Generating nonclassical states of motion using spontaneous emission

Nonclassical motional states of matter are of interest both from a fundamental perspective but also for their potential technological applications as resources in various quantum processing tasks such as quantum teleportation, sensing, communication, and computation. In this work we explore the motional effects of a harmonically trapped, excited two-level emitter coupled to a one-dimensional photonic system. As the emitter decays it experiences a momentum recoil that entangles its motion with the emitted photon pulse. In the long-time limit the emitter relaxes to its electronic ground state, while its reduced motional state remains entangled with the outgoing photon. We find photonic systems where the long-time reduced motional state of the emitter, though mixed, is highly nonclassical and in some cases approaches a pure motional Fock state. Motional recoil engineering can be simpler to experimentally implement than complex measurement and feedback based methods to engineer novel quantum mechanical states of motion.