The fast-developing quantum technology is propelling thermal machine, which lies at the heart of thermodynamics, into a new golden era. Being stochastic because of the non-negligible thermal and quantum fluctuations, the efficiency and power of a finite-time quantum heat engine exhibit a trade-off, preventing the simultaneous achievement of high power and high efficiency. Conventional studies treat the statistics of a heat engine by assuming canonical thermalization, which is valid only under weak-coupling conditions. We here investigate the noncanonical effect on the statistics of the efficiency and power for a finite-time quantum Otto cycle. It is revealed that their average values and variances are highly controllable by engineering the energy spectrum structure of the composite system consisting of the working substance and the bath. Near the quantum critical point induced by the formation of a bound state in the energy spectrum, the average efficiency and power can be boosted simultaneously, meanwhile, both of their variances are decreased. Deepening our understanding of the usefulness of quantum reservoir engineering in thermodynamics, our result lays the foundation for the realization of efficient and stable quantum energy devices.
The fast-developing quantum technology is propelling thermal machine, which lies at the heart of thermodynamics, into a new golden era. Being stochastic because of the non-negligible thermal and quantum fluctuations, the efficiency and power of a finite-time quantum heat engine exhibit a trade-off, preventing the simultaneous achievement of high power and high efficiency. Conventional studies treat the statistics of a heat engine by assuming canonical thermalization, which is valid only under weak-coupling conditions. We here investigate the noncanonical effect on the statistics of the efficiency and power for a finite-time quantum Otto cycle. It is revealed that their average values and variances are highly controllable by engineering the energy spectrum structure of the composite system consisting of the working substance and the bath. Near the quantum critical point induced by the formation of a bound state in the energy spectrum, the average efficiency and power can be boosted simultaneously, meanwhile, both of their variances are decreased. Deepening our understanding of the usefulness of quantum reservoir engineering in thermodynamics, our result lays the foundation for the realization of efficient and stable quantum energy devices.
The quantum heat engines have drawn much attention due to miniaturization of devices recently. We study the dynamics of the quantum Otto heat engine using the driven-dissipative Schrödinger equation. Starting from different initial states, we simulate the time evolutions of the internal energy, power and heat-work conversion efficiency. The initial state impacts on these thermodynamic quantities before the Otto cycle reaches stable. In the transition period, the efficiency and power may be higher or lower than the corresponding values in the cyclostationary state. Remarkably, the efficiency could surpass the Otto limit and even the Carnot limit and the power could be much higher than the rated power. The efficiency anomaly is due to the energy in the initial state. Thus, we suggest that periodically pumping could take the similar role of a hot bath but could be manipulated flexibly. Furthermore, we propose a new quantum engine working in a single reservoir to convert the pump energy into mechanical work. This manipulative engine could potentially be applied to working in the microenvironments without a large temperature difference, such as the biological tissues in vivo. Our protocol is expected to model a new quantum engine with the advantage of applicability and controllability.
With the development of any quantum technology comes a need for precise control of quantum systems. Here, we evaluate the impact of control noise on a quantum Otto cycle. While it is postulated that noiseless quantum engines can approach maximal Otto efficiency in finite times, the existence of white noise on the controls is shown to negatively affect average engine performance. Two methods of quantum enhancement, counterdiabatic driving and quantum lubrication, are implemented and found to improve the performance of the noisy cycle only in specified parameter regimes. To gain insight into performance fluctuations, projective energy measurements are used to construct a noise-averaged probability distribution without assuming full thermalization or adiabaticity. From this, the variances in thermodynamic currents are observed to increase as average power and efficiency improve, and are also shown to be consistent with known bounds from thermodynamic uncertainty relations. Lastly, by comparing the average functioning of the unmonitored engine to a projectively measured engine cycle, the role of coherence in work extraction for this quantum engine model is investigated.
Thermodynamic constraints impose a trade-off between power and efficiency in heat engines, preventing the simultaneous achievement of high power and high efficiency. For classical microscopic engines, explicit inequalities have been discovered, demonstrating the inherent inevitability of this power-efficiency trade-off. However, extensions of these results to quantum engines have so far been limited to cases of slow operation. In this study, we derive a power-efficiency trade-off relation for a paradigmatic quantum engine operating within a finite time, specifically the Otto cycle of a quantum harmonic oscillator. By utilizing a phase-space approach based on quasiprobability representations, we establish a universal trade-off relation applicable to arbitrary time-dependent protocols during the adiabatic processes. Our results reveal that the power of the quantum engine vanishes as the efficiency approaches the quantum-mechanical efficiency bound, which is stricter than the Carnot bound. Furthermore, we identify the conditions under which the upper bound is attained, which indicate maximum power is achieved when the generation of quantum coherence is reduced, and the difference in time durations of the isochoric processes increases. These findings are validated through numerical calculations, which confirm their applicability across various types of protocols for heat engine cycles.
