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We have directly measured the carrier-density dependence and the temporal evolution of the band-gap renormalization in a suitably designed GaAs/Alₓ{Ga}_{1{{-}}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 ${n}1/3$ carrier-density dependence.
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Cingolani et al. (1990) studied this question.
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