Superradiant Quantum Heat Engine

Thermodynamics of a minimal interacting heat engine: Comparison between engine designs

Collective effects stemming from many interacting units have attracted remarkable recent interest, not only for their presence in several systems in nature but also for the possibility of being used for the construction of efficient engine setups. Notwithstanding, little is known about the influence of the engine design, and most studies are restricted to the simplest cases (e.g., simultaneous contact with two thermal baths), not necessarily constituting a realistic setup implementation. In order to investigate the design and its influence on the performance, we introduce the collisional also referred as sequential description for a minimal model for interacting heat engines, composed of two coupled nanomachines placed in contact with a distinct thermal reservoir and subjected to a nonequilibrium work source at each stage. Thermodynamic quantities are exactly obtained irrespective of the model details. Distinct kinds of work sources are investigated and the influence of the interaction, temperature, period, and time asymmetry has been undertaken. Results show that a careful design of interaction provides superior performance than the interactionless case, including optimal power outputs and efficiencies at maximum power greater than known bounds or even the system presenting efficiencies close to the ideal (Carnot) limit. As a complementary analysis, we also show that the case of the system simultaneously placed in contact with two thermal reservoirs constitutes a particular case of our framework.

Energy-Conversion Device Using a Quantum Engine with the Work Medium of Two-Atom Entanglement

Although entanglement is considered as an essential resource for quantum information processing, whether entanglement helps for energy conversion or output in the quantum regime is still lack of experimental witness. Here, we report on an energy-conversion device operating as a quantum engine with the working medium acted by two entangled ions confined in a harmonic potential. The two ions are entangled by virtually coupling to one of the vibrational modes shared by the two ions, and the quantum engine couples to a quantum load, which is another shared vibrational mode. We explore the energy conversion efficiency of the quantum engine and investigate the useful energy (i.e., the maximum extractable work) stored in the quantum load by tuning the two ions in different degrees of entanglement as well as detecting the change of the phonons in the load. Our observation provides, for the first time, quantitative evidence that entanglement fuels the useful energy produced by the quantum engine, but not helpful for the energy conversion efficiency. We consider that our results may be useful to the study of quantum batteries for which one of the most indexes is the maximum extractable energy.

Atom-doped photon engine: Extracting mechanical work from a quantum system via radiation pressure

The possibility of efficiently converting heat into work at the microscale has triggered an intense research effort to understand quantum heat engines, driven by the hope of quantum superiority over classical counterparts. In this work, we introduce a model featuring an atom-doped optical quantum cavity propelling a classical piston through radiation pressure. The model, based on the Jaynes-Cummings Hamiltonian of quantum electrodynamics, demonstrates the generation of mechanical work through thermal energy injection. We establish the equivalence of the piston expansion work with Alicki's work definition, analytically for quasistatic transformations and numerically for finite-time protocols. We further employ the model to construct quantum Otto and Carnot engines, comparing their performance in terms of energetics, work output, efficiency, and power under various conditions. This model thus provides a platform to extract useful work from an open quantum system to generate net motion, and it sheds light on the quantum concepts of work and heat.

Energy transfer in N-component nanosystems enhanced by pulse-driven vibronic many-body entanglement

The processing of energy by transfer and redistribution, plays a key role in the evolution of dynamical systems. At the ultrasmall and ultrafast scale of nanosystems, quantum coherence could in principle also play a role and has been reported in many pulse-driven nanosystems (e.g. quantum dots and even the microscopic Light-Harvesting Complex II (LHC-II) aggregate). Typical theoretical analyses cannot easily be scaled to describe these general N-component nanosystems; they do not treat the pulse dynamically; and they approximate memory effects. Here our aim is to shed light on what new physics might arise beyond these approximations. We adopt a purposely minimal model such that the time-dependence of the pulse is included explicitly in the Hamiltonian. This simple model generates complex dynamics: specifically, pulses of intermediate duration generate highly entangled vibronic (i.e. electronic-vibrational) states that spread multiple excitons - and hence energy - maximally within the system. Subsequent pulses can then act on such entangled states to efficiently channel subsequent energy capture. The underlying pulse-generated vibronic entanglement increases in strength and robustness as N increases.

