  This paper theoretically studies the quantum coherence of an electronic state
on an artificial chiral Tomonaga-Luttinger (TL) liquid. Coulomb interaction
between copropagating integer quantum Hall edge channels causes the TL liquid
nature of charge excitations, resulting in the splitting of an electronic state
into bosonic eigenmodes. We investigate the single-electron coherence under the
splitting process by calculating the Aharonov-Bohm (AB) oscillations in an
electronic Mach-Zehnder interferometer employing copropagating spin-up and
spin-down edge channels as the interference paths. We investigate the voltage
bias dependence of the AB oscillations at zero temperature, taking the
inter-channel interaction into account using the bosonization technique. The
calculation results of the visibility and the phase of the AB oscillations show
non-monotonical bias dependence when the copropagating channels are
electrostatically asymmetric. These observations are interpreted as the
signatures of the second-order interference between the fractionalized spin
excitations with different phase evolutions. We also report finite entanglement
entropy between the bosonic eigenmodes split from an electron, which presents
an analogy between the `electron splitting' in a TL liquid and the Cooper-pair
splitting at a superconducting junction.
