Ultrafast carrier relaxation and vertical-transport phenomena in semiconductor superlattices: A Monte Carlo analysis - Meier, Torsten; Rossi, F.; Thomas, P.; Koch, S.W.; Selbmann, P.E.; Molinari, E. (Physical Review B)
The ultrafast dynamics of photoexcited carriers in semiconductor superlattices is studied theoretically on the basis of a Monte Carlo solution of the coupled Boltzmann transport equations for electrons and holes. The approach allows a kinetic description of the relevant interaction mechanisms such as intra- miniband and interminiband carrier-phonon scattering processes. The energy relaxation of photoexcited carriers, as well as their vertical transport, is investigated in detail. The effects of the multiminiband nature of the superlattice spectrum on the energy relaxation process are discussed with particular emphasis on the presence of Bloch oscillations induced by an external electric field. The analysis is performed for different superlattice structures and excitation conditions. It shows the dominant role of carrier–polar-optical-phonon interaction in determining the nature of the carrier dynamics in the low-density limit. In particular, the miniband width, compared to the phonon energy, turns out to be a relevant quantity in predicting the existence of Bloch oscillations.

Signatures of Fano-resonances in four-wave mixing experiments - Meier, Torsten; Schulze, A.; Thomas, P.; Vaupel, H.; Maschke, K. (Physical Review B)
Optical transitions into discrete levels coupled to an optically active continuum lead to asymmetrical Fano lines in the linear absorption spectra, reflecting interference between the excitation channels. We investigate the corresponding four-wave-mixing spectra for the nonlinear optical response within a model of noninteracting electrons. Our results show that four-wave-mixing experiments provide a useful tool to identify Fano resonances.

Linear and Non-linear Optical Properties of Semiconductor Superlattices: Excitonic and Field-Induced Effects - Meier, Torsten; Rossi, F.; Je, K.-C; Hader, J.; Thomas, P.; Koch, S.W. (Proceedings of IV International Conference on Optics of Excitons in Confined Systems)
The effective dimensionality of excitons can be drastically changed by applying an alternating electric field. On the basis of a full three-dimensional description of both coherent and incoherent phenomena in anisotropic structures it is found that appropriate applied oscillating fields change the exciton wave function from anisotropic three dimensional to basically two dimensional. This effective-dimension change is caused by dynamic localization which leads to an increase of the exciton binding energy and of the corresponding oscillator strength.

Electric-Field-Induced Exciton Ionization in a GaAs/AlGaAs Superlattice - Meier, Torsten; von Plessen, G.; Koch, M.; Feldmann, J.; Koch, S.W.; Thomas, P.; Göbel, E.O.; Goosen, K.W.; Kuo, J.M.; Kopf, R.F. (Proceedings of IV International Conference on Optics of Excitons in Confined Systems)
We study exciton ionization induced by an axial electric field in a strongly coupled GaAs/Al0.3 Ga0.7 As superlattice at low temperatures. The field-induced ionization times of the heavy-hole 1s exciton in the miniband field regime are determined from transient four-wave-mixing experiments and theoretical model calculations. They are found to lie between the field ionization times of excitons in bulk semiconductors, and in strongly confined quantum well systems.

Quantum beats from biexcitons in narrow quantum wells: polarization and density dependence - Meier, Torsten; Albrecht, T.F.; Schulze, A.; Koch, M.; Bott, K.; Feldmann, J.; Stolz, W.; Kuhl, J.; Mayer, E.J.; Koch, S.W.; Göbel, E.O.; Cundiff, S.T. (Quantum Electronics and Laser Science Conference)
Transient four-wave mixing (TFWM) has been extensively used during the last few years to study exciton dynamics in semiconductors and in semiconductor heterostructures. These studies have provided significant insight into exciton dynamics in both ordered and disordered systems. There are, nevertheless, still certain aspects of the excitonic TFWM response that are not completely understood. In particular, a complete understanding of the polarization and intensity dependences of the signai strength, the decay of the time-integrated signal, and the temporal characteristics of the time-resolved signal has proven elusive. Recent theoretical and experimental work has indicated that exciton-exciton interactions are important.1·2 Such interactions include incoherent processes, such as excitation-induced dephasing, and the formation of biexcitons. Additionally, some of the phenomena result from disorder, making them sample dependent.