Universal Scaling Bounds on a Quantum Heat Current

In this Letter, we derive new bounds on a heat current flowing into a quantum L-particle system coupled with a Markovian environment. By assuming that a system Hamiltonian and a system-environment interaction Hamiltonian are extensive in L, we prove that the absolute value of the heat current scales at most as Θ(L^{3}) in a limit of large L. Furthermore, we present an example of noninteracting particles globally coupled with a thermal bath, for which this bound is saturated in terms of scaling. However, the construction of such a system requires many-body interactions induced by the environment, which may be difficult to realize with the existing technology. To consider more feasible cases, we consider a class of the system where any nondiagonal elements of the noise operator (derived from the system-environment interaction Hamiltonian) become zero in the system energy basis, if the energy difference exceeds a certain value ΔE. Then, for ΔE=Θ(L^{0}), we derive another scaling bound Θ(L^{2}) on the absolute value of the heat current, and the so-called superradiance belongs to a class for which this bound is saturated. Our results are useful for evaluating the best achievable performance of quantum-enhanced thermodynamic devices, including far-reaching applications such as quantum heat engines, quantum refrigerators, and quantum batteries.

Enhancement of Quantum Heat Engine by Encircling a Liouvillian Exceptional Point

Quantum heat engines are expected to outperform the classical counterparts due to quantum coherences involved. Here we experimentally execute a single-ion quantum heat engine and demonstrate, for the first time, the dynamics and the enhanced performance of the heat engine originating from the Liouvillian exceptional points (LEPs). In addition to the topological effects related to LEPs, we focus on thermodynamic effects, which can be understood by the Landau-Zener-Stückelberg process under decoherence. We witness a positive net work from the quantum heat engine if the heat engine cycle dynamically encircles a LEP. Further investigation reveals that a larger net work is done when the system is operated closer to the LEP. We attribute the enhanced performance of the quantum heat engine to the Landau-Zener-Stückelberg process, enabled by the eigenenergy landscape in the vicinity of the LEP, and the exceptional point-induced topological transition. Therefore, our results open new possibilities toward LEP-enabled control of quantum heat engines and of thermodynamic processes in open quantum systems.

Quantum Battery Based on Hybrid Field Charging

A quantum battery consisting of an ensemble two-level atom is investigated. The battery is charged simultaneously by a harmonic field and an electrostatic field. The results show that the hybrid charging is superior to the previous case of only harmonic field charging in terms of battery capacity and charging power, regardless of whether the interaction between atoms is considered or not. In addition, the repulsive interaction between atoms will increase the battery capacity and charging power, while the attractive interaction between atoms will reduce the battery capacity and discharge power.

A Schmidt Decomposition Approach to Quantum Thermodynamics

The development of a self-consistent thermodynamic theory of quantum systems is of fundamental importance for modern physics. Still, despite its essential role in quantum science and technology, there is no unifying formalism for characterizing the thermodynamics within general autonomous quantum systems, and many fundamental open questions remain unanswered. Along these lines, most current efforts and approaches restrict the analysis to particular scenarios of approximative descriptions and semi-classical regimes. Here, we propose a novel approach to describe the thermodynamics of arbitrary bipartite autonomous quantum systems based on the well-known Schmidt decomposition. This formalism provides a simple, exact, and symmetrical framework for expressing the energetics between interacting systems, including scenarios beyond the standard description regimes, such as strong coupling. We show that this procedure allows straightforward identification of local effective operators suitable for characterizing the physical local internal energies. We also demonstrate that these quantities naturally satisfy the usual thermodynamic notion of energy additivity.

Impurity reveals distinct operational phases in quantum thermodynamic cycles

We analyze the effect of impurity on the work output and efficiency of quantum Otto and quantum Carnot heat cycles, modeled as a single quantum particle in an infinite square well potential, which is the working substance. We solve this quantum mechanical system perturbatively up to first and second order in strength of the impurity for strong- and weak-coupling regimes, respectively. We derive the analytical expressions of work and efficiency for the strong-coupling regime to the first order in the strength parameter. The threshold value of the strength parameter in weak coupling is obtained up to which the numerical result agrees with the perturbative result for a repulsive and attractive impurity. To our surprise, an embedded impurity unlocks new operational phases in the system, such as a quantum heat engine, quantum refrigerator, and quantum cold pump. In addition, the efficiency of the quantum Otto heat engine is seen to reach Carnot efficiency for some parameter regimes. The cooling power and coefficient of performance of the quantum refrigerator and quantum cold pump are nontrivially affected by the impurity.

