The formulation of models describing quantum versions of heat engines plays an important role in the quest toward establishing the laws of thermodynamics in the quantum regime. Of particular importance is the description of stroke-based engines which can operate at finite-time. In this paper we put forth a framework for describing stroboscopic, two-stroke engines, in generic quantum chains. The framework is a generalization of the so-called SWAP engine and is based on a collisional model, which alternates between pure heat and pure work strokes. The transient evolution towards a limit-cycle is also fully accounted for. Moreover, we show that once the limit-cycle has been reached, the energy of the internal sites of the chain no longer changes, with the heat currents being associated exclusively to the boundary sites. Using a combination of analytical and numerical methods, we show that this type of engine offers multiple ways of optimizing the output power, without affecting the efficiency. Finally, we also show that there exists an entire class of models, characterized by a specific type of inter-chain interaction, which always operate at Otto efficiency, irrespective of the operating conditions of the reservoirs.
We put forth a quantum simulation of a stroboscopic two-stroke thermal engine in the IBMQ processor. The system consists of a quantum spin chain connected to two baths at their boundaries, prepared at different temperatures using the variational quantum thermalizer algorithm. The dynamics alternates between heat and work strokes, which can be separately designed using independent quantum circuits. The results show good agreement with theoretical predictions, showcasing IBMQ as a powerful tool to study thermodynamics in the quantum regime, as well as the implementation of variational quantum al…
We propose and analyze the theoretical model for a two-stroke quantum heat engine with one of the heat baths replaced by a non-selective quantum measurement. We show that the engine's invariant reference state depends on whether the cycle is monitored or unmonitored via diagnostic measurements to determine the engine's work output. We explore in detail the average work output and fluctuations of the proposed heat engine for the monitored and unmonitored cases. We also identify unitary work strokes for which the invariant states can support coherences in the energy basis leading to differing pr…
A four stroke quantum engine which alternately interacts with a measurement apparatus and a single heat bath is discussed in detail with respect to the average work and heat as well as to the fluctuations of work and heat. The efficiency and the reliability of such an engine with a harmonic oscillator as working substance are analyzed under different conditions such as different speeds of the work strokes, different temperatures of the heat bath and various strengths of the energy supplying measurement. For imperfect thermalization strokes of finite duration also the power of the engine is ana…
In order to build a quantum analog of traditional Carnot engine, a common choice is replacing the two thermodynamic adiabatic processes with two quantum mechanical adiabatic processes. In general, such quantum Carnot engine has six strokes. We analyze the efficiency of such six-stroke quantum Carnot engine in a perturbative way.
Floquet operator engineering for quantum state stroboscopic stabilization
Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS（图卢兹大学、法国国家科学研究中心碰撞聚合反应联合研究实验室）；Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303（勃艮第卡尔诺跨学科实验室）
It is investigated whether non-Markovianity, i.e., the memory effects resulting from the coupling of the system to its environment, can be beneficial for the performance of quantum heat engines. Specifically, two physical models are considered. The first one is a well known single-qubit Otto engine; the non-Markovian behaviour is there implemented by replacing standard thermalization strokes with so-called extremal thermal operations which cannot be realized without the memory effects. The second one is a three-stroke engine in which the cycle consists of two extremal thermal operations and a …
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.
