Role of excitation-induced shift in the coherent optical response of semiconductors

Abstract

A transient four-wave-mixing signal is shown to arise from an excitation induced shift. In semiconductors, this signal can be comparable to or stronger than signals arising from saturation, local fields, or excitation induced dephasing. Calculations using modified optical Bloch equations show that multiple peaks in the transient four-wave-mixing spectrum are a signature of an excitation induced shift contributing to the signal. We observe this experimentally from a semiconductor multiple quantum well and confirm the presence of a shift directly using spectrally resolved differential transmission.The interaction between light and semiconductors provides fundamental insight into the dynamics of the optically created excitations. This is particularly true when techniques that are sensitive to coherence are employed. Coherent spectroscopy is well understood for a dilute vapor, where only isolated atoms or molecules need to be considered. 1 In dense materials, such as semiconductors or a dense atomic vapor, many-body interactions lead to dramatic differences from the dilute limit. 2 These effects can completely alter the interpretation of spectroscopic measurements and the performance of optoelectronic devices.Substantial progress has been made in understanding how interactions among elementary optical excitations ͑excitons or unbound electron-hole pairs͒ influence the coherent optical response of semiconductors, which is typically observed using transient four-wave mixing ͑TFWM͒. Early work 3-5 was interpreted based on the optical Bloch equations ͑OBE's͒, 6 which are appropriate in the dilute limit. Subsequently, it was realized that in addition to the signals arising from saturation, which are described by the OBE's, there were additional signals due to the interactions. The appearance of a signal for ''negative'' delay in a two-pulse TFWM experiment and a delay in the emission as a function of real time 7,8 are the most dramatic signatures. These effects can be calculated using a full many-body treatment. 9,10 In addition, they can be described phenomenologically in a few-level approach as arising from local fields, 11,12 excitation induced dephasing ͑EID͒, 13-15 and biexcitonic effects. 16,17 The phenomenological approach yields corrections to the OBE's, which can produce very good agreement with experiment 18 including complex polarization selection rules. 19 While the full many-body treatment is clearly based on a stronger theoretical foundation, the phenomenological description is usually easier to understand in terms of the underlying physics. The foundation provided by the full many-body treatment has been used to develop a microscopic basis for the phenomenological few level approach. 20 We show that an excitation induced shift ͑EIS͒ can result in a TFWM signal similar to that produced by the other mechanisms listed above. EIS is a manifestation of fundamental many-body interactions that result in a modification of the excitonic frequency in the presence of an excited carrier population. While the presence o...

Coherent two-exciton dynamics measured using two-quantum rephasing two-dimensional electronic spectroscopy

“…This result is the same for third-order modified optical Bloch equations [10]. Extended to fifth order, the modified optical Bloch equations contain more states and terms that couple the differential equations, but the physical intuition underlying the equations remains largely the same.…”

“…Phase-coherent nonlinear spectroscopic measurements such as four-wave-mixing are sensitive to the changes that occur when excitons interact through Coulomb forces [5] or local fields [6]. Early nonlinear 'self-diffraction' measurements revealed a signal at 'negative' delays due to many-body interactions (MBIs) [6][7][8], but since the exciton coherence frequencies could not be correlated with the emitted coherence frequencies, the contributions due to MBIs such as excitationinduced dephasing (EID) [9], excitation-induced energy shift (EIS) [10], and local field effects (LFEs) [6] could not be distinguished. EID and EIS result in density-dependent collisional broadening and renormalization of the exciton energy, respectively.…”

Polarization-dependent optical 2D Fourier transform spectroscopy of semiconductors

“…The first and most prominent was a signal for the ''wrong'' time delay in a two-pulse TFWM experiment. Theoretically, such signals could arise from several effects including local fields (3,4), biexcitons (5), excitation-induced dephasing (6, 7), or excitation-induced shift (8). Time resolving the signal also provided evidence for many-body contributions (9,10), although it did not resolve the ambiguity regarding the underlying phenomena.…”

Polarized Optical Two-dimensional Fourier Transform Spectroscopy of Semiconductors

“…For bulk GaAs with a cubic symmetry, the conduction band at the Brillouin zone center has s-orbital character with a two-fold degeneracy since the electron spin J = 1 2 . The valence band around k = 0 has p-orbital character, which can be described by wavefunctions with a total angular momentum J = 3 2 for the upper two sub-bands and J = of the Brillouin zone are [31]: 6) where k xy and k z are the respective in-plane (x-ŷ direction) and perpendicular (ẑ direction) component of the hole wavevector, in a frame defined by the corresponding quantum well geometry. m 0 is the free electron mass and γ 1 and γ 2 are the Luttinger parameters with values of γ 1 6.9 and γ 2 2.4 for GaAs [31].…”

“…Various experiments, including time-integrated, time-resolved, and spectrally-resolved FWM, have demonstrated that the many-body interactions among excitons and carriers dominate the nonlinear optical properties [2]. Phenomenological effects such as local field correction (LFC) [3], biexciton formation [4], excitation-induced dephasing (EID) [5], and excitation-induced shift (EIS) [6] describe the many-body interactions. Although conventional FWM spectroscopies have revealed rich information about excitons and carriers, there are some difficulties.…”