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arXiv:2008.05002

Energy Optimization Of Two-Level Quantum Otto Machines

Satnam Singh, Obinna Abah

Published Mar 14, 2022• 6 citations
arXivHTMLPDF

Abstract

Abstract We present the quantum Otto machine under different optimization criterion when function either as a heat engine or a refrigerator. We examine the optimal performance of the heat engine and refrigerator depending on their efficiency, output power and maximum entropy production. For heat engine case, we obtain the expression for the upper and lower bounds efficiencies at maximum power and maximum ecological function. The optimal ecological performance is laying between the maximum efficiency and the maximum power output. On the other hand, the quantum Otto refrigerator coefficient of performance is optimized for three different criterion – cooling power, χ criterion(product of performance and power) and ecological function. We further study the dimen-sionless power loss to the cold reservoir when the machine is operating as a heat engine as well as its counterpart for the refrigerator case. We find that the maximum operation of the heat engine (refrigerator) cycle is when optimized with respect to hot (cold) reservoir frequency.

DOI
10.21203/rs.3.rs-1443501/v1

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Abstract We present the quantum Otto machine under different optimization criterion when function either as a heat engine or a refrigerator. We examine the optimal performance of the heat engine and refrigerator depending on their efficiency, output power and maximum entropy production. For heat engine case, we obtain the expression for the upper and lower bounds efficiencies at maximum power and maximum ecological function. The optimal ecological performance is laying between the maximum efficiency and the maximum power output. On the other hand, the quantum Otto refrigerator coefficient of performance is optimized for three different criterion – cooling power, χ criterion(product of performance and power) and ecological function. We further study the dimen-sionless power loss to the cold reservoir when the machine is operating as a heat engine as well as its counterpart for the refrigerator case. We find that the maximum operation of the heat engine (refrigerator) cycle is when optimized with respect to hot (cold) reservoir frequency.
Abstract We consider a quantum endoreversible Otto engine cycle and its inverse operation-Otto refrigeration cycle, employing two-level systems as the working substance and operating in dual-squeezed reservoirs. We demonstrate that the efficiency of heat engines at maximum work output and the coefficient of performance for refrigerators at the maximum χ criterion will degenerate to η − = η C/(2 – η C) and ε − = ( 9 + 8 ε C − 3 ) / 2 when symmetric squeezing is satisfied, respectively. We also investigated the influences of squeezing degree on the performance optimization of quantum Otto heat engines at the maximum work output and refrigerators at the maximum χ criterion. These analytical results show that the efficiency of heat engines at maximum work output and the coefficient of performance for refrigerators at the maximum χ criterion can be improved, reduced or even inhibited in asymmetric squeezing. Furthermore, we also find that the efficiency of quantum Otto heat engines at maximum work output is lower than that obtained from the Otto heat engines based on a single harmonic oscillator system. However, the coefficient of performance of the corresponding refrigerator is higher.
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 and pawl model which is a steady-state classical heat engine. For the sudden switch of frequencies, we obtain loop-like behavior of the efficiency-work curve, which is characteristic of irreversible heat engines. Finally, we discuss the behavior of cooling power at maximum Ω function.
Abstract We investigate the optimal performance of the quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator under a trade-off figure of merit for both adiabatic and nonadiabatic (sudden-switch) frequency modulations. For heat engines (refrigerators), the chosen trade-off figure of merit is an objective function defined by the product of efficiency (coefficient of performance) and work output (cooling load), thus representing a compromise between them. We obtain analytical expressions for the efficiency and coefficient of performance of the harmonic Otto cycle for the optimal performance of the thermal machine in various operational regimes. Particularly, in the sudden-switch regime, we discuss the implications of the nonadiabatic driving on the performance of the thermal machine under consideration and obtain analytic expressions for the maximum achievable efficiency and coefficient of performance of the harmonic Otto thermal machine. Particularly, we show that the quantum harmonic Otto cycle driven by sudden-switch protocol cannot work as a heat engine or refrigerator in the low-temperature limit. Finally, we show that in the high-temperature limit, the frictional effects give rise to a richer structure of the phase diagram of the harmonic Otto cycle. We identify the parametric regime for the operation of the Otto cycle as a heat engine, refrigerator, accelerator, and heater.
We study the optimal performance of a three-level quantum refrigerator using two different objective functions: cooling power and χ function. For both cases, we obtain general expressions for the coefficient of performance (COP) and derive its well-known lower and upper bounds for the limiting cases when the ratio of system-bath coupling constants at the hot and cold contacts approaches infinity and zero, respectively. We also show that the cooling power can be maximized with respect to one control frequency, while χ function can be maximized globally with respect to two control frequencies. Additionally, we show that in the low-temperature regime, our model of refrigerator can be mapped to Feynman's ratchet and pawl model, a classical mesoscopic heat engine. In the parameter regime where both cooling power and χ function can be maximized, we compare the cooling power of the quantum refrigerator at maximum χ function with the maximum cooling power.
We present a detailed study of a three-level quantum heat engine operating at maximum efficient power function, a trade-off objective function defined by the product of the efficiency and power output of the engine.The efficient power function represents a trade-off between the power output and efficiency of a heat engine.Engines working in the maximum efficient power regime operate at finite power, with finite efficiency lying in between the regimes of maximum power and maximum efficiency (Carnot efficiency).First, for near-equilibrium conditions, we find a general expression for the efficiency and establish the universal nature of efficiency at maximum power and maximum efficient power.Then in the high-temperature limit, optimizing with respect to one parameter while constraining the other one, we obtain the lower and upper bounds on the efficiency for both strong as well as weak matter-field coupling conditions.Except for the weak matter-field coupling condition, the obtained bounds on the efficiency exactly match with the bounds already known for some models of classical heat engines.Further for weak matter-field coupling, we derive some new bounds on the efficiency of the engine which lie beyond the range covered by bounds obtained for strong matter-field coupling.We conclude by comparing the performance of our three-level quantum heat engine in maximum power and maximum efficient power regimes and show that the engine operating at maximum efficient power produces at least 88.89% of the maximum power output while considerably reducing the power loss due to entropy production.Finally, to complete our analysis, we review the experimental setup of a recently realized effective three-level quantum engine.
We consider the finite-time operation of a quantum heat engine whose working substance is composed of a two-level atomic system. The engine cycle, consisting of two quantum adiabatic and two quantum isochoric (constant-frequency) processes and working between two heat reservoirs at temperatures Th{T}_{h}Th​ and Tc{T}_{c}Tc​(<(<(<Th){T}_{h})Th​), is a quantum version of the classical Otto cycle. By optimizing the power output with respect to two frequencies, we obtain the efficiency at maximum power output (EMP) and analyze numerically the effects of the times taken for two adiabatic and two isochoric processes on the EMP. In the absence of internally dissipative friction, we find that the EMP is bounded from the upper side by a function of the Carnot efficiency ${\ensuremath{\eta}}_{C}$, ${\ensuremath{\eta}}_{+}={\ensuremath{\eta}}_{C}^{2}/[{\ensuremath{\eta}}_{C}\ensuremath{-}(1\ensuremath{-}{\ensuremath{\eta}}_{C})\mathrm{ln}(1\ensuremath{-}{\ensuremath{\eta}}_{C})]$, with ${\ensuremath{\eta}}_{C}=1\ensuremath{-}{T}_{c}/{T}_{h}$. This analytic expression is confirmed by our exact numerical result and is identical to the one derived in an engine model based on a mesoscopic or macroscopic system. If the internal friction is included, we find that the EMP decreases as the friction coefficient increases.