Quantum Otto Heat Engine Research Articles

Quantum Otto Heat Engine Using Polar Molecules in Pendular States

Quantum heat engines (QHEs) are established by applying the principles of quantum thermodynamics to small−scale systems, which leverage quantum effects to gain certain advantages. In this study, we investigate the quantum Otto cycle by employing the dipole−dipole coupled polar molecules as the working substance of QHE. Here, the molecules are considered to be trapped within an optical lattice and located in an external electric field. We analyze the work output and the efficiency of the quantum Otto heat engine (QOHE) as a function of various physical parameters, including electric field strength, dipole−dipole interaction and temperatures of heat baths. It is found that by adjusting these physical parameters the performance of the QOHE can be optimized effectively. Moreover, we also examine the influences of the entanglement and relative entropy of coherence for the polar molecules in thermal equilibrium states on the QOHE. Our results demonstrate the potential of polar molecules in achieving QHEs.

A quantum otto heat engine driven by three quantum dots

A quantum heat engine composed of three coupled quantum dots as a working substance is proposed. Since quantum dots naturally obey the Fermi Hubbard Hamiltonian, the strong coupling interaction regime allows the working substance to be evaluated under an effective Heisenberg Hamiltonian. Indeed, the influence of the strength coupling, between the three dots, on quantum machine efficiency and work in the presence of a homogeneous magnetic field is also examined. Furthermore, the influence of entanglement on the efficiency & work of the quantum dot Otto heat engine is well analyzed. As a tripartite working substance, we are interested in analyzing the local work and efficiency associated with each single and pair of quantum dots. The results show that the local efficiency associated with a pair of quantum dots achieves a maximum value, unlike the global efficiency. Indeed, the entanglement impact on Global/local work is studied.

Work and efficiency fluctuations in a quantum Otto cycle with idle levels.

We study the performance of a quantum Otto heat engine with two spins coupled by a Heisenberg interaction, taking into account not only the mean values of work and efficiency but also their fluctuations. We first show that, for this system, the output work and its fluctuations are directly related to the magnetization and magnetic susceptibility of the system at equilibrium with either heat bath. We analyze the regions where the work extraction can be done with low relative fluctuation for a given range of temperatures, while still achieving an efficiency higher than that of a single spin system heat engine. In particular, we find that, due to the presence of "idle" levels, an increase in the interspin coupling can either increase or decrease fluctuations, depending on the other parameters. In all cases, however, we find that the relative fluctuations in work or efficiency remain large, implying that this microscopic engine is not very reliable as a source of work.

Monitored nonadiabatic and coherent-controlled quantum unital Otto heat engines: First four cumulants.

Recently, measurement-based quantum thermal machines have drawn more attention in the field of quantum thermodynamics. However, the previous results on quantum Otto heat engines were either limited to special unital and nonunital channels in the bath stages, or a specific driving protocol at the work strokes and assuming the cycle being time-reversal symmetric, i.e., V^{†}=U (or V=U). In this paper, we consider a single spin-1/2 quantum Otto heat engine, by first replacing one of the heat baths by an arbitrary unital channel, and then we give the exact analytical expression of the characteristic function from which all the cumulants of heat and work emerge. We prove that under the effect of monitoring, ν_{2}>ν_{1} is a necessary condition for positive work, either for a symmetric or asymmetric-driven Otto cycle. Furthermore, going beyond the average we show that the ratio of the fluctuations of work and heat is lower and upper-bounded when the system is working as a heat engine. However, differently from the previous results in the literature, we consider the third and fourth cumulants as well. It is shown that the ratio of the third (fourth) cumulants of work and heat is not upper-bounded by unity nor lower-bounded by the third (fourth) power of the efficiency, as is the case for the ratio of fluctuations. Finally, we consider applying a specific unital map that plays the role of a heat bath in a coherently superposed manner, and we show the role of the initial coherence of the control qubit on efficiency, on the average work and its relative fluctuations.

Quantum Otto heat engine with Pöschl–Teller potential in contact with coherent thermal bath

Work and efficiency of quantum Otto heat engines (QOHEs) can increase by using non-thermal baths or by inhomogeneous scaling of energy levels of the working substance. Given these points, at first, we construct the coherent thermal state for a trigonometric Pöschl–Teller (PT) potential. Then using a particle in this potential, which has unequally spaced energy levels, as a working substance, we investigate the work extraction and the efficiency of QOHEs that operates between cold and hot coherent thermal baths. The results show that changing the PT potential parameters in the adiabatic processes of QOHE, which causes an inhomogeneous shift in energy levels or/and make use of the hot coherent thermal bath, improve work extraction and efficiency of QOHE relative to the classical counterpart.

