  Short pulses from mode-locked lasers can produce background-free atomic
fluorescence by allowing temporal separation of the prompt incidental scatter
from the subsequent atomic emission. We use this to improve quantum state
detection of optical-frequency and electron-shelved trapped ion qubits by more
than 2 orders of magnitude. For direct detection of qubits defined on atomic
hyperfine structure, however, the large bandwidth of short pulses is greater
than the hyperfine splitting, and repeated excitation is not qubit state
selective. Here, we show that the state resolution needed for projective
quantum measurement of hyperfine qubits can be recovered by applying techniques
from coherent control to the orbiting valence electron of the queried ion. We
demonstrate electron wavepacket interference to allow readout of the original
qubit state using broadband pulses, even in the presence of large amounts of
background laser scatter.