Work extraction from single-mode thermal noise by measurements: How important is information?

Our goal in this article is to elucidate the rapport of work and information in the context of a minimal quantum-mechanical setup: a converter of heat input to work output, the input consisting of a single oscillator mode prepared in a hot thermal state along with a few much colder oscillator modes. The core issues we consider, taking account of the quantum nature of the setup, are as follows: (i) How and to what extent can information act as a work resource or, conversely, be redundant for work extraction? (ii) What is the optimal way of extracting work via information acquired by measurements? (iii) What is the bearing of information on the efficiency-power tradeoff achievable in such setups? We compare the efficiency of work extraction and the limitations of power in our minimal setup by different, generic, measurement strategies of the hot and cold modes. For each strategy, the rapport of work and information extraction is found and the cost of information erasure is allowed for. The possibilities of work extraction without information acquisition, via nonselective measurements, are also analyzed. Overall, we present, by generalizing a method based on optimized homodyning that we have recently proposed, the following insight: extraction of work by observation and feedforward that only measures a small fraction of the input is clearly advantageous to the conceivable alternatives. Our results may become the basis of a practical strategy of converting thermal noise to useful work in optical setups, such as coherent amplifiers of thermal light, as well as in their optomechanical and photovoltaic counterparts.

Dynamical control of quantum heat engines using exceptional points

A quantum thermal machine is an open quantum system coupled to hot and cold thermal baths. Thus, its dynamics can be well understood using the concepts and tools from non-Hermitian quantum systems. A hallmark of non-Hermiticity is the existence of exceptional points where the eigenvalues of a non-Hermitian Hamiltonian or a Liouvillian superoperator and their associated eigenvectors coalesce. Here, we report the experimental realization of a single-ion heat engine and demonstrate the effect of Liouvillian exceptional points on the dynamics and the performance of a quantum heat engine. Our experiments have revealed that operating the engine in the exact- and broken-phases, separated by a Liouvillian exceptional point, respectively during the isochoric heating and cooling strokes of an Otto cycle produces more work and output power and achieves higher efficiency than executing the Otto cycle completely in the exact phase where the system has an oscillatory dynamics and higher coherence. This result opens interesting possibilities for the control of quantum heat engines and will be of interest to other research areas that are concerned with the role of coherence and exceptional points in quantum processes and in work extraction by thermal machines.

Quantum-Enhanced Heat Engine Based on Superabsorption

We propose a quantum-enhanced heat engine with entanglement. The key feature of our scheme is superabsorption, which facilitates enhanced energy absorption by entangled qubits. Whereas a conventional engine with N separable qubits provides power with a scaling of P=Θ(N), our engine uses superabsorption to provide power with a quantum scaling of P=Θ(N^{2}). This quantum heat engine also exhibits a scaling advantage over classical ones composed of N-particle Langevin systems. Our work elucidates the quantum properties allowing for the enhancement of performance.

Nonadiabatic coupled-qubit Otto cycle with bidirectional operation and efficiency gains

We study a quantum Otto cycle that uses a 2-qubit working substance whose Hamiltonian does not commute with itself at different times during unitary strokes. We investigate how the cycle responds to the loss of quantum adiabaticity when these strokes are operated with a finite duration. We find that qualitative features such as the possibility of counter-rotating cycles operating as heat engines, or a cycle efficiency that can increase with a decrease in the temperature difference between the baths, are resilient even to highly nonadiabatic strokes. However, cycle efficiency rapidly decreases, although it can still remain above the standard Otto value for small degrees of quantum nonadiabaticity.

Extracting work from random collisions: A model of a quantum heat engine

We study the statistical distribution of the ergotropy and of the efficiency of a single-qubit battery ad of a single-qubit Otto engine, respectively fueled by random collisions. The single qubit, our working fluid, is assumed to exchange energy with two reservoirs: a nonequilibrium "hot" reservoir and a zero-temperature cold reservoir. The interactions between the qubit and the reservoirs are described in terms of a collision model of open system dynamics. The qubit interacts with the nonequilibrium reservoir (a large ensemble of qudits all prepared in the same pure state) via random unitary collisions and with the cold reservoir (a large ensemble of qubits in their ground state) via a partial swap. Due to the random nature of the interaction with the hot reservoir, fluctuations in ergotropy, heat, and work are present, shrinking with the size of the qudits in the hot reservoir. While the mean, "macroscopic" efficiency of the Otto engine is the same as in the case in which the hot reservoir is a thermal one, the distribution of efficiencies does not support finite moments, so that the mean of efficiencies does not coincide with the macroscopic efficiency.

