The extension of quantum thermodynamics to situations that go beyond standard thermodynamic settings comprises an important and interesting aspect of its development. One such situation is the analysis of the thermodynamic consequences of structured environments that induce a non-Markovian dynamics. We study a quantum Otto refrigerator where the standard Markovian cold reservoir is replaced by a specific engineered cold reservoir which may induce a Markovian or non-Markovian dynamics on the quantum refrigerant system. The two dynamical regimes can be interchanged by varying the coupling between the refrigerant and the reservoir. An increase of non-Markovian effects will be related to an increase of the coupling strength, which in turn will make the energy stored in the interaction Hamiltonian, the interaction energy, increasingly relevant. We show how the figures of merit, the coefficient of performance and the cooling power, change for non-negligible interaction energies, discussing how neglecting this effect would lead to an overestimation of the refrigerator performance. Finally, we also consider a numerical simulation of a spin quantum refrigerator with experimentally feasible parameters to better illustrate the non-Markovian effects induced by the engineered cold reservoir. We argue that a moderate non-Markovian dynamics performs better than either a Markovian or a strong non-Markovian regime of operation.
We investigate quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator operating under the conditions of maximum $Ω$-function, a trade-off objective function which represents a compromise between energy benefits and losses for a specific job, for both adiabatic and nonadiabatic (sudden) frequency modulations. We derive analytical expressions for the efficiency and coefficient of performance of the Otto cycle. For the case of adiabatic driving, we point out that in the low-temperature regime, the harmonic Otto engine (refrigerator) can be mapped to Feynman's ratchet…
Quantum refrigerators pump heat from a cold to a hot reservoir. In the few-particle regime, counter-diabatic (CD) driving of, originally adiabatic, work-exchange strokes is a promising candidate to overcome the bottleneck of vanishing cooling power. Here, we present a finite-time many-body quantum refrigerator that yields finite cooling power at high coefficient of performance, that considerably outperforms its non-adiabatic counterpart. We employ multi-spin CD driving and numerically investigate the scaling behavior of the refrigeration performance with system size. We further prove that opti…
We consider a quantum Otto refrigerator cycle of a time-dependent harmonic oscillator. We investigate the coefficient of performance at maximum figure of merit for adiabatic and nonadiabatic frequency modulations. We obtain analytical expressions for the optimal performance both in the high-temperature (classical) regime and in the low-temperature (quantum) limit. We moreover analyze the breakdown of the cooling cycle for strongly nonadiabatic driving protocols and derive analytical estimates for the minimal driving time allowed for cooling.
We investigate the performance of a quantum Otto refrigerator operating in finite time and exploiting local counterdiabatic techniques. We evaluate its coefficient of performance and cooling power when the working medium consists a quantum harmonic oscillator with a time-dependent frequency. We find that the quantum refrigerator outperforms its conventional counterpart, except for very short cycle times, even when the driving cost of the local counterdiabatic driving is included. We moreover derive upper bounds on the performance of the thermal machine based on quantum speed limits and show th…
We consider a quantum Otto cycle operating between two squeezed thermal reservoirs. The influences of the squeezing degree on the optimization performance of quantum Otto heat engines and refrigerators are investigated. We demonstrate that under symmetric condition, the efficiency at maximum power (EMP) of heat engines and the coefficient of performance (COP) at maximum \c{hi} criterion of refrigerators are equal to Curzon-Ahlborn (CA) efficiency and CA COP, respectively. We also found that under asymmetric condition, the EMP of heat engines can be improved when the squeezing degree of hot the…
We analyze the performance of a quantum Otto cycle, employing 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 the earlier studies claiming unit efficiency under the effect of squeezed reservoir. Then, 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 independen…
We analyse a quantum Otto refrigerator based on a superconducting qubit coupled to two LC-resonators each including a resistor acting as a reservoir. We find various operation regimes: nearly adiabatic (low driving frequency), ideal Otto cycle (intermediate frequency), and non-adiabatic coherent regime (high frequency). In the nearly adiabatic regime, the cooling power is quadratic in frequency, and we find substantially enhanced coefficient of performance $ε$, as compared to that of an ideal Otto cycle. Quantum coherent effects lead invariably to decrease in both cooling power and $ε$ as comp…
We investigate a heat engine with a finite length Kitaev chain in an Otto cycle. Finite size effects are taken into account using method of Hill's nano-thermodynamics as well as using the method of temperature dependent energy levels. We distinguish the bulk and boundary contributions to the efficiency and the work output of Kitaev chain engine and identify them as non-Otto heat engine and refrigerator cycles, respectively. Possibility of separately running Otto engine cycles associated with the bulk and the whole system, and an Otto refrigerator at the boundary is pointed out. It is found tha…
