  We consider a quantum harmonic oscillator coupled with a graviton bath and
discuss the loss of coherence in the matter sector due to the matter-graviton
vertex interaction. Working in the quantum-field-theory framework, we obtain a
master equation by tracing away the gravitational field at the leading order
$\mathcal{\sim O}(G)$ and $\sim\mathcal{O}(c^{-2})$. We find that the
decoherence rate is proportional to the cube of the harmonic trapping frequency
and vanishes for a free particle, as expected for a system without a mass
quadrupole. Furthermore, our quantum model of graviton emission recovers the
known classical formula for gravitational radiation from a classical harmonic
oscillator for coherent states with a large occupation number. In addition, we
find that the quantum harmonic oscillator eventually settles in a steady state
with \emph{a remnant coherence} of the ground and first excited states. While
classical emission of gravitational waves would make the harmonic system loose
all of its energy, our quantum field theory model does not allow the number
states $\vert 1\rangle$ and $\vert 0\rangle$ to decay via graviton emission. In
particular, the superposition of number states
$\frac{1}{\sqrt{2}}\left[\vert0\rangle+\vert1\rangle\right]$ is a steady state
and never decoheres.
