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arXiv:1611.01475 · Europhysics Letters (EPL)

A photonic Carnot engine powered by a spin-star network

Deniz Türkpençe, Ferdi Altintas, Mauro Paternostro, Özgür Esat Müstecaplıoğlu

Published Mar 1, 2017• 58 citations
arXivHTMLPDF

Abstract

We propose a spin-star network, where a central spin-(1/2), acting as a quantum fuel, is coupled to N outer spin-(1/2) particles. If the network is in thermal equilibrium with a heat bath, the central spin can have an effective temperature, higher than that of the bath, scaling nonlinearly with N . Such temperature can be tuned with the anisotropy parameter of the coupling. Using a beam of such central spins to pump a micromaser cavity, we determine the dynamics of the cavity field using a coarse-grained master equation. We find that the central-spin beam effectively acts as a hot reservoir to the cavity field and brings it to a thermal steady state whose temperature benefits from the same nonlinear enhancement with N and results in a highly efficient photonic Carnot engine. The validity of our conclusions is tested against the presence of atomic and cavity damping using a microscopic master equation method for typical microwave cavity-QED parameters. The role played by quantum coherence and correlations on the scaling effect is pointed out. An alternative scheme where the spin-(1/2) is coupled to a macroscopic spin- particle is also discussed.

DOI
10.1209/0295-5075/117/50002

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We propose a spin-star network, where a central spin-(1/2), acting as a quantum fuel, is coupled to N outer spin-(1/2) particles. If the network is in thermal equilibrium with a heat bath, the central spin can have an effective temperature, higher than that of the bath, scaling nonlinearly with N . Such temperature can be tuned with the anisotropy parameter of the coupling. Using a beam of such central spins to pump a micromaser cavity, we determine the dynamics of the cavity field using a coarse-grained master equation. We find that the central-spin beam effectively acts as a hot reservoir to the cavity field and brings it to a thermal steady state whose temperature benefits from the same nonlinear enhancement with N and results in a highly efficient photonic Carnot engine. The validity of our conclusions is tested against the presence of atomic and cavity damping using a microscopic master equation method for typical microwave cavity-QED parameters. The role played by quantum coherence and correlations on the scaling effect is pointed out. An alternative scheme where the spin-(1/2) is coupled to a macroscopic spin- particle is also discussed.
We investigate scaling of work and efficiency of a photonic Carnot engine with a number of quantum coherent resources. Specifically, we consider a generalization of the "phaseonium fuel" for the photonic Carnot engine, which was first introduced as a three-level atom with two lower states in a quantum coherent superposition by M. O. Scully, M. Suhail Zubairy, G. S. Agarwal, and H. Walther [Science 299, 862 (2003)SCIEAS0036-807510.1126/science.1078955], to the case of N+1 level atoms with N coherent lower levels. We take into account atomic relaxation and dephasing as well as the cavity loss and derive a coarse-grained master equation to evaluate the work and efficiency analytically. Analytical results are verified by microscopic numerical examination of the thermalization dynamics. We find that efficiency and work scale quadratically with the number of quantum coherent levels. Quantum coherence boost to the specific energy (work output per unit mass of the resource) is a profound fundamental difference of quantum fuel from classical resources. We consider typical modern resonator set ups and conclude that multilevel phaseonium fuel can be utilized to overcome the decoherence in available systems. Preparation of the atomic coherences and the associated cost of coherence are analyzed and the engine operation within the bounds of the second law is verified. Our results bring the photonic Carnot engines much closer to the capabilities of current resonator technologies.