We analyze an autonomous thermoelectric engine composed of two superconducting qubits coupled to separate heat baths and connected by a Josephson junction. Work and heat are process quantities and not observables of the engine quantum system, but their rates can be derived from the steady state expectation value of appropriate system observables and their fluctuations are given by correlation functions determined with the GKLS master equation and quantum regression theorem. The correlation functions also reveal a cyclical, dynamical transfer of energy - the strokes of the engine - hiding under…
In this work, we introduce a three-stroke quantum engine with a single-qubit work-ing substance whose cycle consists of two strokes arise due to performing two distinctgeneral quantum measurements and it is completed by thermalization through contactwith a finite temperature thermal reservoir. It is demonstrated that energy is importedinto the engine by first measurement channel and work (usefulenergy) is extracted fromit, in a frictionless isentropic manner, by the second measurement channel. It is par-ticularly shown that the engine is capable to have perfect efficiency. In continuation,we e…
We study how a quantum heat engine based on a single trapped ion performs in finite time. The always-on thermal environment acts like the hot bath, while the motional degree of freedom of the ion plays the role of the effective cold bath. The hot isochoric stroke is implemented via the interaction of the ion with its hot environment, while a projective measurement of the internal state of the ion is performed as an equivalent to the cold isochoric stroke. The expansion and compression strokes are implemented via suitable change in applied magnetic field. We study in detail how the finite durat…
School of Physics, The University of Sydney（悉尼大学物理学院）；RIKEN Center for Quantum Computing, RIKEN（理研量子计算中心）；Quantum Research Institute and Department of Physics, University of Michigan（密歇根大学量子研究所和物理系）
A multilevel four-stroke engine where the thermalization stokes are generated by unitary collisions with bath particles is analyzed. Our model is solvable even when the engine operates far from thermal equilibrium and in the strong system-bath coupling. Necessary operation conditions for the heat machine to perform as an engine or a refrigerator are derived. We relate the work and efficiency of the device to local and non-local statistical properties of the baths (purity, mutual coincidence etc.). In particular, we relate the Clausius inequality to the symmetrized relative entropy of the baths…
We investigate heat engines whose working substance is made of two coupled qubits performing a generalised Otto cycle by varying their applied magnetic field or their interaction strength during the compression and expansion strokes. During the heating and cooling strokes, the two qubits are coupled to local and common environments that are not necessarily at equilibrium. We find instances of quantum engines coupled to non equilibrium common environments exhibiting non-trivial connections to quantum correlations as witnessed by a monotonic dependence of the work produced on quantum discord and…
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…
We unveil a mechanism for generating oscillations with arbitrary multiplets of the period of a given external drive, in long-range interacting quantum many-particle spin systems. These oscillations break discrete time translation symmetry as in time crystals, but they are understood via two intertwined stroboscopic effects similar to the aliasing resulting from video taping a single fast rotating helicopter blade. The first effect is similar to a single blade appearing as multiple blades due to a frame rate that is in resonance with the frequency of the helicopter blades' rotation; the second …
High-order quantum nonlinearity is an important prerequisite for the advanced quantum technology leading to universal quantum processing with large information capacity of continuous variables. Levitated optomechanics, a field where motion of dielectric particles is driven by precisely controlled tweezer beams, is capable of attaining the required nonlinearity via engineered potential landscapes of mechanical motion. Importantly, to achieve nonlinear quantum effects, the evolution caused by the free motion of mechanics and thermal decoherence have to be suppressed. For this purpose, we devise …
In this work, we study the efficiency of charging a quantum battery through optical pumping. The battery consists of a qutrit and it is connected to a natural thermal reservoir and an external coherent drive in the limit where its upper energy level can be adiabatically eliminated from the dynamics. In this scenario, the drive plus spontaneous emission optically pumps the intermediate energy level of the qutrit and the battery can be understood as being charged by an effective higher temperature reservoir that takes it out of equilibrium with the natural reservoir and stores useful energy in i…
We consider the optimization of the work output and fluctuations of a finite-time quantum Otto heat engine cycle consisting of compression and expansion work strokes of unequal duration. The asymmetry of the cycle is characterized by a parameter $r_u$ giving the ratio of the times for the compression and expansion work strokes. For such an asymmetric quantum Otto engine cycle, with working substance chosen as a harmonic oscillator or a two-level system, we find that the optimal values of $r_u$ maximising the work output and the reliability (defined as the ratio of average work output to its st…
The precise estimation of small parameters is a challenging problem in quantum metrology. Here, we introduce a protocol for accurately measuring weak magnetic fields using a two-level magnetometer, which is coupled to two (hot and cold) thermal baths and operated as a two-stroke quantum thermal machine. Its working substance consists of a two-level system (TLS), generated by an unknown weak magnetic field acting on a qubit, and a second TLS arising due to the application of a known strong and tunable field on another qubit. Depending on this field, the machine may either act as an engine or a …
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 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,…
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 present a quantum Otto engine model 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 operates under maximal power by optimizing the control parameter, the efficiency shows certain universal behavior.
