Generation of Schr\"odinger's cat states in a planar semiconductor heterostructure

We propose a nanodevice based on a typical planar semiconductor heterostructure with lateral confinement potential created by voltages applied to local electrodes. We show how to obtain near parabolical confinement along the nanodevice, and how to use coherent states of the harmonic oscillator for spatial separation of electron densities corresponding to opposite spin directions. In such a way, an entangled state of Schr\"odinger's cat type is created. We performed simulations of a realistic nanodevice model by numerical solving the time-dependent Schr\"odinger's equation together with simultaneous tracking of the controllable confinement potential via solution of the Poisson's equation at every time step.