Polarization dependence of quantum beats between light-hole and heavy-hole excitons in GaAs quantum wells - Meier, Torsten; Kuhl, J.; Mayer, E.J.; Smith, G.O.; Bott, K.; Heuckeroth, V.; Thomas, P.; Koch, M.; Hey, R.; Ploog, K. (Quantum Electronics and Laser Science Conference)
The appearance of quantum beats (QBs) between heavy-hole (hh) and light-hole (lh) excitons in GaAs quantum wells (QWs) has been observed in many degenerate-four- wave-mixing (DFWM) experiments with subpicosecond optical pulses. Although the variation of the beat amplitude and phase with polarization of the incident pulses was recognized early on, a consistent theoretical interpretation of exciton coherence for the case of simultaneous excitation of hh and lh excitons is still missing.

Influence of scattering on the formation of Wannier-Stark ladders and Bloch oscillations in semiconductor superlattices - Meier, Torsten; von Plessen, G.; Feldmann, J.; Göbel, E.O.; Thomas, P.; Goosen, K.W.; Kuo, J.M.; Kopf, R.F. (Physical Review B)
We study the critical field for the formation of Wannier-Stark ladders and Bloch oscillations in GaAs/AlxGa1−xAs superlattices at low temperatures. From the results of photocurrent and transient four-wave mixing experiments, we conclude that the critical field is higher for superlattices with wide minibands than for superlattices, with narrow minibands. The explanation for this dependence is that intraminiband scattering due to LO-phonon emission is excluded in minibands narrower than the LO-phonon energy.

Coherent electric-field effects in semiconductors - Meier, Torsten; von Plessen, G.; Thomas, P.; Koch, S.W. (Physical Review Letters)
We present a microscopic analysis of coherent effects induced by electric fields in photoexcited semiconductors in the presence of the Coulomb interaction. Both the terahertz emission and four-wave-mixing signals arising from Bloch oscillations in a semiconductor superlattice are computed consistently. It is predicted that Bloch oscillations should be observable also for miniband widths on the order of the exciton binding energy.

Coherent Dynamics of Exciton Wavepackets in Semiconductor Heterostructures - Meier, Torsten; Koch, M.; Feldmann, J.; Göbel, E.O.; Jahnke, F.; Schäfer, W.; Thomas, P.; Koch, S.W.; Nickel, H.; Luttgen, S.; Stolz, W. (Proceedings der 8. International Winterschool on New Developments in Physics)
The coherent dynamics of exciton wavepackets in (GaIn)As/GaAs as well as (GaIn)As/Ga(PAs) multiple quantum well structures is studied by means of transient four-wave mixing (FWM) experiments. The wavepackets are generated by simultaneous excitation of several exciton transitions with laser pulses of about 100 fs duration. The time-integrated FWM signals exhibit a pronounced modulation superimposed on the overall decay which can be attributed to the quantum interference of the different eigenstates. In the time-resolved FWM signals this interference is not present, reflecting the interplay between many-body Coulomb effects and inhomogeneous broadening. This experimental technique is then employed to extract the exciton binding energies in pseudomorphic symmetrically strained (GaIn)As/GaIPAs) with various In contents.

Vertical transport studied by sub-picosecond four-wave mixing experiments - Meier, Torsten; Feldmann, J.; von Plessen, G.; Thomas, P.; Göbel, E.O.; Goosen, K.W.; Miller, D.A.B.; Cunningham, J.E. (Coherent Optical Interactions in Semiconductors)
Since the realization of semiconductor heterostructures vertical transport of electrically injected carriers has been one of the most interesting topics in semiconductor physics. Precise engineering of semiconductor layers and thus electronic energy levels allows the tailoring of transport properties over a wide range and has even led to the invention of semiconductor devices relying on ballistic electron transport. In addition, negative differential resistance (NDR) can be realized by using tunneling diodes containing double-barrier heterostructures or a superlattice structure.5,6 Actually, the proposal of Esaki and Tsu5 to use electronic Bloch oscillations in the miniband of a semiconductor superlattice to realize NDR marked the starting point for the physics and applications of semiconductor heterostructures.

Theory of polarization-dependent four-wave mixing using the optical Bloch equations - Meier, Torsten; Bennhardt, D.; Thomas, P.; Hu, Y.Z.; Binder, R.; Koch, S.W. (Coherent Optical Interactions in Semiconductors)
Transient four-wave mixing (TFWM) experiments have been widely used to study the excitation dynamics of excitons in quantum wells [1]. Recently is has been observed that TFWM signals, especially quantum beats between heavy-hole (hh) and light-hole (lh) excitons, strongly depend on the polarization of the incident laser pulses [2–6]. This dependence is presently being investigated.

