27.11.2019 Thermodynamics of controlling quantum systems: an application to quantum heat engines

Last two decades have witnessed a rapid development of quantum information theory which mainly, and in the most general sense, deals with the problem of manipulating quantum systems in order to process information. Due to inherent fragility of quantum systems under the effect of an environment, such manipulations need to be performed faster than the time scale within which the subject system decoheres. In addition, dictated by the quantum adiabatic theorem, adiabatic processes in quantum systems have the necessity of being performed very slowly. Nevertheless, there are various techniques to ensure fast and robust of control of these systems, which eventually guarantee that the system reaches the desired target state. Recently, such techniques that fasten an otherwise slow quantum process are known under the name of shortcuts to adiabaticity (STA). However, all STA methods require an additional external control on the system, which is expected to have an energetic cost that needs to be addressed carefully.

Moreover, quantum thermodynamics is an emerging field of research that aims to explore the thermodynamics of non-equilibrium processes in quantum systems using mainly the tools of quantum information theory. Following the developments in this field, there are various proposals on making of an Otto engine with its working medium constituted by quantum systems. A standard Otto cycle consists of four stages: isochoric heating and cooling stages, together with isentropic expansion and compression stages. The efficiency of this engine attains its maximum when the cycle is performed adiabatically such that the compression and expansion of the working medium is made quasi-statically to ensure there are no unwanted transitions between the energy levels. This, however, implies that the engine will have a vanishing power output due to infinitely long time it takes to complete the cycle. It is possible to improve the performance of these engines by employing techniques of STA which allows one to mimic an adiabatic transformation at a finite-time by externally driving the system. We investigate the trade-offs between these STA costs and the thermodynamic figures of merit of a finite-time quantum Otto engine which have qubits as its working medium.