  We demonstrate that under specific conditions, a finite-time quantum Otto
engine, employing a spin-1/2 particle as the working substance, despite
undergoing incomplete Otto cycles, can achieve higher efficiency than an ideal
quantum Otto engine. A finite-time quantum Otto engine refers to an Otto engine
where the two isochoric strokes are prematurely terminated before reaching
thermal equilibrium with their respective hot and cold baths. We observe that
the enhancement of efficiency of a finite-time quantum Otto engine over the
ideal one can be realized by adjusting the initial temperature of the working
substance within the temperature range of the hot and cold baths. We also find
that incorporating an auxiliary qubit, and activating specific interactions
between the single-qubit working substance and the auxiliary one, can enhance
the efficiency of a finite-time as well as an ideal quantum Otto engine.
Furthermore, we analyze the impact of glassy disorder within the system-bath
coupling during the two isochoric strokes on the efficiency of a finite-time
quantum Otto engine. We find that as strength of disorder increases, efficiency
of a finite-time quantum Otto engine tends to decrease, albeit with relatively
modest reduction even for strong disorder. However, the advantage in efficiency
of the finite-time quantum Otto engine over the ideal one, obtained by tuning
the initial state temperature, and the efficiency enhancement obtained by
incorporating an auxiliary over the without-auxiliary scenario, persists even
in presence of substantial disorder. Additionally, we show that while this
disorder does not affect the ideal efficiency, it does influence the duration
of isochoric strokes needed for an Otto engine to reach ideal efficiency. This
stroke duration remains nearly constant until a specific disorder strength,
beyond which it increases rapidly.
