Photon Echoes from Semiconductor Band-to-Band Continuum Transitions in the Regime of Coulomb Quantum Kinetics

Abstract

We show that the coherent response of semiconductor band-to-band continuum transitions at room temperature, excited by 11 fs pulses at elevated carrier densities, deviates substantially from that expected for an ideal photon echo. A microscopic non-Markovian quantum kinetic theory of both electron-electron and electron-LO-phonon scattering reproduces these unusual experimental observations qualitatively and, furthermore, the famous scaling of the decay time t with carrier density n eh according to Consider a dense gas of electrons and holes generated at random places in pairs with opposite momentum in coherent quantum states in a semiconductor. It is clear that the particles will move in such a way that they screen their mutual Coulomb interaction. How long does it take that screening is built up and that scattering has destroyed the initially quantum mechanically coherent state? About one decade ago, Shank et al. addressed this fundamental question when they studied the variation of the Coulomb scattering in a dense gas of optically excited crystal electrons and holes [1,2] with density n eh using ഠ10 fs pulses and a photon echo technique. They reported that the decay time t of the photon echo signal at room temperature scales approximately according to t~n 21͞D eh , where D is the dimension of either bulk GaAs ͑D 3͒ or GaAs quantum wells ͑D 2͒. At that time, it was tempting and appealing to interpret this seemingly simple result in terms of the nearest-neighbor scattering of D-dimensional hard spheres in which case it is simple to show that the average time between different collisions scales~n 21͞D eh indeed. Today, a number of important questions are still unanswered. (i) Is it a photon echo? In analogy with a spin echo this would mean that a first short pulse excites the system, a second pulse arrives after time delay t 21 , and the coherent collective response of the system, the photon echo, peaks at yet another time delay t 21 later. Without real-time resolution [1,2], however, one only measures the energy of the echo signal versus t 21 and its decay time t. For a phenomenological dephasing time T 2 it is known that T 2 4t holds for a four-wave mixing (FWM) geometry under these conditions. Not a single experiment, however, has shown directly that the coherent real-time response of semiconductor band-to-band continuum transitions under these conditions is a photon echo indeed. Under quite different conditions (T 4 K, 100 fs pulses, and much lower carrier densities), Ref. [3] showed that the total response is not a photon echo. Only after spectral filtering (behind the sample) of those components of the FWM-signal resonant with the band-to-band continuum, were they able to isolate a contribution which corresponded to an echo. The position of this signal shifted with time delay as expected [4], its width was constant (150 fs) and given by the time resolution of their setup for all conditions. The picosecond response of inhomogeneously broadened excitonic transitions [5] as well as the response of modulation-...

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

“…[15] is numerically too demanding under these conditions. Hence, we employ a phenomenological description-with parameters based on earlier findings [15,16]. For the dephasing of the off-diagonal density matrix elements we take into account that the damping is the sum of a constant contribution due to LO-phonon scattering and a term proportional to the third root of the carrier density n [16].…”

“…At large excess energies, where the dephasing is stronger, only an irreversible increase of the inversion is left after the pulse has passed. Based on our experience with quantum kinetics [15,16], we expect that the window of coherent dynamics would be widened to a certain extent by the use of a non-Markovian retarded description of electron-electron scattering. We have checked that replacing the above electron-phonon scattering by electron-phonon quantum kinetics leads to no significant changes.…”

“…Hence, we employ a phenomenological description-with parameters based on earlier findings [15,16]. For the dephasing of the off-diagonal density matrix elements we take into account that the damping is the sum of a constant contribution due to LO-phonon scattering and a term proportional to the third root of the carrier density n [16]. To account for the additional energy dependence, we use the following dephasing for the various interband polarization (p) components (n Þ m), @ @t nm ; t coll ÿ p ; t nm ; t ; (6) where is the excess energy with respect to the unrenormalized band gap and the density-and energy-dependent damping rate is given by…”

Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing

“…These fits are indicated by the solid curves in Figure 3. If many-body effects play a strong role in the sample under study, a more complicated analysis may be required 34,35 . This is the case for the SR-FWM data in low-temperature grown GaAs in Figure 2(a) at the exciton (1.515 eV), where the signal is mediated by exciton scattering with free carrier transitions 34 .…”

Semiconductor polarization dynamics from the coherent to the incoherent regime: Theory and experiment

“…1,2 However, most of the work, experimental or theoretical, concentrates on either one of two completely different experimental situations, involving, respectively, coherently driven states [3][4][5][6][7] or incoherently relaxing distributions. [8][9][10][11][12][13][14] In real life this distinction is artificial since an initially coherently driven system naturally relaxes and eventually reaches thermodynamic equilibrium. When electron-hole pairs (e-h) are excited by a short laser pulse they start oscillating coherently between the valence and conduction levels forming polarization waves whose quantum-mechanical phase is defined by that of the laser fields.…”