Motional $N$-phonon Bundle States of A Trapped Atom with Clock Transitions

Quantum manipulation of individual phonons could offer new resources for studying fundamental physics and creating an innovative platform in quantum information science. Here, we propose to generate quantum states of strongly correlated phonon bundles associated with the motion of a trapped atom. Our scheme operates in the atom-phonon resonance regime where the energy spectrum exhibits strong anharmonicity such that energy eigenstates with different phonon numbers can be well-resolved in the parameter space. Compared to earlier schemes operating in the far dispersive regime, the bundle states generated here contain a large steady-state phonon number. Therefore, the proposed system can be used as a high quality multiphonon source. Our results open up the possibility of using long-lived motional phonons as quantum resources, which could provide a broad physics community for applications in quantum metrology.