Light-Induced Gaps in Semiconductor Band-to-Band Transitions

Abstract

We observe a triplet around the third harmonic of the semiconductor band gap when exciting 50 -100 nm thin GaAs films with 5 fs pulses at 3 10 12 W=cm 2 . The comparison with solutions of the semiconductor Bloch equations allows us to interpret the observed peak structure as being due to a twoband Mollow triplet. This triplet in the optical spectrum is a result of light-induced gaps in the band structure, which arise from coherent band mixing. The theory is formulated for full tight-binding bands and uses no rotating-wave approximation. DOI: 10.1103/PhysRevLett.92.217403 PACS numbers: 78.20.Bh, 42.50.Md, 42.65.Re, 78.47.+p When an intense light field at frequency ! 0 excites band-to-band transitions in a semiconductor, additional energy gaps can evolve within the original bands [ Fig. 1(b)]. These so-called light-induced gaps [1][2][3][4][5] are the analog of the induced doublets, split by the Rabi frequency R , in a resonantly excited two-level system [ Fig. 1(a)]. Here, two out of the four possible optical transitions are energetically degenerate. Hence, the optical spectrum consists of three peaks -the famous Mollow triplet for atoms [6,7] or excitons [8,9]. In the semiconductor band case, the light-induced gap in, e.g., the conduction band arises because the original conduction band and the one-photon sideband of the valence band lead to an avoided crossing. The corresponding Hopfield coefficients [1] determine the amount of conduction band admixture. It is crucial to note that this admixture can be finite even far away from the fictitious crossing point. This statement becomes particularly important for Rabi energies h R approaching the photon energy h! 0 , while it can be neglected for small Rabi energies. The latter case is tacitly assumed in previous graphical representations of calculated light-induced gaps. Importantly, as a result of this finite admixture, optical transitions between the induced bands are possible throughout an appreciable fraction of momentum space. Consequently, the transitions acquire considerable spectral weight. Again, two out of the four sets of possible optical transitions are energetically degenerate and a triplet results, which we will refer to as the two-band Mollow triplet in what follows.Light-induced gaps in semiconductor bands have not unambiguously been observed yet. In order to observe the splitting, it clearly has to be larger than the damping. As typical electron dephasing times under relevant conditions are on the order of 10 fs or less, the Rabi oscillation period has to be shorter than this value. This brings one close to Rabi frequencies approaching the frequency of light -a regime which has previously been referred to as carrier-wave Rabi flopping [10]. In this regime, a splitting in the third-harmonic spectra has been observed [11]. However, as the measurements have been compared only with calculations on the basis of two-level systems [11], skepticism has been expressed whether this interpretation was correct indeed. Furthermore, later theoretical work [12...

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