  We show that strong parametric driving of a quantum harmonic oscillator
coupled to a thermal bath allows one to distinguish between different
microscopic models for the oscillator-bath coupling. We consider a bath with an
Ohmic spectral density and a model where the system-bath interaction can be
tuned continuously between position and momentum coupling via the coupling
angle $\alpha$. We derive a master equation for the reduced density operator of
the oscillator in Born-Markov approximation and investigate its quasi-steady
state as a function of the driving parameters, the temperature of the bath and
the coupling angle $\alpha$. We find that the time-averaged variance of
position and momentum exhibits a strong dependence on these parameters. In
particular, we identify parameter regimes that maximise the $\alpha$-dependence
and provide an intuitive explanation of our results.
