  In this paper we examine some foundational issues of a class of quantum
engines where the system consists of a single quantum parametric oscillator,
operating in an Otto cycle consisting of 4 stages of two alternating phases:
the isentropic phase is detached from any bath (thus a closed system) where the
natural frequency of the oscillator is changed from one value to another, and
the isothermal phase where the system (now rendered open) is put in contact
with one or two squeezed baths of different temperatures, whose nonequilibrium
dynamics follows the Hu-Paz-Zhang (HPZ) master equation for quantum Brownian
motion. The HPZ equation is an exact nonMarkovian equation which preserves the
positivity of the density operator and is valid for a) all temperatures, b)
arbitrary spectral density of the bath, and c) arbitrary coupling strength
between the system and the bath. Taking advantage of these properties we
examine some key foundational issues of theories of quantum open and squeezed
systems for these two phases of the quantum Otto engines. This include, i) the
nonMarkovian regimes for non-Ohmic, low temperature baths, ii) what to expect
in nonadiabatic frequency modulations, iii) strong system-bath coupling, as
well as iv) the proper junction conditions between these two phases. Our aim
here is not to present ways for attaining higher efficiency but to build a more
solid theoretical foundation for quantum engines of continuous variables
covering a broader range of parameter spaces hopefully of use for exploring
such possibilities.
