Efficiency at maximum power of a laser quantum heat engine enhanced by noise-induced coherence

Anisotropy-assisted thermodynamic advantage of a local-spin quantum thermal machine

We study quantum Otto thermal machines with a two-spin working system coupled by anisotropic interaction. Depending on the choice of different parameters, the quantum Otto cycle can function as different thermal machines, including a heat engine, refrigerator, accelerator, and heater. We aim to investigate how the anisotropy plays a fundamental role in the performance of the quantum Otto engine (QOE) operating in different timescales. We find that while the engine's efficiency increases with the increase in anisotropy for the quasistatic operation, quantum internal friction and incomplete thermalization degrade the performance in a finite-time cycle. Further, we study the quantum heat engine (QHE) with one of the spins (local spin) as the working system. We show that the efficiency of such an engine can surpass the standard quantum Otto limit, along with maximum power, thanks to the anisotropy. This can be attributed to quantum interference effects. We demonstrate that the enhanced performance of a local-spin QHE originates from the same interference effects, as in a measurement-based QOE for their finite-time operation.

Cooperation and Competition in Synchronous Open Quantum Systems

Synchronization between limit cycle oscillators can arise through entrainment to an external drive or through mutual coupling. The interplay between the two mechanisms has been studied in classical synchronizing systems, but not in quantum systems. Here, we point out that competition and cooperation between the two mechanisms can occur due to phase pulling and phase repulsion in quantum systems. We study their interplay in collectively driven degenerate quantum thermal machines and show that these mechanisms either cooperate or compete depending on the working mode of the machine (refrigerator or engine). The entrainment-mutual synchronization interplay persists with an increase in the number of degenerate levels, while in the thermodynamic limit of degeneracy, mutual synchronization dominates. Overall, our work investigates the effect of degeneracy and multilevel scaling of quantum synchronization and shows how different synchronizing mechanisms can cooperate and compete in quantum systems.

Performance of Quantum Heat Engines Enhanced by Adiabatic Deformation of Trapping Potential

We present a quantum Otto engine model alternatively driven by a hot and a cold heat reservoir and consisting of two isochoric and two adiabatic strokes, where the adiabatic expansion or compression is realized by adiabatically changing the shape of the potential. Here, we show that such an adiabatic deformation may alter operation mode and enhance machine performance by increasing output work and efficiency, even with the advantage of decreasing work fluctuations. If the heat engine in the sudden limit operates under maximal power by optimizing the control parameter, the efficiency shows certain universal behavior, η*=ηC/2+ηC2/8+O(ηC3), where ηC=1-βhr/βcr is the Carnot efficiency, with βhr(βcr) being the inverse temperature of the hot (cold) reservoir. However, such efficiency under maximal power can be produced by our machine model in the regimes where the machine without adiabatic deformation can only operate as a heater or a refrigerator.

Laser Cooling Beyond Rate Equations: Approaches from Quantum Thermodynamics

Solids can be cooled by driving impurity ions with lasers, allowing them to transfer heat from the lattice phonons to the electromagnetic surroundings. This exemplifies a quantum thermal machine, which uses a quantum system as a working medium to transfer heat between reservoirs. We review the derivation of the Bloch-Redfield equation for a quantum system coupled to a reservoir, and its extension, using counting fields, to calculate heat currents. We use the full form of this equation, which makes only the weak-coupling and Markovian approximations, to calculate the cooling power for a simple model of laser cooling. We compare its predictions with two other time-local master equations: the secular approximation to the full Bloch-Redfield equation, and the Lindblad form expected for phonon transitions in the absence of driving. We conclude that the full Bloch-Redfield equation provides accurate results for the heat current in both the weak- and strong- driving regimes, whereas the other forms have more limited applicability. Our results support the use of Bloch-Redfield equations in quantum thermal machines, despite their potential to give unphysical results.

