Proposal for creating spatial superposition of a large mass in a RF trap

Engineering coherent spatial superpositions of levitated large masses is an ongoing challenge. Borrowing from recent experimental work, we consider a charged mass of hundreds of nanometers size (``nanoparticle'') co-trapped with an ion in a Paul trap, and propose a scheme to manipulate its spatial state through the Coulomb interaction with the ion. We focus on the achievable delocalisation, only sketching the other challenges of the protocol (initial cooling, preservation of coherence for long-enough times, and detection). We prove that our scheme can displace coherently the nanoparticle by a few nanometers, and give an estimate of the allowed noise. Though smaller than the nanoparticle's size, the nanoparticle displacement is much larger than the wavefunction of the trap's ground state. Thus the co-trapping scheme is in principle able to demonstrate the delocalisation of a charged nanoparticle if the required noise isolation can be realised.