Teraherz Field Effects Overview

Resonant laser excitation of semiconductors induces a coherent interband polarization between conductionband electron and valence-band hole states. Through interaction and scattering processes this optical polarization may be converted into incoherent populations of unbound or bound electron-hole pairs (excitons). Even though excitonic features of the coherent polarization arewell understood [20, 21], the study of its decay into incoherent many-body states is an area of active research. Several recent experiments have applied terahertz (THz) fields to directly probe the optically generated many-body system. So far, this approach has been used to detect and monitor conductivity [22], plasmons [23], and bound exciton formation [24]. At the same time, tunable terahertz (THz) sources evolve rapidly ranging from free-electron [25] and quantum-cascade lasers [26] to sources with difference-frequency generation [27]. Since the semiconductor quasi-particle excitations strongly interact with THz radiation, it is an interesting question to see if an excitonic system could actually be used to generate THz radiation, or even to provide THz amplification, i.e. THz gain.
In order to explore the THz properties of resonantly excited semiconductors, we study the build-up of exciton populations in different quantum states. Besides the conversion of excitonic polarizations at the 1s or 2s resonances into incoherent s-type populations, we show that Coulomb induced scattering can efficiently convert excitonic coherences with a strict s-type radial symmetry into an incoherent p-type population. We show that this process may even lead to a population inversion between the 2p and 1s states, giving rise to THz probe gain.
As a model system, we analyze quantum-wire structures but we show that the main results are equally valid for quantum-well systems. The electronic excitations are described by Fermion operators ac(v),k and a+ c(v),k related to an electron with carrier momentum k in the conduction (valence) band. We include the carrier-carrier Coulomb interaction as well as the couplings to light fields and phonons [21].

FIG. 1: (a) For excitation at the 1s exciton resonance with a 4 ps laser pulse (dot-dashed line), the temporal evolution of the induced optical polarization |P|² (shaded area), together with the generated incoherent 1s (dashed line) and 2p (solid line) exciton densities [10⁴ cm^-1] are shown. The inset shows the pump (shaded area) and linear absorption (solid line) spectra; E_1s is the 1s-exciton energy.
(b) The polarization to population conversion efficiency for 1s (dashed line) and 2p excitons (solid line) is plotted as function of excitation density n. The arrow indicates the density at which the dynamics is shown in a). The shaded area represents the result obtained without the phonon scattering.

FIG. 2: Same as Fig .1 but for excitation at the 2s exciton resonance (inset).
(a) Dynamics of optical polarization |P|² (dot-dashed line) and incoherent densities of 2s (shaded area) and 2p (solid line) excitons [10⁴ cm^-1].
(b) Conversion efficiency for 1s (dashed line), 2p (solid line), and 2s (shaded area) excitons as function of excitation density n.

FIG. 3: Terahertz gain spectra g(w) for different time delays corresponding to the conditions of
(a) 1s excitation as in Fig. 1a and
(b) 2s excitation as in Fig. 2a. All curves are identically scaled but shifted with respect to another. Here, E₂₁ is the energy difference between the 1s and 2p exciton states.