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 $^{40}\mathrm{Ca}^{+}$ 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.
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.
We investigate the thermodynamics and fluctuations of a finite-time quantum Otto engine alternatively 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. These results are explained by our theoretical analysis that incorporates the effect of reservoir squeezing on the irreversibility associated with quantum friction and coherence due to finite time. An experimental scheme for realizing this quantum heat engine is proposed using a single-electron spin pertaining to a trapped 40Ca+ ion. We provide a general framework for reliably studying the finite-time quantum heat engine and derive important insights into the novel thermodynamic behaviors beyond the classical thermal machines.
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 cycle, which are dependent on the time duration along each process. With these, we derive the analytical expressions for the thermodynamic quantities of the two-level heat engine, such as total work, thermodynamic efficiency, entropy production, and work fluctuations, in which effects of coherence, squeezing, inner friction and finite-time heat exchange are included. We then numerically determine the thermodynamic quantities and the fluctuations using the parameters employed in the experimental implementation. Our results clarify the role of coherence and squeezing in the performance and fluctuations in the quantum Otto engines.
We consider the finite-time performance of a quantum Otto engine working between a hot squeezed and a cold thermal bath at inverse temperatures ${\ensuremath{\beta}}_{h}$ and ${\ensuremath{\beta}}_{c}(>{\ensuremath{\beta}}_{h})$ with $({k}_{B}\ensuremath{\equiv}1)\ensuremath{\beta}=1/T$. We derive the analytical expressions for work, efficiency, power, and power fluctuations, in which the squeezing parameter is involved. By optimizing the power output with respect to two frequencies, we derive the efficiency at maximum power as ${\ensuremath{\eta}}_{mp}={({\ensuremath{\eta}}_{C}^{\mathrm{gen}})}^{2}/[{\ensuremath{\eta}}_{C}^{\mathrm{gen}}\ensuremath{-}(1\ensuremath{-}{\ensuremath{\eta}}_{C}^{\mathrm{gen}})ln(1\ensuremath{-}{\ensuremath{\eta}}_{C}^{\mathrm{gen}})]$, where the generalized Carnot efficiency ${\ensuremath{\eta}}_{C}^{\mathrm{gen}}$ in the high-temperature or small squeezing limit simplifies to an analytic function of squeezing parameter $\ensuremath{\gamma}$: ${\ensuremath{\eta}}_{C}^{\mathrm{gen}}=1\ensuremath{-}{\ensuremath{\beta}}_{h}/[{\ensuremath{\beta}}_{c}cosh(2\ensuremath{\gamma})]$. Within the context of irreversible thermodynamics, we demonstrate that the expression of efficiency at maximum power satisfies a general form derived from nonlinear steady state heat engines. We show that, the power fluctuations are considerably increased, although the engine efficiency is enhanced by squeezing.
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.
Abstract We work on a comprehensive theoretical investigation of a three-level quantum heat engine operating with engineered squeezed thermal reservoirs. Unlike conventional quantum heat engines that use thermal reservoirs, we demonstrate that squeezed reservoirs can significantly enhance the engine's performance by increasing both efficiency and output power. Using a rigorous open-quantum-system approach, we derive the full Lindblad master equation for a three-level system interacting with hot and cold squeezed thermal baths. Through a detailed analysis of the steady-state thermodynamics, we obtain explicit expressions for heat currents, work output, and efficiency. Our results reveal that moderate squeezing parameters (r≈0.5) combined with optimal squeezing phase (ϕ=π/2) enhance the engine efficiency by up to 40\% compared to the classical Carnot limit for the same temperature ratio. The power output shows a non-monotonic behavior with squeezing, exhibiting an optimal squeezing parameter that maximizes performance. We identify three distinct operational regimes: (i) heat engine regime, (ii) refrigerator regime, and (iii) heat pump regime, which can be tuned by adjusting the squeezing phase. The efficiency at maximum power follows a universal scaling ηMP≈ηCarnot/2+Δη(r), where Δη(r) represents the squeezing-induced enhancement. Our findings provide fundamental insights into the role of non-thermal reservoirs in quantum thermodynamics and offer practical guidelines for designing high-performance quantum heat engines using squeezed light and engineered baths.
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.