Efficiency at maximum power of a quantum heat engine based on two coupled oscillators

Abstract

We propose and theoretically investigate a system of two coupled harmonic oscillators as a heat engine. We show how these two coupled oscillators within undamped regime can be controlled to realize an Otto cycle that consists of two adiabatic and two isochoric processes. During the two isochores the harmonic system is embedded in two heat reservoirs at constant temperatures T(h) and T(c)(<T(h)), respectively, and it is tuned slowly along a protocol to realize an adiabatic process. To illustrate the performance in finite time of the quantum heat engine, we adopt the semigroup approach to model the thermal relaxation dynamics along the two isochoric processes, and we find the upper bound of efficiency at maximum power (EMP) η* to be a function of the Carnot efficiency η(C)(=1-T(c)/T(h)): η*≤η(+)≡η(C)(2)/[η(C)-(1-η(C))ln(1-η(C))], identical to those previously derived from ideal (noninteracting) microscopic, mesoscopic, and macroscopic systems.

Implications of Coupling in Quantum Thermodynamic Machines

“…Here it is important to note that very recently, the performance of coupled harmonic oscillators as a heat engine is studied [30]. But, in contrast to the present work, there the interaction has been considered only between the position degrees of freedom of two oscillators.…”

“…Otto cycle with a single harmonic oscillator (or a spin system) constituting the working medium of the engine is studied in different works [27,30,34,35,38,39]. Here we briefly review this.…”

“…Here, η A and η B are same as that obtained in coupled oscillators given in Equation (30). Therefore, the efficiency of the engine is given as…”

“…The performance of coupled quantum systems as heat engines have been studied widely in recent past [24][25][26][27][28][29][30]. Work and efficiency are two important quantities to characterize the performance of a heat engine.…”

“…But, in contrast to the present work, there the interaction has been considered only between the position degrees of freedom of two oscillators. Furthermore, the authors in [30] have done the efficiency analysis for two different modes separately. But, the actual efficiency of the system has to be defined by the ratio of total work (done by both the modes) to the total heat which we analyze here.…”