Phase dynamics of nonequilibrium distributions of free electron-hole pairs in GaAs quantum wells

The elementary excitations of semiconductors are governed by quantum statistics and Coulomb correlation. Both the amplitude and the phase of their nonlinear optical polarization displays a complex temporal behavior. This was experimentally demonstrated by the observation of nonlinear dynamics of the instantaneous-frequency of coherent wave mixing resonant with excitons. However, the continuum-states, well above the band gap, are much more difficult to study because of the ultrafast relaxation of electrons and holes (e-h). In this paper we address for the first time the question of the phase dynamics in the continuum of states of quasi-free e-h. We show that the temporal evolution of four-wave-mixing (FWM) power spectra (PS) reveals important information on the complex dynamical behavior of the Fermi surface of nonequilibrium e-h distributions. The experiments are performed on a GaAs/GaAlAs quantum well structure, in the self-diffracted FWM configuration using unchirped transform limited 100-fs pulses. For each delay ΔT between the two pulses, the PS of the FWM signal S_FWM, observed in the direction k_s = 2 k₂ - k₁, is recorded with an OMA detector. The laser frequency is tuned 44 meV above the lowest exciton, in the two-dimensional continuum of quasi-free e-h states. The dephasing times T₂ for continuum excitation is of the order of a few tens of fs for excitation densities N in the range 10¹⁰-10¹² cm^-2. In such conditions, no interesting information is obtained from the time integrated FWM signal S_FWM(ΔT), when the pulsewidth exceeds T₂. In contrast, the spectrogram, S_FWM(ω, ΔT), is a direct visualization of the phase dynamics of the emission frequency, as shown with quasi-instantaneous Kerr-media. Figure 1 presents a series of PS obtained with N = 3 × 10¹² cm^-2. Each spectrum has been normalized to unity in order to display the dynamical behavior. The laser spectrum is shown as a dotted curve. A clear dynamical shift of the FWM power spectrum is observed. The maximum of S_FWM(ω, ΔT) is shifted to high energies relative to the laser spectrum at early delays (ΔT < 0). It shifts to the lower energies as ΔT increases. Figure 2 presents the position of the maximum of S_FWM(ω, ΔT) vs. ΔT, showing that the shift can be as large as ΔE ≈ 5 meV. This temporal behavior is density dependent as observed in different sets of measurements. We attribute the above observations to many-body effects that renormalize the optical response of the non-equilibrium e-h Fermi-sea created by the intense pulse. This renormalization originates mostly from the Fermi-sea excitations with very small energy and is therefore concentrated at its two edges.