Quantum Heat Engines with Singular Interactions

By harnessing quantum phenomena, quantum devices have the potential to outperform their classical counterparts. Here, we examine using wave function symmetry as a resource to enhance the performance of a quantum Otto engine. Previous work has shown that a bosonic working medium can yield better performance than a fermionic medium. We expand upon this work by incorporating a singular interaction that allows the effective symmetry to be tuned between the bosonic and fermionic limits. In this framework, the particles can be treated as anyons subject to Haldane’s generalized exclusion statistics. Solving the dynamics analytically using the framework of “statistical anyons”, we explore the interplay between interparticle interactions and wave function symmetry on engine performance.

Performance bounds of nonadiabatic quantum harmonic Otto engine and refrigerator under a squeezed thermal reservoir

We analyze the performance of a quantum Otto cycle, employing a time-dependent harmonic oscillator as the working fluid undergoing sudden expansion and compression strokes during the adiabatic stages, coupled to a squeezed reservoir. First, we show that the maximum efficiency that our engine can achieve is 1/2 only, which is in contrast with earlier studies claiming unit efficiency under the effect of a squeezed reservoir. Then, in the high-temperature limit, we obtain analytic expressions for the upper bound on the efficiency as well as on the coefficient of performance of the Otto cycle. The obtained bounds are independent of the parameters of the system and depend on the reservoir parameters only. Additionally, with a hot squeezed thermal bath, we obtain an analytic expression for the efficiency at maximum work which satisfies the derived upper bound. Further, in the presence of squeezing in the cold reservoir, we specify an operational regime for the Otto refrigerator otherwise forbidden in the standard case. Finally, we find the cost of creating a squeezed state from the thermal state and show that in order to harvest the benefits of squeezing, it is sufficient to squeeze only one mode of the reservoir in resonance with the transition frequency of the working fluid. Further, we show that when the cost of squeezing is included in the definition of the operational efficiency of the engine, the advantages of squeezing fade away. Still, being purely quantum mechanical fuel in nature, squeezed reservoirs are beneficial in their own way by providing us with more compact energy storage medium or offering effectively high-temperature baths without being actually too hot.

Quantum Finite-Time Thermodynamics: Insight from a Single Qubit Engine

Incorporating time into thermodynamics allows for addressing the tradeoff between efficiency and power. A qubit engine serves as a toy model in order to study this tradeoff from first principles, based on the quantum theory of open systems. We study the quantum origin of irreversibility, originating from heat transport, quantum friction, and thermalization in the presence of external driving. We construct various finite-time engine cycles that are based on the Otto and Carnot templates. Our analysis highlights the role of coherence and the quantum origin of entropy production.

Performance of quantum heat engines under the influence of long-range interactions

We examine a quantum heat engine with an interacting many-body working medium consisting of the long-range Kitaev chain to explore the role of long-range interactions in the performance of the quantum engine. By analytically studying two types of thermodynamic cycles, namely, the Otto cycle and Stirling cycle, we demonstrate that the work output and efficiency of a long-range interacting heat engine can be boosted by the long-range interactions, in comparison to the short-range counterpart. We further show that in the Otto cycle there exists an optimal condition for which the maximum enhancement in work output and efficiency can be achieved simultaneously by the long-range interactions. But, for the Stirling cycle, the condition which can give the maximum enhancement in work output does not lead to the maximum enhancement in efficiency. We also investigate how the parameter regimes under which the engine performance is enhanced by the long-range interactions evolve with a decrease in the range of interactions.

Quantum Statistical Enhancement of the Collective Performance of Multiple Bosonic Engines

We consider an ensemble of indistinguishable quantum machines and show that quantum statistical effects can give rise to a genuine quantum enhancement of the collective thermodynamic performance. When multiple indistinguishable bosonic work resources are coupled to an external system, the internal energy change of the external system exhibits an enhancement arising from permutation symmetry in the ensemble, which is absent when the latter consists of distinguishable work resources.