A New Step in the Optimization of the Chambadal Model of the Carnot Engine

This paper presents a new step in the optimization of the Chambadal model of the Carnot engine. It allows a sequential optimization of a model with internal irreversibilities. The optimization is performed successively with respect to various objectives (e.g., energy, efficiency, or power when introducing the duration of the cycle). New complementary results are reported, generalizing those recently published in the literature. In addition, the new concept of entropy production action is proposed. This concept induces new optimums concerning energy and power in the presence of internal irreversibilities inversely proportional to the cycle or transformation durations. This promising approach is related to applications but also to fundamental aspects.

Measurement-based quantum heat engine in a multilevel system

We compare quantum Otto engines based on two different cycle models: a two-bath model, with a standard heat source and sink, and a measurement-based protocol, where the role of heat source is played by a quantum measurement. We furthermore study these cycles using two different "working substances": a single qutrit (spin-1 particle) or a pair of qubits (spin-1/2 particles) interacting via the XXZ Heisenberg interaction. Although both cycle models have the same efficiency when applied on a single-qubit working substance, we find that both can reach higher efficiencies using these more complex working substances by exploiting the existence of "idle" levels, i.e., levels that do not shift while the spins are subjected to a variable magnetic field. Furthermore, with an appropriate choice of measurement, the measurement-based protocol becomes more efficient than the two-bath model.

Heat Modulation on Target Thermal Bath via Coherent Auxiliary Bath

We study a scheme of thermal management where a three-qubit system assisted with a coherent auxiliary bath (CAB) is employed to implement heat management on a target thermal bath (TTB). We consider the CAB/TTB being ensemble of coherent/thermal two-level atoms (TLAs), and within the framework of collision model investigate the characteristics of steady heat current (also called target heat current (THC)) between the system and the TTB. It demonstrates that with the help of the quantum coherence of ancillae the magnitude and direction of heat current can be controlled only by adjusting the coupling strength of system-CAB. Meanwhile, we also show that the influences of quantum coherence of ancillae on the heat current strongly depend on the coupling strength of system—CAB, and the THC becomes positively/negatively correlated with the coherence magnitude of ancillae when the coupling strength below/over some critical value. Besides, the system with the CAB could serve as a multifunctional device integrating the thermal functions of heat amplifier, suppressor, switcher and refrigerator, while with thermal auxiliary bath it can only work as a thermal suppressor. Our work provides a new perspective for the design of multifunctional thermal device utilizing the resource of quantum coherence from the CAB.

Comparative Assessment of Various Low-Dissipation Combined Models for Three-Terminal Heat Pump Systems

Thermally driven heat pump systems play important roles in the utilization of low-grade thermal energy. In order to evaluate and compare the performances of three different constructions of thermally driven heat pump and heat transformer, the low-dissipation assumption has been adopted to establish the irreversible thermodynamic models of them in the present paper. By means of the proposed models, the heating loads, the coefficients of performance (COPs) and the optimal relations between them for various constructions are derived and discussed. The performances of different constructions are numerically assessed. More importantly, according to the results obtained, the upper and lower bounds of the COP at maximum heating load for different constructions are generated and compared by the introduction of a parameter measuring the deviation from the reversible limit of the system. Accordingly, the optimal constructions for the low-dissipation three-terminal heat pump and heat transformer are determined within the frame of low-dissipation assumption, respectively. The optimal constructions in accord with previous research and engineering practices for various three-terminal devices are obtained, which confirms the compatibility between the low-dissipation model and endoreversible model and highlights the validity of the application of low-dissipation model for multi-terminal thermodynamic devices. The proposed models and the significant results obtained enrich the theoretical thermodynamic model of thermally driven heat pump systems and may provide some useful guidelines for the design and operation of realistic thermally driven heat pump systems.

