  In contrast to a free electron system, a Tomonaga-Luttinger (TL) liquid in a
one dimensional (1D) electron system hosts charge and spin excitations as
independent entities. When an electron wave packet is injected into a TL
liquid, it transforms into wave packets carrying either charge or spin that
propagate at different group velocities and move away from each other. This
process, known as spin-charge separation, is the hallmark of TL physics. While
the existence of these TL eigenmodes has been identified in momentum- or
frequency-resolved measurements, their waveforms, which are a direct
manifestation of 1D electron dynamics, have been long awaited to be measured.
In this study, we present a time domain measurement for the
spin-charge-separation process in an asymmetric chiral TL liquid comprising
quantum Hall (QH) edge channels. We measure the waveforms of both charge and
spin excitations by combining a spin filter with a time-resolved charge
detector. Spatial separation of charge- and spin-wave packets over a distance
exceeding 200 um was confirmed. In addition, we found that the 1D electron
dynamics can be controlled by tuning the electric environment. These
experimental results provide fundamental information about non-equilibrium
phenomena in actual 1D electron systems.