Evidence of Biexcitonic Contributions to Four-wave-mixing in GaAs Quantum Wells - Meier, Torsten; Mayer, E.J.; Heuckeroth, V.; Smith, G.O.; Kuhl, J.; Bott, K.; Schulze, A.; Bennhardt, D.; Koch, S.W.; Thomas, P.; Hey, R.; Ploog, K. (Physical Review B)
A three-pulse degenerate four-wave-mixing experiment and its theoretical analysis reveal contributions of local field and biexciton effects to the nonlinear optical response of the two-dimensional exciton. Quantum beats with a frequency equivalent to the biexciton binding energy appear only for specific polarizations. Polarization-dependent spectrally resolved four-wave mixing shows an additional peak that is separated from the 1s heavy-hole exciton line by the biexciton binding energy. These experimental results are in good agreement with the optical selection rules of the theoretical model, providing evidence for biexcitonic contributions to the four-wave mixing.

Simultaneous influence of disorder and Coulomb interaction on photon echoes in semiconductors - Meier, Torsten; Jahnke, F.; Koch, M.; Feldmann, J.; Schäfer, W.; Thomas, P.; Koch, S.W.; Göbel, E.O.; Nickel, H. (Physical Review B)
The effects of disorder and many-body interaction on the four-wave-mixing signal in semiconductor quantum wells are studied experimentally and theoretically. For weakly disordered samples it is shown that the combined influence of Coulomb and disorder effects leads to a characteristic photon-echo signal in time-resolved measurements and to oscillations in the time-integrated signal. Convincing agreement between experiment and theory is demonstrated.

Intrinsic perturbations of Bloch oscillations and Wannier Stark ladders in semiconductor superlattices - Meier, Torsten; von Plessen, G.; Feldmann, J.; Thomas, P.; Göbel, E.O.; Koch, S.W. (Optics and Photonics News)

Contributions of Bound and Unbound Two-Exciton States to the Nonlinear Optical Response of GaAs Quantum Wells - Meier, Torsten; Kuhl, J.; Mayer, E.J.; Smith, G.O.; Bennhardt, D.; Schulze, A.; Thomas, P.; Hey, R.; Ploog, K. (International Conference on Ultrafast Phenomena)
The strong influence of exciton/exciton interaction on the nonlinear optical response of the 2D exciton in GaAs quantum wells has been demonstrated in several recent experimental studies. The theoretical model for the microscopic coupling mechanism is still the subject of controversy, however. In ref. [1], we have presented a model including a density dependent coupling between opposite spin excitons which assumes that the interaction results in a renormalization of the matrix elements, dephasing rates and energies of the transition from the single-exciton state to the two-exciton state with respect to the corresponding quantities for the single exciton transitions. In contrast, Wang et al. claim that all experimental observations are explained by a density induced dephasing rate and that biexciton states play no role [2]. Here we present a new 3-pulse degenerate-four-wave-mixing (DFWM) configuration which is able to differentiate between pure local field effects and biexcitonic contributions to the time-integrated signal. Experiments were performed on an almost homogeneously broadened GaAs/Al0.3Ga0.7As single QW (well width 20 nm, photoluminescence line 0.3 meV, homogenous linewidth 0.15 meV) in the backward reflection geometry. The sample was cooled to 10 K and excited by a sequence of three pulses (1.1 ps duration) with equal intensity, wave vectors 𝑘→1,𝑘→2,𝑘→3 and delays τ12 and τ13 between the second and first and the third and first pulse, respectively. The signal was monitored in the direction 𝑘→𝑠=𝑘→1+𝑘→2−𝑘→3 which provides no signal for the chosen pulse length if local field and renormalization effects are negligible. The peak intensity of the time-integrated DFWM signal has been calculated by solving the optical Bloch for a system of two non-interacting two-level systems (2LS) with opposite circular polarization selection rules (local field effect) and for the renormalized four-level system (4LS) depicted in Fig. 1 which assumes the formation of biexcitons between excitons with opposite spins. The signal strength is proportional to the strength of the local field in the case of the 2LS and to the renormalization for the 4LS. The peak signal intensities expected for pure local field and pure biexction contributions are summarized in the second and third column of Table 1 for eight experimental configurations applying different linear and circularly polarized pulses. The values are normalized to the signal strength predicted for three parallel linearly polarized pulses. Close inspection of the data reveals remarkable differences of the peak amplitude with polarization geometry for the two coupling models.