We investigate the finite-time performance of a quantum endoreversible Carnot engine cycle and its inverse operation — Carnot refrigeration cycle, employing a spin-1/2 system as the working substance. The thermal machine is alternatively driven by a hot boson bath of inverse temperature β h and a cold boson bath at inverse temperature β c (>β h). While for the engine model the hot bath is constructed to be squeezed, in the refrigeration cycle the cold bath is established to be squeezed, with squeezing parameter r. We obtain the analytical expressions for both efficiency and power in heat engines and for coefficient of performance and cooling rate in refrigerators. We find that, in the high-temperature limit, the efficiency at maximum power is bounded by the analytical value η + = 1 − sech ( 2 r ) ( 1 − η C ) , and the coefficient of performance at the maximum figure of merit is limited by ε + = sech ( 2 r ) ( 1 + ε C ) sech ( 2 r ) ( 1 + ε C ) − ε C − 1 , where η C = 1 – β h/β c and ε C = β h/(β c – β h) are the respective Carnot values of the engines and refrigerators. These analytical results are identical to those obtained from the Carnot engines based on harmonic systems, indicating that the efficiency at maximum power and coefficient at maximum figure of merit are independent of the working substance.
The single-atom version of the quantum heat engine based on electromagnetically induced transparency is theoretically investigated in this paper. In contact with a hot and a cold bath, the atom trapped in an optical cavity is coherently coupled by a coherent field, thus generating photons as output through a process that mimics a heat engine. Using semiclassical theory, we obtain the conditions for the classical gain parameter being positive. Then by taking a full quantum approach, we discuss the statistical property of the generated photons depicted by the photon number distribution and Wigner function, and show that it can be effectively tuned by the coupling field. Investigations on the energy and entropy balances of the heat engine process lead to an interesting result that the power of the engine is simply the energy per time provided by the hot reservoir. The coupling field plays a critical role in supporting the heat-engine process. However, the energy that it provides is all dumped into the cold reservoir. The total energy exchange conforms to the first law of thermodynamics. The efficiency of the engine depends on the temperatures of the two reservoirs and the strength of the coupling field. The entropy change of the heat-engine process suggests that when working far above the threshold of lasing, the efficiency approaches that of its atomic-ensemble-based partner.
We theoretically propose and investigate a quantum Otto engine that works with a single-mode radiation field inside an optical cavity and is driven alternately by a hot reservoir and a cold reservoir. The hot reservoir is realized using a beam composed of thermally entangled pairs of two-level atoms that interacts resonantly with the cavity, and the cold reservoir is composed of a collection of noninteracting boson modes. In terms of the quantum discord of the pair of atoms, we derive analytical expressions for the performance parameters (i.e., power and efficiency) and the stability measure (the coefficient of variation of power). We show that nonclassical correlations boost the quantum engine's performance and efficiency, and they may even change the operation mode at specified values of the two bath temperatures. We also demonstrate that the nonclassical correlations improve the stability of the machine by reducing the coefficient of variation of power that satisfies the generalized thermodynamic uncertainty relation. Finally, we find that these results can be transferred to another quantum Otto engine model, in which the optical cavity is coupled alternately to a hot thermal bosonic bath and to a beam composed of pairs of the two correlated atoms that plays the role of a cold reservoir.
Enhancing the efficiency of quantum heat engines (QHEs) is crucial for advancing fundamental research and quantum technology.We here we explore a quantum Stirling cycle using a twoqubit quantum Rabi model with spin-spin coupling as a working medium. We propose parameter optimization strategies to maximize the efficiency of the heat engine, as there are multiple ways for the effective coupling constant to move toward its critical value. In the normal phase of the system, the efficiency can be improved by increasing the temperature ratio of hot-to-cold reservoirs and enhancing spin-mode coupling strength. However, increasing spin-spin coupling strength inhibits the improvement of the efficiency. As the system goes to its critical point, QHE efficiency under low-temperature conditions tends to the Carnot limit. In the superradiant phase, the efficiency approaches the Carnot limit more closely as the cold reservoir's temperature decreases given a constant temperature ratio. Conversely, when the cold reservoir's temperature rises, the efficiency increases due to a higher ratio of spin-mode coupling strength to mode frequency. If the spinspin coupling strength is constant, increasing the hot-to-cold reservoir temperature ratio requires a corresponding increase in spin-mode coupling strength to achieve the Carnot efficiency. Our work deepens the understanding of QHE performance under various conditions and provides operative methods for optimizing the efficiency of QHE.