We introduce a new quantum heat engine, in which the working medium is a quantum system with a discrete level and a continuum. Net work done by this engine is calculated and discussed. The results show that this quantum heat engine behaves like the two-level quantum heat engine in both the high-temperature and the low-temperature limits, but it operates differently in temperatures between them. The efficiency of this quantum heat engine is also presented and discussed.
We consider measurement based single temperature quantum heat engine without feedback control, introduced recently by Yi, Talkner and Kim [Phys. Rev. E 96, 022108 (2017)]. Taking the working medium of the engine to be a one-dimensional Heisenberg model of two spins, we calculate the efficiency of the engine undergoing a cyclic process. Starting with two spin-1/2 particles, we investigate the scenario of higher spins also. We show that, for this model of coupled working medium, efficiency can be higher than that of an uncoupled one. However, the relationship between the coupling constant and th…
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, w…
We study a quantum Otto engine at finite time, where the working substance is composed of a two-level system interacting with a harmonic oscillator, described by the quantum Rabi model. We obtain the limit cycle and calculate the total work extracted, efficiency, and power of the engine by numerically solving the master equation describing the open system dynamics. We relate the total work extracted and the efficiency at maximum power with the quantum correlations embedded in the working substance, which we consider through entanglement of formation and quantum discord. Interestingly, we find …
The minimal-coupling quantum heat engine is a thermal machine consisting of an explicit energy storage system, heat baths, and a working body, which alternatively couples to subsystems through discrete strokes -- energy-conserving two-body quantum operations. Within this paradigm, we present a general framework of quantum thermodynamics, where a work extraction process is fundamentally limited by a flow of non-passive energy (ergotropy), while energy dissipation is expressed through a flow of passive energy. It turns out that small dimensionality of the working body and a restriction only to t…
We consider a semi-classical heat engine with a $q$-deformed quantum oscillator working substance and classical thermal baths. We investigate the influence of the quantum statistical deformation parameter $q$ on the work and efficiency of the engine. In usual heat engines, a Hamiltonian parameter is varied during the work injection and extraction stages while the quantum statistical character of the working substance remains fixed. We point out that even if the Hamiltonian parameters are not changing, work can be harvested by quantum statistical changes of the working substance. Work extractio…
We study a quantum Otto engine operating on the basis of a helical spin- 1/2 multiferroic chain with strongly coupled magnetic and ferroelectric order parameters. The presence of a finite spin chirality in the working substance enables steering of the cycle by an external electric field that couples to the electric polarization. We observe a direct connection between the chirality, the entanglement and the efficiency of the engine. An electric-field dependent threshold temperature is identified above which the pair correlations in the system, as quantified by the thermal entanglement, diminish…
Established heat engines in quantum regime can be modeled with various quantum systems as working substances. For example, in the non-relativistic case, we can model the heat engine using infinite potential well as a working substance to evaluate the efficiency and work done of the engine. Here, we propose quantum heat engine with a relativistic particle confined in the one-dimensional potential well as working substance. The cycle comprises of two isothermal processes and two potential well processes of equal width, which forms the quantum counterpart of the known isochoric process in classic…
The working substance fueling a quantum heat engine may contain coherence in its energy basis, depending on the dynamics of the engine cycle. In some models of quantum Otto heat engines, energy coherence has been associated with entropy production and quantum friction. We considered a quantum Otto heat engine operating at finite time. Coherence is generated and the working substance does not reach thermal equilibrium after interacting with the hot heat reservoir, leaving the working substance in a state with residual energy coherence. We observe an interference-like effect between the residual…