We explore a thermodynamical effect of anharmonicity in quantum mechanical oscillators. We show that small quartic perturbations to the oscillator potential lead to an enhancement of performance of quantum refrigerators for both the Otto and Stirling cycles. A similar nonlinearity driven enhancement of performance is also observed for an analogous spin-qubit model of quantum refrigerators. We further demonstrate the robustness of improvement of the coefficient of performance versus the energy cost for creating anharmonicity. It is shown that the anharmonicity driven improvement in performance …
We study the effect of Kerr nonlinearity in quantum thermal machines having a Kerr-nonlinear oscillator as working substance and operating under the ideal quantum Otto cycle. We first investigate the efficiency of a Kerr-nonlinear heat engine and show that by varying the Kerr-nonlinear strength the efficiency surpasses in up to 2.5 times the efficiency of a quantum harmonic oscillator Otto engine. Moreover, the Kerr-nonlinearity makes the coefficient of performance of the Kerr-nonlinear refrigerator to be as large as 3 times the performance of quantum harmonic oscillator Otto refrigerators. Th…
We use fast periodic control to realize finite-time Otto cycles exhibiting quantum advantage. Such periodic modulation of the working medium - bath interaction Hamiltonian during the thermalization strokes can give rise to non-Markovian anti-Zeno dynamics, and corresponding reduction in the thermalization times. Faster thermalization can in turn significantly enhance the power output in engines, or equivalently, the rate of refrigeration in refrigerators. This improvement in performance of dynamically controlled Otto thermal machines arises due to the time-energy uncertainty relation of quantu…
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 …
We study a limit cycle of a quantum Otto engine whose each cycle consists of two finite-time quantum isochoric (heating or cooling) processes and two quantum adiabatic work-extracting processes. Considering a two-level system as a working substance that weakly interacts with two reservoirs comprising an infinite number of bosons, we investigate the non-Markovian effect (short-time behavior of the reduced dynamics in the quantum isochoric processes (QIPs)) on work extraction after infinite repetition of the cycles. We focus on the parameter region where energy transferred to the reservoir can c…
We study the application of a counter-diabatic driving (CD) technique to enhance the thermodynamic efficiency and power of a quantum Otto refrigerator based on a superconducting qubit coupled to two resonant circuits. Although the CD technique is originally designed to counteract non-adiabatic coherent excitations in isolated systems, we find that it also works effectively in the open system dynamics, improving the coherence-induced losses of efficiency and power. We compare the CD dynamics with its classical counterpart, and find a deviation that arises because the CD is designed to follow th…
The charging of a quantum battery by a four-stroke quantum machine that works either as an engine or a refrigerator is investigated. The presented analysis provides the energetic behavior of the combined system in terms of the heat and workflows of the machine, the average, and variance of the battery's energy as well as the coherent and incoherent parts of its ergotropy. To monitor the battery state its energy is measured either after the completion of any cycle or after a prescribed number of cycles is carried out. The resulting battery performances greatly differ for those two cases. During…
We study the optimization of the performance of arbitrary periodically driven thermal machines. Within the assumption of fast modulation of the driving parameters, we derive the optimal cycle that universally maximizes the extracted power of heat engines, the cooling power of refrigerators, and in general any linear combination of the heat currents. We denote this optimal solution as ``generalized Otto cycle'' since it shares the basic structure with the standard Otto cycle, but it is characterized by a greater number of fast strokes. We bound this number in terms of the dimension of the Hilbe…
Four stroke Otto refrigerator cycles with no classical analogue are studied. Extremely short cycle times with respect to the internal time scale of the working medium characterize these refrigerators. Therefore these cycles are termed sudden. The sudden cycles are characterized by the stable limit cycle which is the invariant of the global cycle propagator. During their operation the state of the working medium possesses significant coherence which is not erased in the equilibration segments due to the very short time allocated. This characteristic is reflected in a difference between the ener…
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…
We show that non-Markovian effects of the reservoirs can be used as a resource to extract work from an Otto cycle. The state transformation under non-Markovian dynamics is achieved via a two-step process, namely an isothermal process using a Markovian reservoir followed by an adiabatic process. From second law of thermodynamics, we show that the maximum amount of extractable work from the state prepared under the non-Markovian dynamics quantifies a lower bound of non-Markovianity. We illustrate our ideas with an explicit example of non-Markovian evolution.