Quantum heat engine with identical particles and level degeneracy

In this paper, the effects of identical particles and energy-level degeneracy on the work output of the quantum Otto and Stirling heat engines are studied. For quantum Otto heat engine, we find the effects of degeneracy in the ground state and in the excited state are same in the high-temperature limitation while the work done by a system with n-fold degeneracy in the excited state (ground state) is n ([Formula: see text]) times the one without degeneracy in the single-particle case. Moreover, the effects of the identical two-level systems with degeneracy in the ground state or excited state as working substances are discussed. The results of such problem for the Stirling and Carnot heat engines are similar. By analytical derivations in two limit conditions, we conclude that for the cycles which are composed of the quantum adiabatic process, isochoric process and isothermal process have similar results.

Interaction-enhanced quantum heat engine

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 tradeoff between the efficiency and the power, comparing the interaction-enhanced cycle with the case where the system remains scale-invariant.

Optimization of asymmetric quantum Otto engine cycles

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} maximizing the work output and the reliability (defined as the ratio of average work output to its standard deviation) shows discontinuities as a function of the total time taken for the cycle. Moreover we identify cycles of some specific duration where both the work output and the reliability take their largest values for the same value of the asymmetry parameter r_{u}.

Negative temperature phenomena in two coupled qubit-ensembles

Negative absolute temperature has a wide range of applications, such as high-efficiency quantum heat engines, quantum refrigerators, and quantum simulation. In a recent paper (2018 Phys. Rev. Lett. 120 060403), the authors proposed two spin ensembles coupled to the same reservoir collectively; one ensemble relaxes to negative temperature since the two ensembles have unbalanced spin sizes. However, the coherent coupling mediated by the common environment is not considered. Here, we discuss negative temperature in a system where two qubit-ensembles are coupled to the same 1D waveguide. In the limit of Markovian approximation, by investigating the coherent coupling and non-cross (cross) collective decay between two qubit-ensembles, we find that the duration of the negative temperature state depends on the distance between the two ensembles. The decrease in negative temperature duration is due to the coherent coupling between the two ensembles that will hybridize the unitary evolution of the system. Some optimal points produce the longest duration of negative temperature, but this could not occur since the distance is out of the range of the appropriate regions. The negative temperature subensemble plays the role of a reservoir in the quantum Otto heat engine, which takes place beyond the Otto limit.

A thermodynamic probe of the topological phase transition in epitaxial graphene based Floquet topological insulator

One can use light to tune certain materials from a trivial to a topological phase. A prime example of such materials, classified as Floquet topological insulators (FTIs), is epitaxial graphene. In this paper, we probe the topological phase transition of a FTI via the efficiency and work output of quantum Otto and quantum Stirling heat engines. A maximum/minimum in the efficiency or work output invariably signals the phase transition point. Furthermore, both engines’ work output and efficiency are markedly robust against the polarization direction of light.

The Quantum Otto Heat Engine with a Relativistically Moving Thermal Bath

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 hot and cold bath respectively. 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 systems we obtain the total produced work, the efficiency and the efficiency at maximum power. The maximum efficiency of the Otto quantum heat engine depends only on the ratio of the minimum and maximum energy gaps. On the contrary, the efficiency at maximum power and the extracted work decreases with the velocity since the motion of the heat bath has an energy cost for the quantum heat engine. Furthermore, the efficiency at maximum power depends on the nature of the working medium.

Bounds on fluctuations for finite-time quantum Otto cycle.

For quantum Otto engine driven quasistatically, we provide exact full statistics of heat and work for a class of working fluids that follow a scale-invariant energy eigenspectra under driving. Equipped with the full statistics we go on to derive a universal expression for the ratio of nth cumulant of output work and input heat in terms of the mean Otto efficiency. Furthermore, for nonadiabatic driving of quantum Otto engine with working fluid consisting of either a (i) qubit or (ii) a harmonic oscillator, we show that the relative fluctuation of output work is always greater than the corresponding relative fluctuation of input heat absorbed from the hot bath. As a result, the ratio between the work fluctuation and the input heat fluctuation receives a lower bound in terms of the square value of the average efficiency of the engine. The saturation of the lower bound is received in the quasistatic limit of the engine.

Two-level quantum Otto heat engine operating with unit efficiency far from the quasi-static regime under a squeezed reservoir

Recent theoretical and experimental studies in quantum heat engines show that, in the quasi-static regime, it is possible to have higher efficiency than the limit imposed by Carnot, provided that engineered reservoirs are used. The quasi-static regime, however, is a strong limitation to the operation of heat engines, since an infinitely long time is required to complete a cycle. In this paper we propose a two-level model as the working substance to perform a quantum Otto heat engine surrounded by a cold thermal reservoir and a squeezed hot thermal reservoir. Taking advantage of this model we show a striking achievement, that is to attain unity efficiency even at non-null power.

Optimization performance of quantum Otto heat engines and refrigerators with squeezed thermal reservoirs

We consider a quantum Otto cycle, consisting of two isentropic processes (quantum adiabatic processes) and two isochoric processes, 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 work output (EMW) of heat engines and the coefficient of performance (COP) at maximum χ∗ criterion of refrigerators are equal to Curzon–Ahlborn (CA) efficiency and CA COP, respectively. We also found that under asymmetric condition, the EMW of heat engines can be improved when the squeezing degree of hot thermal reservoir is greater than that of the cold thermal reservoir, while be reduced or even inhibited in the opposite condition. However, the COP at maximum χ∗ criterion of refrigerators can be enhanced when the squeezing degree of cold thermal reservoir is greater than that of the hot thermal reservoir, otherwise will be suppressed.

