  Quantum states superposed across multiple particles or degrees of freedom are
of crucial importance for the development of quantum technologies. Creating
these states deterministically and with high effciency is an ongoing challenge.
A promising approach is the repeated excitation of multi-level quantum
emitters, which have been shown to naturally generate light with quantum
statistics. Here we describe how to create one class of higher dimensional
quantum state, a so called W-state, which is superposed across multiple time
bins. We do this by repeated Raman scattering of photons from a charged quantum
dot in a pillar microcavity. We show this method can be scaled to larger
dimensions with no reduction in coherence or single photon character. We
explain how to extend this work to enable the deterministic creation of
arbitrary time-bin encoded qudits.
