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We study the dynamics of the charged and neutral excitons in a modulation-doped GaAs quantum well by time-resolved photoluminescence under a resonant excitation. The radiative lifetime of the charged exciton is found to be surprisingly short, 60 ps. This time is temperature independent between 2 and 10 K, and increases by a factor of 2 at 6 T. We discuss our findings in view of present theories of exciton radiative decay. ͓S0163-1829͑98͒03143-9͔The negatively charged exciton (X Ϫ ), which consists of two electrons bound to a hole, is the semiconductor analogue of the hydrogen ion H Ϫ . The existence of X Ϫ was proposed nearly 40 years ago, 1 but it was only recently identified in semiconductor quantum wells ͑QW͒. 2-6 Charged excitons show up in the photoluminescence ͑PL͒ and absorption spectra of a QW as a sharp line at an energy below the neutral exciton (X) line. The energy separation between the neutral and charged exciton lines ͑ϳ1 meV in GaAs/Al x Ga 1Ϫx As QW͒ represents the binding energy of the second electron to the exciton.It is clear that an excess density of electrons, which could bind to the photo excited electron-hole pairs, is needed for the X Ϫ to be formed. Indeed, X Ϫ is observed in structures where extra electrons are created by modulation doping, 2-4 tunneling, 5 or optical excitation. 6 The appearance of X and X Ϫ in modulation-doped QW is correlated with the electron gas conductivity. 3 This finding and recent studies by nearfield spectroscopy 7 have led us to the conclusion that the X Ϫ is created in modulation-doped QW by binding of a photoexcited electron-hole pair to a localized electron. The electrons are localized, separately one from another, in the minima of a random potential due to the remote ionized donors. This long-range potential does not alter significantly the internal structure of X Ϫ .In this work we present a comprehensive time-resolved PL study of the X-X Ϫ system in modulation doped GaAs/Al x Ga 1Ϫx As QW. Recombination dynamics of excitons in semiconductor QW has been a subject of intense theoretical and experimental research over the last decade. It was found that the two dimensional ͑2D͒ nature of free excitons in QW suppresses the polariton splitting, 8 which precludes the radiative recombination of exciton polaritons in bulk semiconductors. Instead, each exciton state couples to a 1D continuum of photon states, resulting in its fast decay. 9 Indeed, short radiative decay times, of a few tens of picoseconds, were calculated 10,11 and measured 12,13 for excitons in a GaAs QW. The X-X Ϫ system is especially interesting, as it allows us to study and compare the radiative decay of free and bound excitons.An experimental aspect of exciton lifetime measurements, which is often overlooked, is the importance of using the excitation light energy resonant with the exciton transition. Under nonresonant excitation a mixture of electron-hole

The spectroscopic properties of a spin polarized two-dimensional hole gas are studied in modulation doped Cd1−xMnxTe quantum wells with variable carrier density up to 5 10 11 cm −2 . The giant Zeeman effect which is characteristic of diluted magnetic semiconductors, induces a significant spin splitting even at very small values of the applied field. Several methods of measuring the carrier density (Hall effect, filling factors of the Landau levels at high field, various manifestations of MossBurstein shifts) are described and calibrated. The value of the spin splitting needed to fully polarize the hole gas, evidences a strong enhancement of the spin susceptibility of the hole gas due to carriercarrier interaction. At small values of the spin splitting, whatever the carrier density (non zero) is, photoluminescence lines are due to the formation of charged excitons in the singlet state. Spectral shifts in photoluminescence and in transmission (including an "excitonic Moss-Bustein shift") are observed and discussed in terms of excitations of the partially or fully polarized hole gas. At large spin splitting, and without changing the carrier density, the singlet state of the charged exciton is destabilized in favour of a triplet state configuration of holes. The binding energy of the singlet state is thus measured and found to be independent of the carrier density (in contrast with the splitting between the charged exciton and the neutral exciton lines). The state stable at large spin splitting is close to the neutral exciton at low carrier density, and close to an uncorrelated electron-hole pair at the largest values of the carrier density achieved. The triplet state gives rise to a characteristic double-line structure with an indirect transition to the ground state (with a strong phonon replica) and a direct transition to an excited state of the hole gas.

Excitons and trions in a CdTe modulation-doped quantum well are investigated by picosecond three-pulse four-wave mixing experiments as a function of temperature in the low-density regime. We show that trions are mobile for high enough temperatures. The diffusivity of trions and excitons increases with temperature but, like their mobilities, is limited by acoustic-phonon scattering. Consistently, studying the decay of the interband coherence reveals an increase of the homogeneous broadening as the temperature is raised. At low temperatures, excitonic complexes are localized by both interface roughness scattering and by the electrostatic potential due to remote ionized donors.

We report on the nonlinear optical dynamical properties of excitonic complexes in CdTe modulation-doped quantum wells, due to many-body interactions among excitons, trions, and electrons. These were studied by time and spectrally resolved pump-probe experiments. The results reveal that the nonlinearities induced by trions differ from those induced by excitons, and in addition they are mutually correlated. We propose that the main source of these subtle differences comes from the Pauli exclusion-principle through phase-space filling and short-range fermion exchange. Many-body interactions are the main source of nonlinear optical properties in condensed matter physics, and more particularly in semiconductors. In undoped semiconductors, Coulomb interaction gives rise to the electron-hole bound states (excitons) that play a crucial role in determining the optical properties near the band edge. Exciton resonances show a number of interesting features, both in the linear and in the nonlinear regimes making their study a very active field of research over the last 20 years. 1 The nonlinear dynamical properties of excitons are a very direct probe of the many-body interactions occurring in quantum wells, which might eventually find some useful applications in optoelectronic. The optical spectrum of moderately doped quantum wells also features a trion (charged exciton) resonance, which is situated only few meV below the exciton line. 2,3 The way many-body interactions are modified by the presence of an additional electron gas is clearly a topic of major interest for applications such as transport of light by a charged exciton 4 and for the quantum-information science. 5Current proposals for a solid-state implementation of an alloptical spin-based quantum computer are relying on Coulomb interaction between electrons and excited excitons either via electron exchange due to electron-exciton interaction 6 or via electron-charged excitonic states (trions). 7 Modulation-doped quantum well provides a model system in which electrons, excitons, and charged excitons, cohabit in the same well. The many-body interactions among electrons excitons and trions may be probed through the nonlinear behavior of trion and exciton optical resonances.In this paper, we report the experimental results on the dynamical nonlinear optical properties of trions and excitons in modulation-doped quantum wells. We evidence correlated behavior of excitons and trions under excitation which manifests itself by crossed trion-exciton effects. We observe a wealth of phenomena encompassing bleaching, crossed bleaching, induced-absorption and energy shifts of the resonances. Significant differences are found between the nonlinear optical effects induced by an exciton and a trion population. The main source of these distinct differences is proposed to come from the Pauli exclusion-principle, which is at the origin of phase-space filling and short-range fermion exchanges.We use here a high quality sample that was already fully characterized in previous studies. [8...