Period-doubling and Hopf bifurcations in far-infrared driven quantum well intersubband transitions

The behavior of $n-\delta$-doped wide quantum well (QW) heterostructures in the presence of intense far-infrared (FIR) radiation is studied using the semiconductor Bloch equations, in the time-dependent Hartree version and without the rotating-wave approximation. A QW is designed where one can either obtain a strong subharmonic (period doubling) or a strong incommensurate (Hopf) frequency response by varying the sheet density and field strength. These strong responses should be attainable with current technology, and the field amplitudes and frequencies of the drive are well within the range of FIR free-electron lasers.