  We present a detailed study of an asymmetrically driven quantum Otto engine
with a time-dependent harmonic oscillator as its working medium. We obtain
analytic expressions for the upper bounds on the efficiency of the engine for
two different driving schemes having asymmetry in the expansion and compression
work strokes. We show that the Otto cycle under consideration cannot operate as
a heat engine in the low-temperature regime. Then, we show that the friction in
the expansion stroke is significantly more detrimental to the performance of
the engine as compared to the friction in the compression stroke. Further, by
comparing the performance of the engine with sudden expansion, sudden
compression, and both sudden strokes, we uncover a pattern of connections
between the operational points, and we indicate the optimal operation regime
for each case. Finally, we analytically characterize the complete phase diagram
of the Otto cycle for both driving schemes and highlight the different
operational modes of the cycle as a heat engine, refrigerator, accelerator, and
heater.