Certifying Quantum Signatures in Thermodynamics and Metrology via Contextuality of Quantum Linear Response

I identify a fundamental difference between classical and quantum dynamics in the linear response regime by showing that the latter is, in general, contextual. This allows me to provide an example of a quantum engine whose favorable power output scaling unavoidably requires nonclassical effects in the form of contextuality. Furthermore, I describe contextual advantages for local metrology. Given the ubiquity of linear response theory, I anticipate that these tools will allow one to certify the nonclassicality of a wide array of quantum phenomena.

Universal two-level quantum Otto machine under a squeezed reservoir

We study an Otto heat machine whose working substance is a single two-level system interacting with a cold thermal reservoir and with a squeezed hot thermal reservoir. By adjusting the squeezing or the adiabaticity parameter (the probability of transition) we show that our two-level system can function as a universal heat machine, either producing net work by consuming heat or consuming work that is used to cool or heat environments. Using our model we study the performance of these machine in the finite-time regime of the isentropic strokes, which is a regime that contributes to make them useful from a practical point of view.

Effect of Finite-Size Heat Source's Heat Capacity on the Efficiency of Heat Engine

Heat engines used to output useful work have important practical significance, which, in general, operate between heat baths of infinite size and constant temperature. In this paper, we study the efficiency of a heat engine operating between two finite-size heat sources with initial temperature difference. The total output work of such heat engine is limited due to the finite heat capacity of the sources. We firstly investigate the effects of different heat capacity characteristics of the sources on the heat engine's efficiency at maximum work (EMW) in the quasi-static limit. Moreover, it is found that the efficiency of the engine operating in finite-time with maximum power of each cycle is achieved follows a simple universality as η=ηC/4+OηC2, where ηC is the Carnot efficiency determined by the initial temperature of the sources. Remarkably, when the heat capacity of the heat source is negative, such as the black holes, we show that the heat engine efficiency during the operation can surpass the Carnot efficiency determined by the initial temperature of the heat sources. It is further argued that the heat engine between two black holes with vanishing initial temperature difference can be driven by the energy fluctuation. The corresponding EMW is proved to be ηMW=2-2.

Steady-State Analysis of Light-Harvesting Energy Transfer Driven by Incoherent Light: From Dimers to Networks

The question of how quantum coherence facilitates energy transfer has been intensively debated in the scientific community. Since natural and artificial light-harvesting units operate under the stationary condition, we address this question via a nonequilibrium steady-state analysis of a molecular dimer irradiated by incoherent sunlight and then generalize the key predictions to arbitrarily complex exciton networks. The central result of the steady-state analysis is the coherence-flux-efficiency relation: η = c∑_i≠jF_ijκ_j = 2c∑_i≠jJ_ijIm[ρ_ij]κ_j, where c is the normalization constant. In this relation, the first equality indicates that the energy transfer efficiency, η, is uniquely determined by the trapping flux, which is the product of the flux, F, and branching ratio, κ, for trapping at the reaction centers, and the second equality indicates that the energy transfer flux, F, is equivalent to the quantum coherence measured by the imaginary part of the off-diagonal density matrix, that is, F_ij = 2J_ijIm[ρ_ij]. Consequently, maximal steady-state coherence gives rise to optimal efficiency. The coherence-flux-efficiency relation holds rigorously and generally for any exciton network of arbitrary connectivity under the stationary condition and is not limited to incoherent radiation or incoherent pumping. For light-harvesting systems under incoherent light, the nonequilibrium energy transfer flux (i.e., steady-state coherence) is driven by the breakdown of detailed balance and by the quantum interference of light excitations and leads to the optimization of energy transfer efficiency. It should be noted that the steady-state coherence or, equivalently, efficiency is the combined result of light-induced transient coherence, inhomogeneous depletion, and the system-bath correlation and is thus not necessarily correlated with quantum beatings. These findings are generally applicable to quantum networks and have implications for quantum optics and devices.

