VOLUME 61, NUMBER 14 PHYSICAL REVIEW LETTERS 3 OCTOBER 1988 Femtosecond Photon Echoes from Band-to-Band Transitions in GaAs P. C. Becker, H. L. Fragnito, ' C. H. Brito Cruz, ' R. L. Fork, J. E. Cunningham, J. E. Henry, and C. U. Shank ATd'cT Bell Laboratories, Holmdel, New Jersey 07733 {Received 19 May 1988) We report the first observation of femtosecond photon echoes from the band-to-band transitions in a bulk semiconductor. The time decay of the echo, found to vary from 3.5 to 11 fs, has allowed us to determine the polarization dephasing rate in GaAs. This rate was found to depend on the carrier density in the experimental range covered, 1. 5&10' to 7&10' cm, indicating the dominance of carrier- carrier scattering as the principal dephasing mechanism. The observed functional dependence of the de- phasing rate on the carrier density has yielded previously unavailable information on Coulomb screening in a nonequilibrium carrier distribution. PACS numbers: 72.20.Jv, 78.47.+p The photon-echo' or time-delayed four-wave mixing technique has become an important tool for investigating dephasing processes in gases, solids, and glasses. The use of coherent optical transients to study such pro- cesses for band-to-band transitions in semiconductors has been frustrated by the rapid time scale on which such processes occur. Recent advances in short pulse techniques which have led to the generation of optical pulses as short as 6 fs have made such investigations possible. With this increased time resolution we have been able to make the first observation of two-pulse pho- ton echoes from direct transitions in GaAs and have determined the polarization dephasing rate. The polarization dephasing rate measured in the ex- periments described here provides a direct measure of the process of momentum dephasing. At high carrier densities the carrier momentum loses phase coherence primarily through the screened Coulomb interaction be- tween carriers. Both elastic and inelastic carrier-carrier collisions contribute to the momentum dephasing. At low carrier densities electron-phonon interactions begin to dominate in the intrinsic material. The density depen- dence of the polarization dephasing rate provides impor- tant information concerning the carrier-carrier interac- tion. In the experiments reported here we observe photon echoes using a two-pulse sequence. Two pulses, one hav- ing wave vector kl and the other wave vector k2, gen- erate an echo in the momentum-matched direction 2k2 — ki. The angle between k~ and k2 is small. The echo is then separated spatially from the exciting pulses. Since there is a sizable frequency spread in each pulse due to its short duration, there is an angular spread of the k vectors that make up the echo signal. However, the entire echo signal, which is well separated spatially from the incident beams, is collected by our detection op- tics. The energy of the generated echo is measured as a function of the relative time delay between the exciting pulses. The sample is at room temperature. We can model the band-to-band absorption in a direct semiconductor such as GaAs as a set of Lorentzian two- level transitions having a half-width of 2/Ti. We can write the band-to-band absorption coefficient a(E) as a(E) = dE' (E — E') + (2h/T2) ' where E is the absorption energy, p(E') is the density of states at energy E', fi is Planck's constant divided by 2x, and T2 is the polarization dephasing time. With the above model for the absorption, the energy of the echo can be determined to vary exponentially with the relative time delay z between the two pulses as E(t) ce exp( — r/T„h, ), (2) where T„h, T2/4. Thus by measuring the echo energy as a function of time the polarization dephasing time T2 can be directly determined. The experiment was performed with use of compressed pulses phase corrected to third order in a manner de- scribed previously. The duration of the excitation pulses was measured to be in the range 6 to 10 fs with use of the second-harmonic up-conversion technique. The pulse repetition rate was 8 kHz and the pulse energy was on the order of 1 nJ. The energy of the pulse was much less than that needed for a z pulse so the echoes observed in the experiments described here are in the small-signal perturbation limit. The pulses were split with use of a modified Michelson interferometer configuration to form the two excitation pulses. The two pulses were focused with a 5-cm focal length lens into a 0. 1-pm thick sample of GaAs grown by molecular-beam epitaxy. Both faces of the sample were antireflection coated. The excitation pulse energy at the sample ranged from 0. 1 to 0. 01 nJ per pulse which corresponds to carrier densities ranging from 10' to 10' cm . The carrier density was es- timated by measuring the number of photons absorbed in the material. The spot size of the focused beam was measured to be 30 pm in diameter. 1647