Heinrich Stolz

Giant Rydberg excitons in the copper oxide Cu2O

A highly excited atom having an electron that has moved into a level with large principal quantum number is a hydrogen-like object, termed a Rydberg atom. The giant size of Rydberg atoms leads to huge interaction effects. Monitoring these interactions has provided insights into atomic and molecular physics on the single-quantum level. Excitons—the fundamental optical excitations in semiconductors, consisting of an electron and a positively charged hole—are the condensed-matter analogues of hydrogen. Highly excited excitons with extensions similar to those of Rydberg atoms are of interest because they can be placed and moved in a crystal with high precision using microscopic energy potential landscapes. The interaction of such Rydberg excitons may allow the formation of ordered exciton phases or the sensing of elementary excitations in their surroundings on a quantum level. Here we demonstrate the existence of Rydberg excitons in the copper oxide Cu2O, with principal quantum numbers as large as n = 25. These states have giant wavefunction extensions (that is, the average distance between the electron and the hole) of more than two micrometres, compared to about a nanometre for the ground state. The strong dipole–dipole interaction between such excitons is indicated by a blockade effect in which the presence of one exciton prevents the excitation of another in its vicinity.

Spatially resolved Brillouin spectroscopy to determine the rheological properties of the eye lens

Presbyopia is closely associated with the loss of accommodation, and hence with a decline in the viscoelastic properties of the human eye lens. In this article we describe a method for obtaining spatially resolved in vivo measurements of the rheological properties of the eye lens, based on the spectroscopic analysis of spontaneous Brillouin scattering using a virtually imaged phased array (VIPA). The multi-pass configuration enhances resolution to the extent that measurements are possible in elastic biological tissue characterized by intense scattering. We also present spatially resolved measurements obtained in extracted animal eyes and lenses. The results yield entirely new insights into the aging process of the eye lens.

Condensation of excitons in Cu2O at ultracold temperatures: experiment and theory

We present experiments on the luminescence of excitons confined in a potential trap at milli-Kelvin bath temperatures under continuous-wave (cw) excitation. They reveal several distinct features like a kink in the dependence of the total integrated luminescence intensity on excitation laser power and a bimodal distribution of the spatially resolved luminescence. Furthermore, we discuss the present state of the theoretical description of Bose–Einstein condensation of excitons with respect to signatures of a condensate in the luminescence. The comparison of the experimental data with theoretical results with respect to the spatially resolved as well as the integrated luminescence intensity shows the necessity of taking into account a Bose–Einstein condensed excitonic phase in order to understand the behaviour of the trapped excitons.

Measuring the dynamics of second-order photon correlation functions inside a pulse with picosecond time resolution

We present a detailed discussion of a recently demonstrated experimental technique capable of measuring the correlation function of a pulsed light source with picosecond time resolution. The measurement involves a streak camera in single photon counting mode, which is modified such that a signal at a fixed repetition rate, and well defined energy, can be monitored after each pulsed laser excitation. The technique provides further insight into the quantum optical properties of pulsed light emission from semiconductor nanostructures, and the dynamics inside a pulse, on the sub-nanosecond time scale.

Spatially resolved Brillouin spectroscopy for in vivo determination of the biomechanical properties of the crystalline lenses

Confocal Brillouin spectroscopy is an innovative measurement method for the noninvasive determination of rheological tissue properties. Its application in ophthalmology can offer the possibility to determine in vivo the deformation properties of eye lens with spatial resolution. This seems to be a promising approach concerning current presbyopia research. Due to the spatially resolved detection of the viscoelastic lens properties, a better understanding of the natural aging process of the lens and the influences of different lens opacities on the stiffness is expected. Based on spectral data the refractive index profile, the protein concentration and the density profile within the lens tissue can be derived. A measurement set-up for confocal Brillouin microscopy based on spectral analysis of spontaneous Brillouin scattering signals by using a high-resolution dispersive device is presented. First in vivo measurements results on rabbit eyes are presented and evaluated concerning refractive index distribution, protein concentration, density and rheological significance. These data are compared with known research results of ex vivo lenses.

