Certifying Multilevel Coherence in the Motional State of a Trapped Ion

Quantum coherence is the foundation of almost all departures from classical physics and is exhibited when a quantum 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 that does not produce false positives. 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 that are well suited to noisy intermediate-scale quantum devices.