Bose-Einstein condensates can be used to produce work by tuning the strength of the interparticle interactions with the help of Feshbach resonances. In inhomogeneous potentials, these interaction ramps change the volume of the trapped gas allowing one to create a thermodynamic cycle known as the Feshbach engine. However, in order to obtain a large power output, the engine strokes must be performed on a short timescale, which is in contrast with the fact that the efficiency of the engine is reduced by irreversible work if the strokes are done in a non-adiabatic fashion. Here we investigate how …
Unlike classical systems, a measurement performed on a quantum system always alters its state. In this work, the impacts of two diagnostic schemes to determine the performance of quantum Otto heat engines are compared: In one scheme, the energy of the engine's working substance is measured after each stroke (repeated measurements), and in the other one, the energies after each stroke are recorded in one or two pointer states and measured only after the completion of a prescribed number of cycles (repeated contacts). A single pointer state suffices if one is only interested in either work or he…
We study a minimal quantum Otto heat engine, where the working medium consists of an interacting few-body system in a harmonic trap. This allows us to consider the interaction strength as an additional tunable parameter during the work strokes. We calculate the figures of merit of this engine as a function of the temperature and show clearly in which parameter regimes the interactions assist in engine performance. We also study the finite time dynamics and the subsequent trade-off between the efficiency and the power, comparing the interaction enhanced cycle with the case where the system rema…
We study a four-stroke Otto engine whose working fluid is a quantum Ising chain. The thermodynamic cycle consists in sweeps of the transverse magnetic field occurring in thermal isolation, alternated by thermalisation strokes with reservoirs at different temperatures. The system-environment coupling is modelled in a thermodynamically consistent way by means of a nonlocal Lindblad master equation. We show that the engine may operate in four different operation modes, depending on the various parameters, in particular it can act as a heat engine and as a refrigerator. We detect an enhancement of…
Experimental Demonstration of a Measurement-Feedback Quantum Information Engine
Quantum Information Institute, School of Physics and Laboratory of Zhongyuan Light, Zhengzhou University（郑州大学物理学院量子信息研究所中原光实验室）；Department of Physics, Nanchang University（南昌大学物理系）
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…
Real quantum heat engines lack the separation of time and length scales that is characteristic for classical engines. They must be understood as open quantum systems in non-equilibrium with time-controlled coupling to thermal reservoirs as integral part. Here, we present a systematic approach to describe a broad class of engines and protocols beyond conventional weak coupling treatments starting from a microscopic modeling. For the four stroke Otto engine the full dynamical range down to low temperatures is explored and the crucial role of the work associated with the coupling/decoupling to/fr…
We show that finite system-reservoir coupling imposes a distinct quantum limit on the performance of a non-equilibrium quantum heat engine. Even in the absence of quantum friction along the isentropic strokes, finite system-reservoir coupling induces correlations that result in the generation of coherence between the energy eigenstates of the working system. This coherence acts to hamper the engine's power output, as well as the efficiency with which it can convert heat into useful work, and cannot be captured by a standard Born-Markov analysis of the system-reservoir interactions.
We study the performance of a quantum Otto cycle using a harmonic work medium and undergoing collisional dynamics with finite-size reservoirs. We span the dynamical regimes of the work strokes from strongly non-adiabatic to quasi-static conditions, and address the effects that non-Markovianity of the open-system dynamics of the work medium can have on the efficiency of the thermal machine. While such efficiency never surpasses the classical upper bound valid for finite-time stochastic engines, the behaviour of the engine shows clear-cut effects induced by both the finiteness of the evolution t…
Thermodynamic Performance of a Measurement-Driven Quantum Engine with a Two-Parameter $(p,q)$-Deformed Harmonic Oscillator
Khalifa University of Science and Technology（哈利法科学技术大学）；KU Research Center for Advanced Intelligent Systems (AIS), Khalifa University of Science and Technology（哈利法科学技术大学 KU 先进智能系统研究中心）
Ulm University（乌尔姆大学）；Institute of Theoretical Physics, Ulm University（乌尔姆大学理论物理研究所）；Center for Integrated Quantum Science and Technology (IQST)（集成量子科学与技术中心）
Equivalence of Discrete and Continuous Otto-Like Engines assisted by Catalysts: Mapping Catalytic Advantages from the Discrete to the Continuous Framework
University of Gdańsk（格但斯克大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
Refrigerators use a thermodynamic cycle to move thermal energy from a cold reservoir to a hot one. Implementing this operation principle with mesoscopic components has recently emerged as a promising strategy to control heat currents in micro and nano systems for quantum technological applications. Here, we combine concepts from stochastic and quantum thermodynamics with advanced methods of optimal control theory to develop a universal optimization scheme for such small-scale refrigerators. Covering both the classical and the quantum regime, our theoretical framework provides a rigorous proced…
We consider a finite-time quantum Otto heat engine that consists of two isochoric (thermal-contact) process, where the system is alternatively coupled to a hot squeezed and a cold thermal reservoir, and two unitary driven strokes, where the system is isolated from these two baths and its von Neumann entropy keeps constant. Both quantum inner friction and coherence are generated along the driven stroke and coherence cannot be fully erased after the finite-time hot isochore. Using full counting statistics, we present the probability distribution functions of heat injection and total work per cyc…
