Gain without inversion in a biased superlattice

Intersubband transitions in a superlattice under homogeneous electric field is studied within the tight-binding approximation. Since the levels are equi-populated, the non-zero response appears beyond the Born approximation. Calculations are performed in the resonant approximation with scattering processes exactly taken into account. The absorption coefficient is equal zero for the resonant excitation while a negative absorption (gain without inversion) takes place below the resonance. A detectable gain in the THz spectral region is obtained for the low-doped $GaAs$-based superlattice and spectral dependencies are analyzed taking into account the interplay between homogeneous and inhomogeneous mechanisms of broadening.