  We study the coherence dynamics of a qubit coupled to a harmonic oscillator
with both linear and quadratic interactions. As long as the linear coupling
strength is much smaller than the oscillator frequency, the long time behavior
of the coherence is dominated by the quadratic coupling strength $g_2$. The
coherence decays and revives at a period $2\pi/g_2$, with the width of
coherence peak decreases as the temperature increases, hence providing a way to
measure $g_2$ precisely without cooling. Unlike the case of linear coupling,
here the coherence dynamics never reduces to the classical limit in which the
oscillator is classical. Finally, the validity of linear coupling approximation
is discussed and the coherence under Hahn-echo is evaluated
