We investigate the two-pulse photon echo response of excitons in the mixed lead halide perovskite crystal FA(0.9)Cs(0.1)PbI(2.8)Br(0.2) in dependence on the excitation intensity and polarization of the incident laser pulses. Using spectrally narrow picosecond laser pulses, we address localized excitons with long coherence times T-2 approximate to 100 ps. This approach offers high sensitivity for the observation of excitation-induced changes in the homogeneous line width Gamma(2) = 2h/T-2 on the mu eV scale. Through intensity-dependent measurements, we evaluate the increase of Gamma(2) by 10 mu eV at an exciton density of 10(17) cm(-3) being comparable with the intrinsic line width of 14 mu eV. We observe that the decay of the photon echo and its power dependence are sensitive to the polarization configuration of the excitation pulses, which indicates that spin-dependent exciton-exciton interactions contribute to excitation-induced dephasing. In cross-linear polarization, the decay is faster and its dependence on exciton density is stronger as compared to the copolarized configuration. Using a two-exciton model accounting for different spin configurations we are able to reproduce the experimental results.

The nonlinear optical response of an ensemble of semiconductor quantum dots is analyzed by wave-mixing processes, where we focus on four-wave mixing with two incident pulses. Wave-mixing experiments are often described with semiclassical models, where the light is modeled classically and the material quantum mechanically. Here, however, we use a fully quantized model, where the light is given by a quantum state of light. Quantum light involves more degrees of freedom than classical light as e.g., its photon statistics and quantum correlations, which is a promising resource for quantum devices, such as quantum memories. The light-matter interaction is treated with a Jaynes-Cummings type model and the quantum field is given by a single mode since the quantum dots are embedded in a microcavity. We present numerical simulations of the four-wave-mixing response of a homogeneous system for pulse sequences and find a significant dependence of the result on the photon statistics of the incident pulses. The model constitutes a problem with a large state space which arises from the frequency distribution of the transition energies of the inhomogeneously broadened quantum dot ensemble that is coupled with a quantum light mode. Here we approximate the dynamics by summing over individual quantum dot-microcavity systems. Photon echoes arising from the excitation with different quantum states of light are simulated and compared.

Coherent control of ensembles of light emitters by means of multi-wave mixing processes is key for the realization of high capacity optical quantum memories and information processing devices. In this context, semiconductor quantum dots placed in optical microcavities represent excellent candidates to explore strong light-matter interactions beyond the limits of perturbative non-linear optics and control the unitary evolution of optically driven quantum systems. In this work, we demonstrate that a sequence of two optical picosecond pulses can be used to establish coherent control over the phase evolution of the ensemble of trions in (In,Ga)As quantum dots independent of their initial quantum state. Our approach is based on coherent transfer between degenerate multi-wave-mixing signals in the strong field limit where Rabi rotations in multi-level systems take place. In particular, we use the two-pulse photon echo sequence to uncover the coherent dynamics of the trion ensemble, whereas the areas of two additional control pulses serve as tuning knobs for adjusting the magnitude and timing of the coherent emission. Furthermore, we make use of the spin degeneracy of ground and excited state of trions to control the polarization state of the emitted signal. Surprisingly, we reveal that the use of optical control pulses, whose durations are comparable to the dephasing time of the ensemble, lifts the temporal degeneracy between wave-mixing processes of different order. This phenomenon is manifested in a significant modification of the temporal shape of the coherent optical response for strong optical fields. Lifting the temporal degeneracy allows to smoothly trace the transition from the perturbative to the regime of Rabi rotations and opens up new possibilities for the optical investigation of complex energy level structures in so far unexplored material systems.

Compositional engineering of the optical properties of hybrid organic-inorganic lead halide perovskites is crucial for the realization of efficient solar cells and light-emitting devices. We study the effect of band gap fluctuations on coherent exciton dynamics in a mixed FA0.9Cs0.1PbI2.8Br0.2 perovskite crystal by using photon echo spectroscopy. We reveal a narrow homogeneous exciton line width of 16 μeV at a temperature of 1.5 K. The corresponding exciton coherence time T2 = 83 ps is exceptionally long due to the localization of excitons at the scale of tens to hundreds of nanometers. From spectral and temperature dependences of the two- and three-pulse photon echo decay, we conclude that for low-energy excitons pure decoherence associated with elastic scattering on phonons is comparable with the exciton lifetime, while for excitons with higher energies, inelastic scattering to lower energy states via phonon emission dominates.

We study Rabi rotations arising in intensity-dependent photon echoes from an ensemble of self-assembled InGaAs quantum dots. To achieve a uniform distribution of intensities within the excited ensemble, we introduce flattop intensity profiles of picosecond laser pulses. This allows us to overcome the damping of Rabi rotations imposed by the spatial inhomogeneity of Rabi frequencies by a Gaussian laser profile. Using photon echo polarimetry, we distinguish between the coherent optical responses from exciton and trion ensembles. Here, we demonstrate that a photo-induced charging of the quantum dots leads to a significant reduction of the number of neutral quantum dots under resonant excitation with intensive optical pulses with areas exceeding $\frac{\pi}{2}$. The trion ensemble shows robust Rabi rotations when the area of the refocussing pulse is increased up to 5.5$\pi$. We analyze the remaining attenuation of Rabi rotations by theoretical modeling of excitation induced dephasing, inhomogeneity of dipole moments, and coupling to acoustic phonons. The latter is identified as the dominating mechanism resulting in a loss of optical coherence during the action of the involved optical pulses.

Lead halide perovskites show remarkable performance when used in photovoltaic and optoelectronic devices. However, the peculiarities of light-matter interactions in these materials in general are far from being fully explored experimentally and theoretically. Here we specifically address the energy level order of optical transitions and demonstrate photon echos in a methylammonium lead triiodide single crystal, thereby determining the optical coherence times T_2 for excitons and biexcitons at cryogenic temperature to be 0.79 ps and 0.67 ps, respectively. Most importantly, we have developed an experimental photon-echo polarimetry method that not only identifies the contributions from exciton and biexciton complexes, but also allows accurate determination of the biexciton binding energy of 2.4 meV, even though the period of quantum beats between excitons and biexcitons is much longer than the coherence times of the resonances. Our experimental and theoretical analysis methods contribute to the understanding of the complex mechanism of quasiparticle interactions at moderate pump density and show that even in high-quality perovskite crystals and at very low temperatures, inhomogeneous broadening of excitonic transitions due to local crystal potential fluctuations is a source of optical dephasing.