Tunneling and time-dependent magnetic phase transitions in a bilayer electron system

In this work, we have numerically integrated in space and time the effective-mass nonlinear Schrödinger equation for an electron wave packet in a bilayer electron system. Considering a time-dependent magnetic phase transition from the usual unpolarized ground state to spin-polarized one, we have calculated the tunneling dynamics between the two quantum wells when an external bias is applied. Due to the nonlinear effective-mass equation, it is found that the charge dynamically trapped in both wells produces a reaction field that modifies the system resonant condition. In this way, we have shown the possibility of having another kind of tunneling oscillations between both quantum wells after an optical excitation of the sample.