Unified trade-off optimization of quantum Otto heat engines with squeezed thermal reservoirs

We consider a quantum Otto heat engine cycle operating between two squeezed thermal reservoirs that are characterized by a temperature as well as additional parameters that quantify the degree of squeezing. The optimal efficiency at the unified trade-off optimization criterion representing a compromise between energy benefits and losses for a quantum Otto heat engine is systematically investigated. The analytical expressions for the optimal efficiency are determined in the limit adiabatic and nonadiabatic processes as well as in the high- and low-temperature regimes, respectively. The general unified trade-off efficiency is given as a nonequilibrium efficiency that extends the standard unified trade-off efficiency to a more general nonequilibrium condition.

Two particles in measurement-based quantum heat engine without feedback control

We consider two two-level particles (qubits) as the working substances of measurement-based quantum heat engines. A measurement-based quantum heat engine is similar to a quantum Otto heat engine other than a quantum isochoric process is replaced by the quantum measurement. We discuss two identical Bosons case and two interacting particles case, respectively. For two Bosons, we find the efficiency is same to a single-particle case but the work output is enhanced. It tends to classical-like result in low temperature regime and exhibits strong quantum effects in high temperature regime, which is counterintuitive. For two interacting qubits, we show the work done is always suppressed by the coupling. The efficiency can be improved under certain conditions in local measurement case and is same to a single-particle case when Bell measurement is done.

Unruh quantum Otto heat engine with level degeneracy

We investigate the Unruh quantum Otto heat engine with level degeneracy. An effectively two-level system, where the ground state is non-degenerate and the excited state is n-fold degenerate, is acting as the working substance, and the vacuum of massless free scalar field serves as a thermal bath via the Unruh effect. We calculate the heat and work at each step of the Unruh quantum Otto cycle and study the features of the heat engine. The efficiency of the heat engine depends only on the excited energy values of the two-level system, not on its level degeneracy. However, the degeneracy acts as a kind of thermodynamic resource and helps us to extract more work than in the non-degenerate case. The extractable work has a finite upper bound, corresponding to n→∞.

Boosting the performance of quantum Otto heat engines.

To optimize the performance of a heat engine in a finite-time cycle, it is important to understand the finite-time effect of thermodynamic processes. Previously, we have shown that extra work is needed to complete a quantum adiabatic process in finite time, and proved that the extra work follows a C/τ^{2} scaling for long control time τ. There the oscillating part of the extra work is neglected due to the complex energy-level structure of the particular quantum system. However, such oscillation of the extra work cannot be neglected in some quantum systems with simple energy-level structure, e.g., the two-level system or the quantum harmonic oscillator. In this paper, we build the finite-time quantum Otto engine on these simple systems, and find that the oscillating extra work leads to a jagged edge in the constraint relation between the output power and the efficiency. By optimizing the control time of the adiabatic processes, the oscillation in the extra work is utilized to enhance the maximum power and the efficiency. We further design special control schemes with the zero extra work at the specific control time. Compared to the linear control scheme, these special control schemes of the finite-time adiabatic process improve the maximum power and the efficiency of the finite-time Otto engine.

Quantum mechanical bound for efficiency of quantum Otto heat engine.

The second law of thermodynamics holds that the efficiency of heat engines, classical or quantum, cannot be greater than the universal Carnot efficiency. We discover another bound for the efficiency of a quantum Otto heat engine consisting of a harmonic oscillator. Dynamics of the engine is governed by the Lindblad equation for the density matrix, which is mapped to the Fokker-Planck equation for the quasiprobability distribution. Applying stochastic thermodynamics to the Fokker-Planck equation system, we obtain the ℏ-dependent quantum mechanical bound for the efficiency. It turns out that the bound is tighter than the Carnot efficiency. The engine achieves the bound in the low-temperature limit where quantum effects dominate. Our work demonstrates that quantum nature could suppress the performance of heat engines in terms of efficiency bound, work, and power output.

Coupled quantum Otto heat engine and refrigerator with inner friction

We investigate two coupled spins 1/2 in a magnetic field as the working substance of the quantum Otto cycle. In the quantum adiabatic strokes, finite-time parametric transformations are employed either in the coupling strength or in the magnetic field. The operation regimes, where the mode of the cycle is a refrigerator or a heat engine, are explored. The role of the total allocated time to the quantum adiabatic stages on the performance of the quantum Otto refrigerator and the heat engine is investigated in detail. The finite-time adiabatic transformations are found to increase the Shannon entropy which is quantum in origin. The effect known as the inner friction is found to negatively effect the performances of the quantum heat engine and the refrigerator. The strong frictional losses are also found to induce inactive operation regimes where the mode of the cycle is neither a refrigerator nor a heat engine.