Optimal performance of a three-level quantum refrigerator

We study the optimal performance of a three-level quantum refrigerator using two different objective functions: cooling power and χ function. For both cases, we obtain general expressions for the coefficient of performance (COP) and derive its well-known lower and upper bounds for the limiting cases when the ratio of system-bath coupling constants at the hot and cold contacts approaches infinity and zero, respectively. We also show that the cooling power can be maximized with respect to one control frequency, while χ function can be maximized globally with respect to two control frequencies. Additionally, we show that in the low-temperature regime, our model of refrigerator can be mapped to Feynman's ratchet and pawl model, a classical mesoscopic heat engine. In the parameter regime where both cooling power and χ function can be maximized, we compare the cooling power of the quantum refrigerator at maximum χ function with the maximum cooling power.

Photon Correlation Spectroscopy as a Witness for Quantum Coherence

The development of spectroscopic techniques able to detect and verify quantum coherence is a goal of increasing importance given the rapid progress of new quantum technologies, the advances in the field of quantum thermodynamics, and the emergence of new questions in chemistry and biology regarding the possible relevance of quantum coherence in biochemical processes. Ideally, these tools should be able to detect and verify the presence of quantum coherence in both the transient dynamics and the steady state of driven-dissipative systems, such as light-harvesting complexes driven by thermal photons in natural conditions. This requirement poses a challenge for standard laser spectroscopy methods. Here, we propose photon correlation measurements as a new tool to analyze quantum dynamics in molecular aggregates in driven-dissipative situations. We show that the photon correlation statistics of the light emitted in several models of molecular aggregates can signal the presence of coherent dynamics. Deviations from the counting statistics of independent emitters constitute a direct fingerprint of quantum coherence in the steady state. Furthermore, the analysis of frequency resolved photon correlations can signal the presence of coherent dynamics even in the absence of steady state coherence, providing direct spectroscopic access to the much sought-after site energies in molecular aggregates.

Collective performance of a finite-time quantum Otto cycle

We study the finite-time effects in a quantum Otto cycle where a collective spin system is used as the working fluid. Starting from a simple one-qubit system we analyze the transition to the limit cycle in the case of a finite-time thermalization. If the system consists of a large sample of independent qubits interacting coherently with the heat bath, then the super-radiant equilibration is observed. We show that this phenomenon can boost the power of the engine. Mutual interaction of qubits in the working fluid is modeled by the Lipkin-Meshkov-Glick Hamiltonian. We demonstrate that in this case the quantum phase transitions for the ground and excited states may have a strong negative effect on the performance of the machine. Conversely, by analyzing the work output we can distinguish between the operational regimes with and without a phase transition.

Three-level laser heat engine at optimal performance with ecological function

Although classical and quantum heat engines work on entirely different fundamental principles, there is an underlying similarity. For instance, the form of efficiency at optimal performance may be similar for both types of engines. In this work, we study a three-level laser quantum heat engine operating at maximum ecological function (EF) which represents a compromise between the power output and the loss of power due to entropy production. We present numerical as well as analytic results for the global and local optimization of our laser engine in different operational regimes. Particularly, we observe that in low-temperature regimes, the three-level laser heat engine can be mapped to Feynman's ratchet and pawl model, a steady-state classical heat engine. Then we derive analytic expressions for efficiency under the assumptions of strong matter-field coupling and high bath temperatures. Upper and lower bounds on the efficiency exist in case of extreme asymmetric dissipation when the ratio of system-bath coupling constants at the hot and the cold contacts respectively approaches zero or infinity. These bounds have been established previously for various classical models of Carnot-like engines. Further, for weak (or intermediate) matter-field coupling in the high-temperature limit, we derive some new bounds on the efficiency of the engine. We conclude that while the engine produces at least 75% of the power output as compared with the maximum power conditions, the fractional loss of power is appreciably low in case of the engine operating at maximum EF, thus making this objective function relevant from an environmental point of view.