Bosons outperform fermions: The thermodynamic advantage of symmetry

We examine a quantum Otto engine with a harmonic working medium consisting of two particles to explore the use of wave function symmetry as an accessible resource. It is shown that the bosonic system displays enhanced performance when compared to two independent single particle engines, while the fermionic system displays reduced performance. To this end, we explore the trade-off between efficiency and power output and the parameter regimes under which the system functions as engine, refrigerator, or heater. Remarkably, the bosonic system operates under a wider parameter space both when operating as an engine and as a refrigerator.

Measurement Induced Synthesis of Coherent Quantum Batteries

Quantum coherence represented by a superposition of energy eigenstates is, together with energy, an important resource for quantum technology and thermodynamics. Energy and quantum coherence however, can be complementary. The increase of energy can reduce quantum coherence and vice versa. Recently, it was realized that steady-state quantum coherence could be autonomously harnessed from a cold environment. We propose a conditional synthesis of N independent two-level systems (TLS) with partial quantum coherence obtained from an environment to one coherent system using a measurement able to increase both energy and coherence simultaneously. The measurement process acts here as a Maxwell demon synthesizing the coherent energy of individual TLS to one large coherent quantum battery. The measurement process described by POVM elements is diagonal in energy representation and, therefore, it does not project on states with quantum coherence at all. We discuss various strategies and their efficiency to reach large coherent energy of the battery. After numerical optimization and proof-of-principle tests, it opens way to feasible repeat-until-success synthesis of coherent quantum batteries from steady-state autonomous coherence.

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.

Algorithmic quantum heat engines

We suggest alternative quantum Otto engines, using heat bath algorithmic cooling with a partner pairing algorithm instead of isochoric cooling and using quantum swap operations instead of quantum adiabatic processes. Liquid state nuclear magnetic resonance systems in a single entropy sink are treated as working fluids. The extractable work and thermal efficiency are analyzed in detail for four-stroke and two-stroke types of alternative quantum Otto engines. The role of the heat bath algorithmic cooling in these cycles is to use a single entropy sink instead of two so that a single incoherent energy resource can be harvested and processed using an algorithmic quantum heat engine. Our results indicate a path to programmable quantum heat engines as analogs of quantum computers beyond traditional heat engine cycles. We find that for our NMR system example implementation of quantum algorithmic heat engine stages yields more power due to increased cycle speeds.

Power and efficiency of a thermal engine with a coherent bath

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.

Non-Thermal Quantum Engine in Transmon Qubits

The design and implementation of quantum technologies necessitates the understanding of thermodynamic processes in the quantum domain. In stark contrast to macroscopic thermodynamics, at the quantum scale processes generically operate far from equilibrium and are governed by fluctuations. Thus, experimental insight and empirical findings are indispensable in developing a comprehensive framework. To this end, we theoretically propose an experimentally realistic quantum engine that uses transmon qubits as working substance. We solve the dynamics analytically and calculate its efficiency.

Nonequilibrium dynamics with finite-time repeated interactions

We study quantum dynamics in the framework of repeated interactions between a system and a stream of identical probes. We present a coarse-grained master equation that captures the system's dynamics in the natural regime where interactions with different probes do not overlap, but it is otherwise valid for arbitrary values of the interaction strength and mean interaction time. We then apply it to some specific examples. For probes prepared in Gibbs states, such channels have been used to describe thermalization: while this is the case for many choices of parameters, for others one finds out-of-equilibrium states including inverted Gibbs and maximally mixed states. Gapless probes can be interpreted as performing an indirect measurement, and we study the energy transfer associated with this measurement.

Autonomous thermal machine for amplification and control of energetic coherence

We present a model for an autonomous quantum thermal machine composed of two qubits capable of manipulating and even amplifying the local coherence in a nondegenerate external system. The machine uses only thermal resources, namely, contact with two heat baths at different temperatures, and the external system has a nonzero initial amount of coherence. The method we propose allows for an interconversion between energy, both work and heat, and coherence in an autonomous configuration working in out-of-equilibrium conditions. This model raises interesting questions about the role of fundamental limitations on transformations involving coherence and opens up new possibilities in the manipulation of coherence by autonomous thermal machines.