Recently, Zhang {\em et al.} [PRA, {\bf 75}, 062102 (2007)] extended Kieu's interesting work on the quantum Otto engine [PRL, {\bf 93}, 140403 (2004)] by considering as working substance a bipartite quantum system $AB$ composed of subsystems $A$ and $B$. In this paper, we express the net work done $W_{AB}$ by such an engine explicitly in terms of the macroscopic bath temperatures and information theoretic quantities associated with the microscopic quantum states of the working substance. This allows us to gain insights into the dependence of positive $W_{AB}$ on the quantum properties of the s…
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 w…
We present the exact theory of quantum engines whose working medium is a network of driven oscillators performing an arbitrary cyclic process while coupled to thermal and nonthermal reservoirs. We show that when coupled to a single reservoir work cannot be extracted unless there is population inversion, and prove that the ratio between the heat flowing out and into the working medium cannot be arbitrarily small, satisfying a form of Clausius inequality. We use such identity to prove that the efficiency of linear quantum engines satisfies a generalized bound, which coincides with the Carnot lim…
We study a quantum Otto engine embedding a working substance composed by a two-level system interacting with a harmonic mode. The physical properties of the substance are described by a generalized quantum Rabi model arising in superconducting circuits realizations. We show that light-matter quantum correlations reduction during the hot bath stage and compression stage act as a resource for enhanced work extraction and efficiency respectively. Also, we demonstrate that the anharmonic spectrum of the working subtance has a direct impact on the transition from heat engine into refrigerator as th…
Quantum cycles in established heat engines can be modeled with various quantum systems as working substances. For example, a heat engine can be modeled with an infinite potential well as the working substance to determine the efficiency and work done. However, in this method, the relationship between the quantum observables and the physically measurable parameters i.e., the efficiency and work done is not well understood from the quantum mechanics approach. A detailed analysis is needed to link the thermodynamic variables (on which the efficiency and work done depends) with the uncertainty pri…
A quantum thermodynamic cycle with a chiral multiferroic working substance such as $\textrm{LiCu}_{2}\textrm{O}_{2}$ 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 of the spin and the electric p…
Quantum thermal machines make use of non-classical thermodynamic resources, one of which is interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been earlier shown that the said interaction provides an enhancement of cycle efficiency for two spin-1/2 particles, with an upper bound which is tighter than the Carnot efficiency. However, the necessary conditions g…
Quantum heat engines (QHE) are thermal machines where the working substance is quantum. In the extreme case the working medium can be a single particle or a few level quantum system. The study of QHE has shown a remarkable similarity with the standard thermodynamical models, thus raising the issue what is quantum in quantum thermodynamics. Our main result is thermodynamical equivalence of all engine type in the quantum regime of small action. They have the same power, the same heat, the same efficiency, and they even have the same relaxation rates and relaxation modes. Furthermore, it is shown…
We investigate the quantum thermodynamic cycle of a quantum heat engine carrying out an Otto thermodynamic cycle. We use the thermal properties of a moving heat bath with relativistic velocity with respect to the cold bath. As a working medium, we use a two-level system and a harmonic oscillator that interact with a moving heat bath and a static cold bath. In the current work, the quantum heat engine is studied in the high and low temperatures regime. Using quantum thermodynamics and the theory of open quantum system we obtain the total produced work, the efficiency and the efficiency at maxim…
A quantum model of a heat engine resembling the Otto cycle is employed to explore strategies to suppress frictional losses. These losses are caused by the inability of the engine's working medium to follow adiabatically the change in the Hamiltonian during the expansion and compression stages. By adding external noise to the engine, frictional losses can be suppressed.
A quantum-mechanical analog of the Carnot engine reversibly working at vanishing temperature, shortly termed the quantum-mechanical Carnot engine, is discussed. A general formula for the efficiency of such an engine with an arbitrary confining potential is presented. Its expression is purely given in terms of the structure of the energy spectrum. Dependency of the efficiency on the form of a potential as an analog of the working material in thermodynamics implies nonuniversality of the engine. This may be due to the absence of the second-law-like principle in pure-state quantum mechanics.
