Quantum Gravity Signatures of Gravitons in a Squeezed Coherent State on Detectors within a Harmonic Trap Potential

We have studied the quantum gravity signatures that emerge in a gravitational wave detector placed inside a harmonic potential trap, where the quantum state of the graviton is either coherent, squeezed, or squeezed coherent. We compared the transition probabilities of the detector in scenarios where the gravitational wave is quantized versus when it is treated classically. Assuming the gravitational wave propagates in one direction and has only one type of polarization, we found that for graviton states such as coherent, squeezed, and squeezed coherent states, quantum gravity signatures can emerge in events that would not be possible when the graviton state is a quantum state with $n_G$ particles $(\ket{n_G})$, such as graviton annihilation and the increasing energy level of the detector by two levels in final state.