A finite-time quantum Otto engine with tunnel coupled one-dimensional Bose gases

Abstract

We undertake a theoretical study of a finite-time quantum Otto engine cycle driven by inter-particle interactions in a weakly interacting one-dimensional Bose gas in the quasicondensate regime. Utilizing a $c$-field approach, we simulate the entire Otto cycle, i.e. the two work strokes and the two equilibration strokes. More specifically, the interaction-induced work strokes are modelled by treating the working fluid as an isolated quantum many-body system undergoing unitary evolution. The equilibration strokes, on the other hand, are modelled by treating the working fluid as an open quantum system tunnel-coupled to another quasicondensate which acts as either the hot or cold reservoir, albeit of finite size. We find that, unlike a uniform 1D Bose gas, a harmonically trapped quasicondensate cannot operate purely as a \emph{heat} engine; instead, the engine operation is enabled by additional \emph{chemical} work performed on the working fluid, facilitated by the inflow of particles from the hot reservoir. The microscopic treatment of dynamics during equilibration strokes enables us to evaluate the characteristic operational time scales of this Otto chemical engine, crucial for characterizing its power output, without any \emph{ad hoc} assumptions about typical thermalization timescales. We analyse the performance and quantify the figures of merit of the proposed Otto chemical engine, finding that it offers a favourable trade-off between efficiency and power output, particularly when the interaction-induced work strokes are implemented via a sudden quench. We further demonstrate that in the sudden quench regime, the engine operates with an efficiency close to the near-adiabatic (near maximum efficiency) limit, while concurrently achieving maximum power output.