneracies, and synchronization in quantum systems. Finally, we demonstrate our approach by analyzing two mutually coupled thermal machines and prove that nondegenerate thermal networks cannot be simultaneously energy conserving and synchronous.
We consider a quantum engine driven by repeated weak interactions with a heat bath of identical three-level atoms. This model was first introduced by Scully et al. [Science 299, 862 (2003)SCIEAS0036-807510.1126/science.1078955], who showed that coherence between the energy-degenerate ground states serves as a thermodynamic resource that allows operation of a thermal cycle with a coherence-dependent thermalization temperature. We consider a similar engine out of the quasistatic limit and find that the ground-state coherence also determines the rate of thermalization, therefore increasing the output power and the engine efficiency only when the thermalization temperature is reduced; revealing a more nuanced perspective of coherence as a resource. This allows us to optimize the output power by adjusting the coherence and relative stroke durations.
We consider a recently proposed four-level quantum heat engine (QHE) model to analyze the role of quantum coherences in determining the thermodynamic properties of the engine, such as flux, output power, and efficiency. A quantitative analysis of the relative effects of the coherences induced by the two thermal baths is brought out. By taking account of the dissipation in the cavity mode, we define useful work obtained from the QHE and present some analytical results for the optimal values of relative coherences that maximizes flux (hence output power) through the engine. We also analyze the role of quantum effects in inducing population inversion (lasing) between the states coupled to the cavity mode. The universal behavior of the efficiency at maximum power (EMP\mathrm{EMP}EMP) is examined. In accordance with earlier theoretical predictions, to leading order, we find that $\mathrm{EMP}\ensuremath{\sim}{\ensuremath{\eta}}_{c}/2$, where ${\ensuremath{\eta}}_{c}$ is Carnot efficiency. However, the next higher order coefficient is system dependent and hence nonuniversal.
One of the fundamental questions in quantum thermodynamics concerns the decomposition of energetic changes into heat and work. Contrary to classical engines, the entropy change of the piston cannot be neglected in the quantum domain. As a consequence, different concepts of work arise, depending on the desired task and the implied capabilities of the agent using the work generated by the engine. Each work quantifier---from ergotropy to non-equilibrium free energy---has well defined operational interpretations. We analyse these work quantifiers for a heat-pumped three-level maser and derive the respective engine efficiencies. In the classical limit of strong maser intensities the engine efficiency converges towards the Scovil--Schulz-DuBois maser efficiency, irrespective of the work quantifier.