Quantum coherence, many-body correlations, and non-thermal effects for autonomous thermal machines

One of the principal objectives of quantum thermodynamics is to explore quantum effects and their potential beneficial role in thermodynamic tasks like work extraction or refrigeration. So far, even though several papers have already shown that quantum effect could indeed bring quantum advantages, a global and deeper understanding is still lacking. Here, we extend previous models of autonomous machines to include quantum batteries made of arbitrary systems of discrete spectrum. We establish their actual efficiency, which allows us to derive an efficiency upper bound, called maximal achievable efficiency, shown to be always achievable, in contrast with previous upper bounds based only on the Second Law. Such maximal achievable efficiency can be expressed simply in term of the apparent temperature of the quantum battery. This important result appears to be a powerful tool to understand how quantum features like coherence but also many-body correlations and non-thermal population distribution can be harnessed to increase the efficiency of thermal machines.

Efficiency of Harmonic Quantum Otto Engines at Maximal Power

Recent experimental breakthroughs produced the first nano heat engines that have the potential to harness quantum resources. An instrumental question is how their performance measures up against the efficiency of classical engines. For single ion engines undergoing quantum Otto cycles it has been found that the efficiency at maximal power is given by the Curzon–Ahlborn efficiency. This is rather remarkable as the Curzon–Alhbron efficiency was originally derived for endoreversible Carnot cycles. Here, we analyze two examples of endoreversible Otto engines within the same conceptual framework as Curzon and Ahlborn’s original treatment. We find that for endoreversible Otto cycles in classical harmonic oscillators the efficiency at maximal power is, indeed, given by the Curzon–Ahlborn efficiency. However, we also find that the efficiency of Otto engines made of quantum harmonic oscillators is significantly larger.

Phase-space interference in extensive and nonextensive quantum heat engines

Quantum interference is at the heart of what sets the quantum and classical worlds apart. We demonstrate that quantum interference effects involving a many-body working medium is responsible for genuinely nonclassical features in the performance of a quantum heat engine. The features with which quantum interference manifests itself in the work output of the engine depends strongly on the extensive nature of the working medium. While identifying the class of work substances that optimize the performance of the engine, our results shed light on the optimal size of such media of quantum workers to maximize the work output and efficiency of quantum energy machines.

High-Power Collective Charging of a Solid-State Quantum Battery

Quantum information theorems state that it is possible to exploit collective quantum resources to greatly enhance the charging power of quantum batteries (QBs) made of many identical elementary units. We here present and solve a model of a QB that can be engineered in solid-state architectures. It consists of N two-level systems coupled to a single photonic mode in a cavity. We contrast this collective model ("Dicke QB"), whereby entanglement is genuinely created by the common photonic mode, to the one in which each two-level system is coupled to its own separate cavity mode ("Rabi QB"). By employing exact diagonalization, we demonstrate the emergence of a quantum advantage in the charging power of Dicke QBs, which scales like sqrt[N] for N≫1.

Quantum engine efficiency bound beyond the second law of thermodynamics

According to the second law, the efficiency of cyclic heat engines is limited by the Carnot bound that is attained by engines that operate between two thermal baths under the reversibility condition whereby the total entropy does not increase. Quantum engines operating between a thermal and a squeezed-thermal bath have been shown to surpass this bound. Yet, their maximum efficiency cannot be determined by the reversibility condition, which may yield an unachievable efficiency bound above unity. Here we identify the fraction of the exchanged energy between a quantum system and a bath that necessarily causes an entropy change and derive an inequality for this change. This inequality reveals an efficiency bound for quantum engines energised by a non-thermal bath. This bound does not imply reversibility, unless the two baths are thermal. It cannot be solely deduced from the laws of thermodynamics.

Evaluating maximum conversion efficiency from heat to work using non-thermal baths can lead to meaningless results, when based only on the reversibility requirement. Here, the authors solve this problem by identifying the fraction of exchanged energy that necessarily causes a change in entropy.

Quantum heat engine with coupled superconducting resonators

We propose a quantum heat engine composed of two superconducting transmission line resonators interacting with each other via an optomechanical-like coupling. One resonator is periodically excited by a thermal pump. The incoherently driven resonator induces coherent oscillations in the other one due to the coupling. A limit cycle, indicating finite power output, emerges in the thermodynamical phase space. The system implements an all-electrical analog of a photonic piston. Instead of mechanical motion, the power output is obtained as a coherent electrical charging in our case. We explore the differences between the quantum and classical descriptions of our system by solving the quantum master equation and classical Langevin equations. Specifically, we calculate the mean number of excitations, second-order coherence, as well as the entropy, temperature, power, and mean energy to reveal the signatures of quantum behavior in the statistical and thermodynamic properties of the system. We find evidence of a quantum enhancement in the power output of the engine at low temperatures.