Polarization selection rules for quantum beating between light and heavy holes in GaAs quantum wells - Meier, Torsten; Mayer, E.J.; Smith, G.O.; Kuhl, J.; Schulze, A.; Bennhardt, D.; Koch, S.W.; Thomas, P.; Hey, R.; Ploog, K. (Proceedings of the 5th European Quantum Electronics Conference)
Several recent experimental and theoretical studies have demonstrated the importance of exciton/exciton coupling due to Coulomb interactions for the nonlinear optical response of the 2D exciton in GaAs quantum wells (QWs).1,2 These results imply that multilevel models are required in order to provide a theoretically appropriate description of the nonlinear behavior. Previous application of a renormalized 9-level system has proven successful in describing the third-order response of hh-excitons in GaAs quantum wells.2 We present a comprehensive experimental and theoretical investigation of the polarization selection rules for degenerate- four-wave-mixing (DFWM) and quantum beating of hh and lh transitions in a GaAs QW. Depending on the polarization and temporal sequence of the three pulses simultaneous excitation of the hh and lh transitions generates either quantum beats (QB), no modulation of the signal, or a superposition of QB and polarization interference (PI) effects as proved by spectrally resolved (SR)-DFWM.

Observation of Biexcitons in Time-Resolved Degenerate-Four-Wave-Mixing on GaAs Quantum Wells - Meier, Torsten; Mayer, E.J.; Smith, G.O.; Kuhl, J.; Bennhardt, D.; Schulze, A.; Thomas, P.; Hey, R.; Ploog, K. (International Conference on Ultrafast Phenomena)
Although the importance of exciton/exciton interactions for the nonlinear optical response of GaAs quantum wells (QW) is well established by many experimental observations, the role of biexciton states in these processes is still an open question, even at low excitation densities. Evidence for the formation of biexcitons has been independently derived from pump-probe studies [1], from the density dependence of the photoluminescence (PL) line shape [2] and from signal modulations observed in degenerate-four-wave-mixing (DFWM) with incoherent light pulses [3]. Here, we report on time-resolved DFWM with parallel (PP) and cross-polarized (CP) pulses. Depending on the polarization geometry, the signals reveal strong quantum beats which correspond to the splitting between either the heavy hole (hh) and light hole (lh) exciton or the hh exciton and the biexciton.

Determination of excitonic binding energies in symmetrically strained (GaIn)As/Ga(PAs) multiple quantum wells using quantum beat spectroscopy - Meier, Torsten; Koch, M.; Stolz, W.; Feldmann, J.; Thomas, P.; Göbel, E.O. (Proceedings der 7. International Conference on Superlattices, Microstructures and Microdevices)
We have performed sub-picosecond four-wave mixing experiments on a series of symmetrically strained (GaIn)As/Ga(AsP) multiple quantum wells. We show that these measurements allow a precise determination of exciton binding energies. One of the advantages of this quantum beat method as compared to linear optical methods is that a determination of the exciton binding energy is possible even in the presence of considerable inhomogeneous broadening. In addition, the dependence of the exciton binding energy on the strain in the (GaIn)As quantum well layers suggests that the reduced electron-hole effective mass is not influenced by the increase in strain.

Field-induced dynamics of a wave packet in a wide superlattice miniband - Meier, Torsten; von Plessen, G.; Feldmann, J.; Göbel, E.O.; Thomas, P.; Goossen, K.W.; Kuo, J.M.; Kopf, R.F. (International Quantum Electronics Conference)
In the absence of scattering mechanisms, a crystal electron subjected to a homogeneous electric field undergoes a periodic motion in both momentum and real space. This oscillatory motion is known as Bloch oscillations (BOs) and has recently been detected in transient four-wave mixing (FWM) and Tera-Hertz emission experiments on semiconductor superlattices. It is generally assumed that the minimum field required for the observation of BOs is controlled by the rate of scattering in the material. However, an experimental verification of this point is still lacking.

Direct verification of the existence of biexcitons in GaAs qauntum wells - Meier, Torsten; Smith, G.O.; Mayer, E.J.; Kuhl, J.; Schulze, A.; Bennhardt, D.; Koch, S.W.; Thomas, P.; Hey, R.; Ploog, K. (European Quantum Electronics Conference)
The strong nonlinear optical response of the 2D exciton in GaAs quantum wells at relatively low excitation densities has been observed in many experimental studies in accordance with theoretical predictions. In principle, exciton/exciton interaction results in a renormalization of the transition matrix elements, dephasing rates and frequencies of the excitonic states. Wang et al.1 claimed that all experimental results can be explained by a density- induced enhanced dephasing rate. In a previous paper,2 we have suggested a density dependent coupling between opposite spin excitons, which involves all three renormalization phenomena.