Mott transition of excitons in GaAs-GaAlAs quantum wells

We investigate the breakup of bound electron–hole pairs, known as Mott transition of excitons, in GaAs-GaAlAs quantum wells with increasing excitation, comparing two different theoretical approaches. Firstly, a thermodynamic approach is used to investigate the ionization equilibrium between electrons, holes and excitons, where the abrupt jump of the degree of ionization from 0 to 1 indicates the Mott density. It is extended to a self-consistent quasi-particle approximation (QPA) for the carrier properties, including dynamical screening of the Coulomb interaction between carriers. Secondly, a spectral approach based on the semiconductor Bloch equations within linear optical response is used, considering the quasi-particle (QP) properties of carriers and the dynamical screening between electron–hole pairs. While the first is effectively a one-particle approach, in the second the whole two-particle spectrum is analyzed. Within the thermodynamic approach, a simple criterion for the Mott transition can be given: namely, if the sum of chemical potentials of carriers, reflecting the effective shrinkage of the band edge, crosses the exciton energy with increasing excitation. We demonstrate that this simple picture cannot be maintained in the two-particle approach. Here, a compact quantity, which describes the behavior of the band edge, does not exist. In fact, the behavior of the single states in the spectrum is generated by the interplay of dynamical screening in the interband self-energy and the effective interaction of the electron–hole pairs. Moreover, the band edge cannot be clearly resolved, since it is merged with excited exciton states (e.g. 2s state), which show up only for densities far below the Mott density. Instead of a Mott density, only a density range can be given, where the Mott transition appears. We demonstrate that a small damping as a prerequisite for the validation of the extended QPA in the thermodynamic approach breaks down, analyzing (i) the dephasing processes with increasing excitation, (ii) the strong increase of the excitonic linewidth and (iii) comparing with the lifetime of carriers in the QP description.

Crystallization in mass-asymmetric electron-hole bilayers

We consider a mass-asymmetric electron and hole bilayer. Electron and hole Coulomb correlations and electron and hole quantum effects are treated on first principles by path integral Monte Carlo methods. For a fixed layer separation we vary the mass ratio M of holes and electrons between 1 and 100 and analyze the structural changes in the system. While, for the chosen density, the electrons are in a nearly homogeneous state, the hole arrangement changes from homogeneous to localized, with increasing M, which is verified for both, mesoscopic bilayers in a parabolic trap and for a macroscopic system. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Ex Vivo Measurement of Postmortem Tissue Changes in the Crystalline Lens by Brillouin Spectroscopy and Confocal Reflectance Microscopy

Use of Brillouin spectroscopy in ophthalmology enables noninvasive, spatially resolved determination of the rheological properties of crystalline lens tissue. Furthermore, the Brillouin shift correlates with the protein concentration inside the lens. In vitro measurements on extracted porcine lenses demonstrate that results obtained with Brillouin spectroscopy depend strongly on time after death. The intensity of the Brillouin signal decreases significantly as early as 5 h postmortem. Moreover, the fluctuation of the Brillouin frequency shift inside the lens increases with postmortem time. Images of lens tissue taken with a confocal reflectance microscope between measurements reveal a degenerative aging process. These tissue changes correlate with our results from Brillouin spectroscopy. It is concluded that only in vivo measurements appropriately reflect the rheological properties of the eye lens and its protein concentration.

Strongly correlated indirect excitons in quantum wells in high electric fields

We study the Stark effect on excitonic complexes confined in a GaAs-based single quantum well. We approach this problem using Path Integral Monte Carlo methods to compute the many-body density matrix. The developed method is applied for investigation of the electric field-dependence of energies, particle distribution and effective exciton dipole moment. Using these results as an input we apply thermodynamical Monte Carlo methods to investigate systems of several tens to thousands indirect excitons in a 2D quantum well with a lateral confinement arising from the quantum confined Stark effect. Depending on the field strength, exciton density and temperature different phases (gas, liquid and solid) of indirect excitons are predicted.

Interaction of Rydberg excitons in cuprous oxide with phonons and photons: optical linewidth and polariton effect

We demonstrate that the optical linewidth of Rydberg excitons in Cu2O can be completely explained by scattering with acoustical and optical phonons, whereby the dominant contributions stems from the non-polar optical modes. The consequences for the observation of polariton effects are discussed. We find that an anti-crossing of photon and exciton dispersions exists only for states with main quantum numbers n>28, so polariton effects do not play any role in the experiments reported up to now.