In finite-time quantum heat engines, some work is consumed to drive a working fluid accompanying coherence, which is called `friction'. To understand the role of friction in quantum thermodynamics, we present a couple of finite-time quantum Otto cycles with two different baths: Agarwal versus Lindbladian. We solve them exactly and compare the performance of the Agarwal engine with that of the Lindbladian engine. In particular, we find remarkable and counterintuitive results that the performance of the Agarwal engine due to friction can be much higher than that in the quasistatic limit with the…
We propose a system made of three quantum harmonic oscillators as a compact quantum engine for producing mechanical work. The three oscillators play respectively the role of the hot bath, the working medium and the cold bath. The working medium performs an Otto cycle during which its frequency is changed and it is sequentially coupled to each of the two other oscillators. As the two environments are finite, the lifetime of the machine is finite and after a number of cycles it stops working and needs to be reset. We analyse the entanglement and quantum discord generated during the strokes and s…
We introduce quantum heat engines that perform quantum Otto cycle and the quantum Stirling cycle by using a coupled pair of harmonic oscillator as its working substance. In the quantum regime, different working medium is considered for the analysis of the engine models to boost the efficiency of the cycles. In this work, we present Otto and Stirling cycle in the quantum realm where the phase space is non-commutative in nature. By using the notion of quantum thermodynamics we develop the thermodynamic variables in non-commutative phase space. We encounter a catalytic effect (boost) on the effic…
Quantum many-body systems out of equilibrium can host intriguing phenomena such as transitions to exotic dynamical states. Although this emergent behaviour can be observed in experiments, its potential for technological applications is largely unexplored. Here, we investigate the impact of collective effects on quantum engines that extract mechanical work from a many-body system. Using an opto-mechanical cavity setup with an interacting atomic gas as a working fluid, we demonstrate theoretically that such engines produce work under periodic driving. The stationary cycle of the working fluid fe…
Quantum heat cycles and quantum refrigerators are analyzed using various quantum systems as their working mediums. For example, to evaluate the efficiency and the work done of the Carnot cycle in the quantum regime, one can consider the harmonic oscillator as it's working medium. For all these well-defined working substances (which are analyzed in commutative space structure), the efficiency of the engine is not up to the mark of the Carnot efficiency. So, one inevitable question arise, can one observe a catalytic effect on the efficiency of the engines and refrigerators when the space structu…
We propose a multilevel quantum heat engine with a working medium described by a generalized Rabi model which consists of a two-level system coupled to a single mode bosonic field. The model is constructed to be a continuum limit of a quantum biological description of light harvesting complexes so that it can amplify quantum coherence by a mechanism which is a quantum analog of classical Huygen's clocks. The engine operates in quantum Otto cycle where the working medium is coupled to classical heat baths in the isochoric processes of the four stroke cycle; while either the coupling strength or…
We propose a quantum Otto cycle in a two spin-$1/2$ anisotropic XY model in a transverse external magnetic field. We first characterize the parameter regime that the working medium operates as an engine in the adiabatic regime. Then, we consider finite-time behavior of the engine with and without utilizing a shortcut to adiabaticity (STA) technique. STA schemes guarantee that the dynamics of a system follows the adiabatic path, at the expense of introducing an external control. We compare the performance of the non-adiabatic and STA engines for a fixed adiabatic efficiency but different parame…
Correlations in a quantum switch-based heat engine with measurements: A proof-of-principle demonstration
Federal University of ABC（ABC联邦大学）；University of Gdańsk（格但斯克大学）；Universität Wien（维也纳大学）；ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科技研究院）
By using a laser and maser in tandem, it is possible to obtain laser action in the hot exhaust gases involved in heat engine operation. Such a "quantum afterburner" involves the internal quantum states of working gas atoms or molecules as well as the techniques of cavity quantum electrodynamics and is therefore in the domain of quantum thermodynamics. As an example, it is shown that Otto cycle engine performance can be improved beyond that of the "ideal" Otto heat engine.
A quantum heat engine (QHE) based on the interaction driving of a many-particle working medium is introduced. The cycle alternates isochoric heating and cooling strokes with both interaction-driven processes that are simultaneously isochoric and isentropic. When the working substance is confined in a tight waveguide, the efficiency of the cycle becomes universal at low temperatures and governed by the ratio of velocities of a Luttinger liquid. We demonstrate the performance of the engine with an interacting Bose gas as a working medium and show that the average work per particle is maximum at …
The fundamentals of a quantum heat engine are derived from first principles. The study is based on the equation of motion of a minimum set of operators which is then used to define the state of the system. The relation between the quantum framework and thermodynamical observables is examined. A four stroke heat engine model with a coupled two-level-system as a working fluid is used to explore the fundamental relations. In the model used, the internal Hamiltonian does not commute with the external control field which defines the two adiabatic branches. Heat is transferred to the working fluid b…
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 non-classical 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 …
We present a complete-quantum description of multi-particle Szilard engine which consists of a working substance and a Maxwell's demon. The demon is modeled as a multi-level quantum system with specific quantum control and the working substance consists of identical particles obeying Bose-Einstein or Fermi-Dirac statistics. In this description, a reversible scheme to erase the demon's memory by a lower temperature heat bath is used. We demonstrate that (1) the quantum control of the demon can be optimized for single-particle Szilard engine so that the efficiency of the demon-assisted thermodyn…
Given a quantum heat engine that operates in a cycle that reaches maximal efficiency for a time-dependent Hamiltonian H(t) of the working substance, with overall controllable driving H(t) = g(t) H, we study the deviation of the efficiency from the optimal value due to a generic time-independent perturbation in the Hamiltonian. We show that for a working substance consisting of two two-level systems, by suitably tuning the interaction, the deviation can be suppressed up to the third order in the perturbation parameter-and thus almost retaining the optimality of the engine.