We discuss a model of a closed quantum evolution of two-qubits where the joint Hamiltonian is so chosen that one of the qubits acts as a bath and thermalize the other qubit which is acting as the system. The corresponding exact master equation for the system is derived. Interestingly, for a specific choice of parameters the master equation takes the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) form with constant coefficients, representing pumping and damping of a single qubit system. Based on this model we construct an Otto cycle connected to a single qubit bath and study its thermodynamic pro…
Two qubits form a quantum four-level system. The golden-rule based transition rates between these states are determined by the coupling of the qubits to noise sources. We demonstrate that depending on whether the noise acting on the two qubits is correlated or not, these transitions are governed by different selection rules. In particular, we find that for fully correlated or anticorrelated noise, there is a protected state, and the dynamics of the system depends then on its initialization. For nearly (anti)correlated noise, there is a long time scale determining the temporal evolution of the …
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…
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 (ISW) 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 obta…
We analyze the efficiency of the quantum Otto cycle applied to a superconducting cavity. We consider its description in terms of a full quantum scalar field in a one-dimensional cavity with a time dependent boundary condition that can be externally controlled to perform and extract work unitarily from the system. We study the performance of this machine when acting as a heat engine as well as a refrigerator. It is shown that, in a non-adiabatic regime, the efficiency of the quantum cycle is affected by the dynamical Casimir effect, that induces a sort of quantum friction that diminishes the ef…
The quantum Otto cycle serves as a bridge between the macroscopic world of heat engines and the quantum regime of thermal devices composed from a single element. We compile recent studies of the quantum Otto cycle with a harmonic oscillator as a working medium. This model has the advantage that it is analytically trackable. In addition, an experimental realization has been achieved employing a single ion in a harmonic trap. The review is embedded in the field of quantum thermodynamics and quantum open systems. The basic principles of the theory are explained by a specific example illuminating …
In this work we study how the non-Markovian character of the dynamics can affect the thermodynamic performance of a quantum thermal engine, by analysing the maximum power output of Carnot and Otto cycles departing from the quasi-static and infinite-time-thermalization regime respectively, introducing techniques for their control optimization in general dynamical models. In our model, non-Markovianity is introduced by allowing some degrees of freedom of the reservoirs to be taken into account explicitly and share correlations with the engine by Hamiltonian coupling. It is found that the non-Mar…
A reciprocating quantum refrigerator is studied with the purpose of determining the limitations of cooling to absolute zero. We find that if the energy spectrum of the working medium possesses an uncontrollable gap, then there is a minimum achievable temperature above zero. Such a gap, combined with a negligible amount of noise, prevents adiabatic following during the demagnetization stage which is the necessary condition for reaching $T_c \to 0$. The refrigerator is based on an Otto cycle where the working medium is an interacting spin system with an energy gap. For this system the external c…
Markovian heat engine boosted by quantum coherence
Centre for Bioinformatics and Photonics—CIBioFi（生物信息学与光子学中心）；Departamento de Física, Universidad del Valle（国立谷大学物理系）；Department of Physics, University of Oslo（奥斯陆大学物理系）
According to Clausius formulation of the second law of thermodynamics, for any thermal machine withdrawing heats $Q_{1,2}$ from two heat reservoirs at temperatures $T_{1,2}$, it holds $Q_1/T_1+Q_2/T_2 \leq 0$. Combined with the observation that the quantity $Q_1+Q_2$ is the work $W$ done by the system, that inequality tells that only 4 possible operation modes are possible for the thermal machine, namely heat engine [E], refrigerator [R], thermal accelerator [A] and heater [H]. We illustrate their emergence in the finite time operation of a quantum Otto engine realised with a single qubit. We …
We study the asymptotic dynamics of arbitrary linear quantum open systems which are periodically driven while coupled with generic bosonic reservoirs. We obtain exact results for the heat flowing into the network, which are valid beyond the usual weak coupling or Markovian approximations. We prove the validity of the dynamical third law of thermodynamics (Nernst unattainability principle), showing that the ultimate limit for cooling is imposed by a fundamental heating mechanism which becomes dominant at low temperatures: the non resonant creation of pairs of excitations in the reservoirs induc…
We show that quantum absorption refrigerators, which have traditionally been studied as of three qubits, each of which is connected to a thermal reservoir, can also be constructed by using three qubits and two thermal baths, where two of the qubits, including the qubit to be locally cooled, are connected to a common bath. With a careful choice of the system, bath, and qubit-bath interaction parameters within the Born-Markov and rotating-wave approximations, one of the qubits attached to the common bath achieves a cooling in the steady state. We observe that the proposed refrigerator may also o…
We study energetic exchanges and fluctuations in two-stroke quantum thermodynamic engines where the working fluid is represented by two multilevel quantum systems, i.e. qudits, the heat flow is allowed by relaxation with two thermal reservoirs at different temperatures, and the work exchange is operated by a partial-swap unitary interaction. We identify three regimes of operation (heat engine, refrigerator, and thermal accelerator), present the thermodynamic uncertainty relations between the entropy production and the signal-to-noise ratio of work and heat, and derive the full joint probabilit…
