  Surface acoustic waves (SAW) have large potential to realize
quantum-optics-like experiments with single flying electrons employing their
spin or charge degree of freedom. For such quantum applications, highly
efficient trapping of the electron in a specific moving quantum dot (QD) of a
SAW train plays a key role. Probabilistic transport over multiple moving minima
would cause uncertainty in synchronisation that is detrimental for coherence of
entangled flying electrons and in-flight quantum operations. It is thus of
central importance to identify the device parameters enabling electron
transport within a single SAW minimum. A detailed experimental investigation of
this aspect is so far missing. Here we fill this gap by demonstrating
time-of-flight measurements for a single electron that is transported via a SAW
train between distant stationary QDs. Our measurements reveal the in-flight
distribution of the electron within the moving acousto-electric quantum dots of
the SAW train. Increasing the acousto-electric amplitude, we observe the
threshold necessary to confine the flying electron at a specific, deliberately
chosen SAW minimum. Investigating the effect of a barrier along the transport
channel, we also benchmark the robustness of SAW-driven electron transport
against stationary potential variations. Our results pave the way for highly
controlled transport of electron qubits in a SAW-driven platform for quantum
experiments.