Classical emulation of quantum-coherent thermal machines

The performance enhancements observed in various models of continuous quantum thermal machines have been linked to the buildup of coherences in a preferred basis. But is this connection always an evidence of "quantum-thermodynamic supremacy"? By force of example, we show that this is not the case. In particular, we compare a power-driven three-level continuous quantum refrigerator with a four-level combined cycle, partly driven by power and partly by heat. We focus on the weak driving regime and find the four-level model to be superior since it can operate in parameter regimes in which the three-level model cannot and it may exhibit a larger cooling rate and, simultaneously, a better coefficient of performance. Furthermore, we find that the improvement in the cooling rate matches the increase in the stationary quantum coherences exactly. Crucially, though, we also show that the thermodynamic variables for both models follow from a classical representation based on graph theory. This implies that we can build incoherent stochastic-thermodynamic models with the same steady-state operation or, equivalently, that both coherent refrigerators can be emulated classically. More generally, we prove this for any N-level weakly driven device with a "cyclic" pattern of transitions. Therefore, even if coherence is present in a specific quantum thermal machine, it is often not essential to replicate the underlying energy conversion process.

Thermal rectification and heat amplification in a nonequilibrium V-type three-level system

Thermal rectification and heat amplification are investigated in a nonequilibrium V-type three-level system with quantum interference. By applying the Redfield master equation combined with full counting statistics, we analyze the steady-state heat transport. The noise-induced interference is found to be able to rectify the heat current, which paves a new way to design quantum thermal rectifier. Within the three-reservoir setup, the heat amplification is clearly identified far from equilibrium, which is in absence of the negative differential thermal conductance.

Spin quantum heat engines with shortcuts to adiabaticity

We consider a finite-time quantum Otto cycle with single- and two spin-1/2 systems as its working medium. To mimic adiabatic dynamics at a finite time, we employ a shortcut-to-adiabaticity technique and evaluate the performance of the engine including the cost of the shortcut. We compare our results with the true adiabatic and nonadiabatic performances of the same cycle. Our findings indicate that the use of the shortcut-to-adiabaticity scheme significantly enhances the performance of the quantum Otto engine as compared to its adiabatic and nonadiabatic counterparts for different figures of merit.

Two-level masers as heat-to-work converters

We propose a paradigm of heat-powered maser. In contrast to textbook knowledge, it does not require population inversion or coherent driving and hence can operate with a two-level working medium. Therefore, it is a conceptually different type of maser and, more generally, a conceptually different quantum heat machine. Its autonomous character and “free” power source make this machine technologically enticing.

Heat engines, which cyclically transform heat into work, are ubiquitous in technology. Lasers and masers may be viewed as heat engines that rely on population inversion or coherence in the active medium. Here we put forward an unconventional paradigm of a remarkably simple and robust electromagnetic heat-powered engine that bears basic differences to any known maser or laser: The proposed device makes use of only one Raman transition and does not rely on population inversion or coherence in its two-level working medium. Nor does it require any coherent driving. The engine can be powered by the ambient temperature difference between the sky and the ground surface. Its autonomous character and “free” power source make this engine conceptually and technologically enticing.

Coherence and decoherence in quantum absorption refrigerators

Absorption refrigerators transfer thermal energy from a cold reservoir to a hot reservoir using input energy from a third, so-called work reservoir. We examine the operation of quantum absorption refrigerators when coherences between eigenstates survive in the steady state limit. In our model, the working medium comprises a discrete, four-level system. Several studies on related setups have demonstrated the performance-enhancing potential of steady-state eigenbasis quantum coherences. By contrast, in our model such coherences generally quench the cooling current in the refrigerator, while minimally affecting the coefficient of performance (cooling efficiency). We rationalize the behavior of the four-level refrigerator by studying three-level model systems for energy transport and refrigeration. Our calculations further illuminate the shortcomings of secular quantum master equations and the necessity of employing dynamical equations of motion that retain couplings between population and coherences.