Catalysis of heat-to-work conversion in quantum machines

We propose a hitherto-unexplored concept in quantum thermodynamics: catalysis of heat-to-work conversion by quantum nonlinear pumping of the piston mode which extracts work from the machine. This concept is analogous to chemical reaction catalysis: Small energy investment by the catalyst (pump) may yield a large increase in heat-to-work conversion. Since it is powered by thermal baths, the catalyzed machine adheres to the Carnot bound, but may strongly enhance its efficiency and power compared with its noncatalyzed counterparts. This enhancement stems from the increased ability of the squeezed piston to store work. Remarkably, the fraction of piston energy that is convertible into work may then approach unity. The present machine and its counterparts powered by squeezed baths share a common feature: Neither is a genuine heat engine. However, a squeezed pump that catalyzes heat-to-work conversion by small investment of work is much more advantageous than a squeezed bath that simply transduces part of the work invested in its squeezing into work performed by the machine.

Measurement-induced operation of two-ion quantum heat machines

We show how one can implement a quantum heat machine by using two interacting trapped ions, in presence of a thermal bath. The electronic states of the ions act like a working substance, while the vibrational mode is modelled as the cold bath. The heat exchange with the cold bath is mimicked by the projective measurement of the electronic states. We show how such measurement in a suitable basis can lead to either a quantum heat engine or a refrigerator, which undergoes a quantum Otto cycle. The local magnetic field is adiabatically changed during the heat cycle. The performance of the heat machine depends upon the interaction strength between the ions, the magnetic fields, and the measurement cost. In our model, the coupling to the hot and the cold baths is never switched off in an alternative fashion during the heat cycle, unlike other existing proposals of quantum heat engines. This makes our proposal experimentally realizable using current tapped-ion technology.

Radiative heat transfer as a Landauer-Büttiker problem

We study the radiative heat transfer between two semi-infinite half-spaces, bounded by conductive surfaces in contact with vacuum. This setup is interpreted as a four-terminal mesoscopic transport problem. The slabs and interfaces are viewed as bosonic reservoirs, coupled perfectly to a scattering center consisting of the two planes and vacuum. Using Rytov's fluctuational electrodynamics and assuming Kirchhoff's circuital law, we calculate the heat flow in each bath. This allows for explicit evaluation of a conductance matrix, from which one readily verifies Büttiker symmetry. Thus, radiative heat transfer in layered media with conductive interfaces becomes a Landauer-Büttiker transport problem.

Speed and efficiency limits of multilevel incoherent heat engines

We present a comprehensive theory of heat engines (HE) based on a quantum-mechanical "working fluid" (WF) with periodically modulated energy levels. The theory is valid for any periodicity of driving Hamiltonians that commute with themselves at all times and do not induce coherence in the WF. Continuous and stroke cycles arise in opposite limits of this theory, which encompasses hitherto unfamiliar cycle forms, dubbed here hybrid cycles. The theory allows us to discover the speed, power, and efficiency limits attainable by incoherently operating multilevel HE depending on the cycle form and the dynamical regimes.

Work extraction and energy storage in the Dicke model

We study work extraction from the Dicke model achieved using simple unitary cyclic transformations keeping into account both a nonoptimal unitary protocol and the energetic cost of creating the initial state. By analyzing the role of entanglement, we find that highly entangled states can be inefficient for energy storage when considering the energetic cost of creating the state. Such a surprising result holds notwithstanding the fact that the criticality of the model at hand can sensibly improve the extraction of work. While showing the advantages of using a many-body system for work extraction, our results demonstrate that entanglement is not necessarily advantageous for energy storage purposes, when nonoptimal processes are considered. Our work shows the importance of better understanding the complex interconnections between nonequilibrium thermodynamics of quantum systems and correlations among their subparts.

