Loss of coherence and coherence protection from a graviton bath

We consider a quantum harmonic oscillator coupled with a graviton bath. We discuss the loss of coherence in the matter sector due to the matter-graviton vertex interaction, which leads to a loss of coherence provided that the matter-wave system is allowed to emit gravitons by the kinematics. Working in the quantum-field-theory framework, we obtain a master equation by tracing away the gravitational field at the leading order ∼O(G) and ∼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 a remnant coherence of the ground and first excited states.