We study the finite-time effects in a quantum Otto cycle where a collective spin system is used as the working fluid. Starting from a simple one-qubit system we analyze the transition to the limit cycle in the case of a finite-time thermalization. If the system consists of a large sample of independent qubits interacting coherently with the heat bath, then the super-radiant equilibration is observed. We show that this phenomenon can boost the power of the engine. Mutual interaction of qubits in the working fluid is modeled by the Lipkin-Meshkov-Glick Hamiltonian. We demonstrate that in this case the quantum phase transitions for the ground and excited states may have a strong negative effect on the performance of the machine. Conversely, by analyzing the work output we can distinguish between the operational regimes with and without a phase transition.
We study the finite-time effects in a quantum Otto cycle where a collective spin system is used as the working fluid. Starting from a simple one-qubit system we analyze the transition to the limit cycle in the case of a finite-time thermalization. If the system consists of a large sample of independent qubits interacting coherently with the heat bath, then the super-radiant equilibration is observed. We show that this phenomenon can boost the power of the engine. Mutual interaction of qubits in the working fluid is modeled by the Lipkin-Meshkov-Glick Hamiltonian. We demonstrate that in this case the quantum phase transitions for the ground and excited states may have a strong negative effect on the performance of the machine. Conversely, by analyzing the work output we can distinguish between the operational regimes with and without a phase transition.
We have studied the performance of a measurement-based quantum Otto engine (QOE) in a working system of two spins coupled by Heisenberg anisotropic interaction. A nonselective quantum measurement fuels the engine. We have calculated thermodynamic quantities of the cycle in terms of the transition probabilities between the instantaneous energy eigenstates, and also between the instantaneous energy eigenstates and the basis states of the measurement, when the unitary stages of the cycle operate for a finite time τ. The efficiency attains a large value in the limit of τ→0 and then gradually reaches the adiabatic value in a long-time limit τ→∞. For finite values of τ and for anisotropic interaction, an oscillatory behavior of the efficiency of the engine is observed. This oscillation can be interpreted in terms of interference between the relevant transition amplitudes in the unitary stages of the engine cycle. Therefore, for a suitable choice of timing of the unitary processes in the short time regime, the engine can have a higher work output and less heat absorption, such that it works more efficiently than a quasistatic engine. In the case of an always-on heat bath, in a very short time, the bath has a negligible effect on its performance.
Abstract We undertake a theoretical study of a finite-time quantum Otto engine cycle driven by inter-particle interactions in a weakly interacting one-dimensional (1D) Bose gas in the quasicondensate regime. Utilizing ac-field approach, we simulate the entire Otto cycle, i.e. the two work strokes and the two equilibration strokes. More specifically, the interaction-induced work strokes are modelled by treating the working fluid as an isolated quantum many-body system undergoing unitary evolution. The equilibration strokes, on the other hand, are modelled by treating the working fluid as an open quantum system tunnel-coupled to another quasicondensate which acts as either the hot or cold reservoir, albeit of finite size. We find that, unlike a uniform 1D Bose gas, a harmonically trapped quasicondensate cannot operate purely as aheatengine; instead, the engine operation is enabled by additionalchemicalwork performed on the working fluid, facilitated by the inflow of particles from the hot reservoir. The microscopic treatment of dynamics during equilibration strokes enables us to evaluate the characteristic operational time scales of this Ottothermochemicalengine, crucial for characterizing its power output, without any ad hoc assumptions about typical thermalization timescales. We analyse the performance and quantify the figures of merit of the proposed Otto thermochemical engine, finding that it offers a favourable trade-off between efficiency and power output, particularly when the interaction-induced work strokes are implemented via a sudden quench. We further demonstrate that in the sudden quench regime, the engine operates with an efficiency close to the near-adiabatic (near maximum efficiency) limit, while concurrently achieving maximum power output.
