## Abstract

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 k_{2} - k_{1}, 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 T_{2} for continuum excitation is of the order of a few tens of fs for excitation densities N in the range 10^{10}-10^{12} cm^{-2}. In such conditions, no interesting information is obtained from the time integrated FWM signal S_{FWM}(ΔT), when the pulsewidth exceeds T_{2}. 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 × 10^{12} 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.

Original language | English |
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Title of host publication | Proceedings of the International Quantum Electronics Conference (IQEC'94) |

Publisher | Publ by IEEE |

Pages | 11 |

Number of pages | 1 |

ISBN (Print) | 0780319737 |

State | Published - 1994 |

Externally published | Yes |

Event | Proceedings of the 21st International Quantum Electronics Conference (IQEC'94) - Anaheim, CA, USA Duration: 8 May 1994 → 13 May 1994 |

### Publication series

Name | Proceedings of the International Quantum Electronics Conference (IQEC'94) |
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### Conference

Conference | Proceedings of the 21st International Quantum Electronics Conference (IQEC'94) |
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City | Anaheim, CA, USA |

Period | 8/05/94 → 13/05/94 |