Superadiabatic quantum heat engine with a multiferroic working medium

A quantum thermodynamic cycle with a chiral multiferroic working substance such as LiCu_{2}O_{2} is presented. Shortcuts to adiabaticity are employed to achieve an efficient, finite-time quantum thermodynamic cycle, which is found to depend on the spin ordering. The emergent electric polarization associated with the chiral spin order, i.e., the magnetoelectric coupling, renders possible steering of the spin order by an external electric field and hence renders possible an electric-field control of the cycle. Due to the intrinsic coupling between the spin and the electric polarization, the cycle performs an electromagnetic work. We determine this work's mean-square fluctuations, the irreversible work, and the output power of the cycle. We observe that the work mean-square fluctuations are increased with the duration of the adiabatic strokes, while the irreversible work and the output power of the cycle show a nonmonotonic behavior. In particular, the irreversible work vanishes at the end of the quantum adiabatic strokes. This fact confirms that the cycle is reversible. Our theoretical findings evidence the existence of a system inherent maximal output power. By implementing a Lindblad master equation we quantify the role of thermal relaxations on the cycle efficiency. We also discuss the role of entanglement encoded in the noncollinear spin order as a resource to affect the quantum thermodynamic cycle.

Deterministic generation of large scale atomic W states

We present a deterministic scheme for generating large-scale atomic W states in a cavity QED system via a simple expansion mechanism, which is realized only by a detuned interaction between two identical atoms and a vacuum cavity mode. With the presented scheme, a W-type Bell pair can be created and an n-atom W state can be expanded to a 2n-atom W state with a unit probability of success in principle. No multi-atom gates, quantum memories or quantum non-demolition measurements are required, greatly simplifying the experimental realization of the scheme. The feasibility analysis shows that our expansion scheme can be implemented with state-of-the-art technologies. Our scheme enables advances not only in quantum information and communication but also in quantum thermodynamics, where atomic W states plays a crucial role.

Entropy production and thermodynamic power of the squeezed thermal reservoir

We analyze the entropy production and the maximal extractable work from a squeezed thermal reservoir. The nonequilibrium quantum nature of the reservoir induces an entropy transfer with a coherent contribution while modifying its thermal part, allowing work extraction from a single reservoir, as well as great improvements in power and efficiency for quantum heat engines. Introducing a modified quantum Otto cycle, our approach fully characterizes operational regimes forbidden in the standard case, such as refrigeration and work extraction at the same time, accompanied by efficiencies equal to unity.

Thermal electron-tunneling devices as coolers and amplifiers

Nanoscale thermal systems that are associated with a pair of electron reservoirs have been previously studied. In particular, devices that adjust electron tunnels relatively to reservoirs' chemical potentials enjoy the novelty and the potential. Since only two reservoirs and one tunnel exist, however, designers need external aids to complete a cycle, rendering their models non-spontaneous. Here we design thermal conversion devices that are operated among three electron reservoirs connected by energy-filtering tunnels and also referred to as thermal electron-tunneling devices. They are driven by one of electron reservoirs rather than the external power input, and are equivalent to those coupling systems consisting of forward and reverse Carnot cycles with energy selective electron functions. These previously-unreported electronic devices can be used as coolers and thermal amplifiers and may be called as thermal transistors. The electron and energy fluxes of devices are capable of being manipulated in the same or oppsite directions at our disposal. The proposed model can open a new field in the application of nano-devices.

Quantum fuel with multilevel atomic coherence for ultrahigh specific work in a photonic Carnot engine

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.

Performance limits of multilevel and multipartite quantum heat machines

We present the general theory of a quantum heat machine based on an N-level system (working medium) whose N-1 excited levels are degenerate, a prerequisite for steady-state interlevel coherence. Our goal is to find out the extent to which coherence in the working medium is an asset for heat machines. The performance bounds of such a machine are common to (reciprocating) cycles that consist of consecutive strokes and continuous cycles wherein the periodically driven system is constantly coupled to cold and hot heat baths. Intriguingly, we find that the machine's performance strongly depends on the relative orientations of the transition-dipole vectors in the system. Perfectly aligned (parallel) transition dipoles allow for steady-state coherence effects, but also give rise to dark states, which hinder steady-state thermalization and thus reduce the machine's performance. Similar thermodynamic properties hold for N two-level atoms conforming to the Dicke model. We conclude that level degeneracy, but not necessarily coherence, is a thermodynamic resource, equally enhancing the heat currents and the power output of the heat machine. By contrast, the efficiency remains unaltered by this degeneracy and adheres to the Carnot bound.