Observation of transient band-gap renormalization in quantum wells

We have directly measured the carrier-density dependence and the temporal evolution of the band-gap renormalization in a suitably designed GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum-well heterostructure. The transient behavior of the band-gap renormalization is governed by the carrier lifetime. Good quantitative agreement is found with the expected ${\mathit{n}}^{1/3}$ carrier-density dependence.