Certifying Multilevel Coherence in the Motional State of a Trapped Ion

Quantum coherence is one of the clearest departures from classical physics, exhibited when a system is in a superposition of different basis states. Here the coherent superposition of three motional Fock states of a single trapped ion is experimentally certified, with a procedure provably robust against imperfect operation. As the motional state cannot be directly interrogated, our scheme uses an interference pattern generated by projective measurement of the coupled qubit state. The minimum number of coherently superposed states is inferred from a series of threshold values based on analysis of the interference pattern. This demonstrates that high-level coherence can be verified and investigated with simple, nonideal control methods well-suited to noisy intermediate-scale quantum devices.