We investigate a finite-time quantum Otto engine within the framework of gauge-invariant quantum thermodynamics, using the Lipkin-Meshkov-Glick model as the working medium. In this formulation, thermodynamic quantities are defined on equivalence classes of thermodynamically indistinguishable states, leading naturally to gauge-invariant notions of work, heat, entropy, and efficiency. We derive explicit expressions for these quantities and show that the usual work performed during the unitary strokes decomposes into an invariant contribution, associated with changes in the instantaneous energy spectrum and populations, and a coherent contribution arising from finite-time quantum coherences. This decomposition induces the corresponding splittings of engine efficiency and entropy production, providing a geometric interpretation of finite-time irreversibility and clarifying the role of coherence in work extraction. By analyzing the cycle's dependence on driving speed and system size, we identify the engine's operating region and investigate the influence of criticality. We show that crossing the critical region substantially reduces the parameter space in which the cycle operates as a heat engine. At the same time, whenever the engine condition remains satisfied, the discrepancy between the conventional and gauge-invariant descriptions becomes strongly suppressed, indicating that the gauge-invariant sector predominantly carries the extracted work. These results establish a direct connection between gauge-invariant thermodynamics, finite-time irreversibility, and work extraction in many-body quantum thermal machines.
We discuss the limit cycle regime of a finite-time quantum Otto cycle with a frictionless two-dimensional anisotropic Ising model as the working fluid. From Onsager's exact equilibrium solution, we first find optimal parameters for the operational modes of work extraction and cooling for infinitely slow cycles. The equilibrium points in these optimal cycles correspond to different phases of the model, such that the nonequilibrium dynamics during the cycle bypasses the phase transition. Finite-time cycles allow for finite power extraction or cooling currents, but for such cycles, we point out that-already within the regime of weak system-reservoir coupling-energetic changes of the system during dissipative strokes may contain a significant portion of coupling and decoupling control work and should thus not be directly identified with heat. For ultrafast cycles, the required control work spoils performance, such that to maximize work extraction or cooling heat per cycle time, there is an optimal cycle duration. We also find that net-zero-energy transitions may lead to undesired reservoir heating.
We study a driven harmonic oscillator operating an Otto cycle by strongly interacting with two thermal baths of finite size. Using the tools of Gaussian quantum mechanics, we directly simulate the dynamics of the engine as a whole, without the need to make any approximations. This allows us to understand the non-equilibrium thermodynamics of the engine not only from the perspective of the working medium, but also as it is seen from the thermal baths' standpoint. For sufficiently large baths, our engine is capable of running a number of perfect cycles, delivering finite power while operating very close to maximal efficiency. Thereafter, having traversed the baths, the perturbations created by the interaction abruptly deteriorate the engine's performance. We additionally study the correlations generated in the system, and, in particular, we find a direct connection between the build up of bath–bath correlations and the degradation of the engine's performance over the course of many cycles.
Heat engines usually operate by exchanging heat with thermal baths at different (positive) temperatures. Nonthermal baths may, however, lead to a significant performance boost. We here experimentally analyze the power output of a single-atom quantum Otto engine realized in the quasi-spin states of individual Cesium atoms interacting with an atomic Rubidium bath. From measured time-resolved populations of the quasi-spin state, we determine the dynamics during the cycle of both the effective spin temperature and of the quantum fluctuations of the engine, which we quantify with the help of the Shannon entropy. We find that power is enhanced in the negative temperature regime, and that it reaches its maximum value at half the maximum entropy. Quantitatively, operating our engine at negative effective temperatures increases the power by up to 30% compared to operation at positive temperatures, including even the case of infinite temperature. At the same time, entering the negative temperature regime allows for reducing the entropy to values close to zero, offering highly stable operation at high power output. We furthermore numerically investigate the influence of the size of the Hilbert space on the performance of the quantum engine by varying the number of levels of the working medium. Our work thereby paves the way to fluctuation control in the operation of high-power and efficient single-atom quantum engines.