Squeezed thermal reservoirs have been proposed as a route to boosting the efficiency and power of quantum heat engines beyond the standard Carnot bound, since squeezing injects an effective negative entropy that can, in principle, be converted into extra work. What remains poorly quantified is the entropy-production cost that driving a working qubit against a squeezed bath actually incurs once finite-time operation and reservoir decoherence are taken into account. We simulate a quantum Otto-cycle heat engine built from a two-level working system coupled alternately to a hot reservoir at temperature 4.2 K, squeezed with squeezing parameter r ranging from 0 to 1.2, and an unsqueezed cold reservoir at 0.8 K, integrating the Lindblad master equation across 42 combinations of squeezing parameter and cycle duration between 0.05 and 2.0 (in units of the inverse qubit gap). At r = 0, mean entropy production per cycle was 0.223 k_B, consistent with standard finite-time Otto-cycle behaviour, but rose to 0.361 k_B at r = 1.2, a 62% increase, even as extractable work per cycle increased by 41%, from 0.184 to 0.259 (in units of the qubit gap). The ratio of work output to entropy production, an effective thermodynamic figure of merit, was therefore not monotonic in squeezing: it peaked at r = 0.6, where work per unit entropy produced reached 0.98, 15% above the unsqueezed value of 0.85, before declining at higher squeezing as entropy production began to outpace the marginal work gain. Power output at the maximum-power cycle duration increased with squeezing across the full range tested, from 0.31 (gap units) at r = 0 to 0.52 at r = 1.2, a 68% gain, but efficiency at maximum power fell from 0.41 to 0.33 over the same range, a trade-off traced out in detail in Table 1. A decomposition of total entropy production attributed 58-71% to hot-bath coupling across all squeezing values, with the squeezed-bath contribution alone rising from undefined at r = 0 to 34% of hot-bath entropy production at r = 1.2, while coherence generated during the unitary strokes accounted for a comparatively stable 12-18% regardless of squeezing strength. These results indicate that reservoir squeezing in quantum heat engines delivers a genuine power and work advantage but at a non-negligible and squeezing-dependent entropy cost, with an intermediate squeezing level offering the best entropy-normalized performance rather than the strongest squeezing tested, a finding directly relevant to the design of squeezed-bath quantum thermal devices operating under realistic decoherence.
We investigate the thermodynamics and fluctuations of a finite-time quantum Otto engine alter- natively driven by a hot-squeezed and a cold thermal reservoir. We show that reservoir squeezing significantly enhances the performance by increasing the thermodynamic efficiency and the power and enables higher stability by decreasing the relative power fluctuations and speeding up the convergence of quantum efficiency to its most probable value. We also demonstrate the counterintuitive result that the efficiency can be larger than the Otto limit in the finite-time operation. Experimental demonstration of this quantum heat engine can be available, based on a single-electron spin pertaining to a trapped 40Ca+ ion [D. von Lindenfels et al., Phys. Rev. Lett. 123, 080602 (2019)]. We provide a general framework for reliably studying the finite-time nanoengine in finite-time operation which accounts for quantum friction and coherence, deriving important insights into the thermodynamic behaviors beyond the classical thermal machines.
Enhancement of thermal efficiency of quantum heat engines has been discussed mainly in terms of quantumness of working substances. In the present study, we propose as another possibility to utilize a quantum-mechanical (reversible) feature of system-reservoir interaction, which reveals itself in the short-time regime as a non-Markovian effect on the reduced dynamics of the substance, before asymptotically approaching irreversible processes. For this purpose, we study a limit cycle of the quantum Otto engine comprising a working two-level system and two reservoirs, including the non-Markovian effect for the finite-time isochoric processes while the work-extracting processes are kept quantum adiabatic. Assuming that the system interacts weakly with the reservoirs consisting of infinite bosons, we find a parameter regime beyond the Carnot efficiency in which a positive work is extracted by including a non-Markovian effect called energy backflow. We also find that the interaction energy is finite and contributes to the positive work even for the weak interaction. The work diminishes if we include into the work the energy for detaching the working substance from reservoirs.