  We propose an all-electrically controlled nanodevice - a gated semiconductor
nanowire - capable of generating a coherent state of a single electron trapped
in a harmonic oscillator or superposition of such coherent states - the
Schr\"odinger cat state. In the proposed scheme, electron in the ground state
of the harmonic potential is driven by resonantly oscillating Rashba spin-orbit
coupling. This allows for the creation of the Schr\"odinger cat state with
superposition amplitudes depending on the initial electron spin state. Such a
method can be used for initialization of a single spin qubit defined in a
coherent state. The harmonic confinement potential along the InSb nanowire and
the modulation of the Rashba spin-orbit coupling is obtained by proper gating.
The results are supported by realistic three-dimensional time-dependent self
consistent Poisson-Schr\"odinger calculations.