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.
Energy exchanges under form of heat is neither the most natural or efficient way to operate an engine in the quantum realm. Recently there have been in the literature several proposals for "quantum measurement engines" where energy is fed into the machine by operations which otherwise would be conducive to quantum measurements on the working substance (henceforth "the system"). In the analysis of the working of these devices, oftentimes it is assumed that the only effect of measurement is to turn the state of the system from whatever prior state to an eigenstate of the measured property, and e…
When a reciprocating heat engine is started it eventually settles to a stable mode of operation. The approach of a first principle quantum heat engine toward this stable limit cycle is studied. The engine is based on a working medium consisting of an ensemble of quantum systems composed of two coupled spins. A four stroke cycle of operation is studied, with two {\em isochore} branches where heat is transferred from the hot/cold baths and two {\em adiabats} where work is exchanged. The dynamics is generated by a completely positive map. It has been shown that the performance of this model resem…
We consider the optimization of a finite-time Carnot engine characterized by small dissipations. We bound the power with a simple inequality and show that the optimal strategy is to perform small cycles around a given working point, which can be thus chosen optimally. Remarkably, this optimal point is independent of the figure of merit combining power and efficiency that is being maximized. Furthermore, for a general class of dynamics the power output becomes proportional to the heat capacity of the working substance. Since the heat capacity can scale supra-extensively with the number of const…
We propose and analyze a microscopic Stirling heat engine based on an optomechanical system. The working fluid is a single vibrational mode of a mechanical resonator, which interacts by radiation pressure with a feedback-controlled optical cavity. The cavity light is used to engineer the thermal reservoirs and to steer the resonator through a thermodynamic cycle. In particular, the feedback is used to properly modulate the light fluctuations inside the cavity and hence to realize efficient thermodynamic transformations with realistic optomechanical devices.
Dynamical phases are obtained for a quantum thermal engine, whose working medium is a single harmonic oscillator. The dynamics of this engine is obtained by using four steps where in two steps the time dependent frequency is changing. In the other two steps, the thermal engine is coupled alternatively to hot and cold heat baths. Similar dynamical phases are obtained in a quantum thermal engine whose working medium is spin 1/2 system. The role of times durations of such steps in the quantum engines for getting maximal efficiency is analyzed. The dynamic of charge pumping in a quantum dot couple…
A Szilard Engine is a hypothetical device which is able to extract work from a single thermal reservoir by measuring the position of particles within the engine. We derive the amount of work that can be extracted from such a device in the low temperature limit. Interestingly, we show this work is determined by the information gain of the initial measurement rather than by the number and type of particles which constitute the working substance. Our work provides another clear connection between information gain and extractable work in thermodynamical processes.
We suggest alternative quantum Otto engines, using heat bath algorithmic cooling with partner pairing algorithm instead of isochoric cooling. Liquid state nuclear magnetic resonance systems in one entropy sink are considered as working fluids. Then, the extractable work and thermal efficiency are analyzed in detail for four-stroke and two-stroke type of quantum Otto engines. The role of heat bath algorithmic cooling in these cycles is to use a single entropy sink instead of two. Also, this cooling algorithm increases the power of engines reducing the time required for one cycle.
We study the thermodynamic performance of the finite-time non-regenerative Stirling cycle used as a quantum heat engine. We consider specifically the case in which the working substance (WS) is a two-level system. The Stirling cycle is made of two isochoric transformations separated by a compression and an expansion stroke during which the working substance is in contact with a thermal reservoir. To describe these two strokes we derive a non-Markovian master equation which allows to study the dynamics of a driven open quantum system with arbitrary fast driving. We found that the finite-time dy…
