Interactions of 1S Excitons in Cu2O: A High Resolution Spectroscopy Study
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Beschreibung
More than 80 years ago Albert Einstein predicted the macroscopic occupation of the ground state of a Bose gas. The so-called Bose- Einstein condensation (BEC) is one of the most stringent manifestations of the quantum character of matter. The phase transition to a condensate was first demonstrated for alkali atoms at nanokelvin temperatures in a potential trap. BEC is related to phenomena like superfluidity and lasing. In principle, BEC occurs in every system of quasiparticles with integer spin if sufficiently high densities for T below a critical temperature TC are reached. Indeed, for magnons in magnetic semiconductors and polaritons in microcavities recent observations have been interpreted as BEC. Though showing very promising results, condensate-like phenomena in the polariton system are most likely obtained far from equilibrium due to rather short carrier lifetimes.
Excitons as bound electron-hole pairs resemble atoms of usual matter and thus are particularly interesting for a BEC. Excitons behave as bosons close to the Mott transition, where the fermionic constituents become prominent in a fully ionized electron-hole plasma. Since the exciton mass is rather small, the phase transition could occur at critical temperatures of a few 10 K for exciton densities n oc 1018/cm3.
The most promising candidate for a quasi-equilibrium excitonic BEC are the 1S excitons, in particular the paraexciton, of the yellow series in cuprous oxide (Cu2O). This is based on the large exciton binding energy of 150 meV, which shifts the Mott transition to 1019/cm3. As the composing electron and hole have almost equal masses close to the free electron mass, the system resembles a positronium atom. This is of interest as a candidate for BEC since it opens the way to a gamma ray laser at 511 keV.
The 1S excitons consist of the paraexciton and the split-off orthoex- citons. In most experiments concerning BEC in Cu2O nonresonant or resonant excitation of the orthoexcitons was studied. Because of the energy shift of 12 meV this scheme of paraexciton excitation leads to hot paraexcitons, which have to cool down by exciton-exciton and/or acoustic phonon interaction to exhibit at high densities BEC with a macroscopic population at wave number k = 0. Direct excitation by absorption at k = k0 (photon wave number) yields ultracold excitons, which then thermalize to a Bose-distributed exciton gas. A BEC related phase transition, however, was not observed up to now.
At low temperatures, thermalization of the exciton gas is caused by scattering with phonons and exciton-exciton scattering. A weak inter- action of excitons is also a prerequisite for a stable condensate since condensation is related to phase coherence of the wavefunction. In this work the scattering mechanisms that lead to thermalization of the paraexciton gas are investigated by high resolution spectroscopy techniques. The scattering with acoustic phonons is examined by po- lariton propagation beats, effects of exciton-exciton scattering are ob- served in density dependent shifts of the exciton resonance. The ob- servation of a blueshift of the paraexciton resonance with increasing density is a clear indication of a repulsive interaction, whereas with the redshift of orthoexcitons an attractive interaction of the paraexciton and orthoexcitons is demonstrated. From the analysis of the blueshift we derive exciton densities.
This thesis is structured as follows: In Chapter 2 the basic prop- erties of Cu2O are introduced, particularly the characteristics of the 1S excitons with regard to symmetry and their coupling to photons and phonons. Afterwards, in Chapter 3 the experimental technique of high resolution spectroscopy on bulk solids, which requires high quality strain free samples, is explained in detail. Chapter 4 deals with the paraexciton quadrupole polariton. Basic properties like absorption and its magnetic field dependence as well as the fundamental polariton effect of propagation beats are examined. From the polariton propagation beats long dephasing times due to a small acoustic phonon scattering rate are deduced. Also, a new effect in the Faraday rotation spectrum is presented that is related to the quadrupole polariton character of the paraexciton.
In Chapter 5 the interaction of paraexcitons is investigated. Elastic exciton-exciton scattering is studied with regard to the possible S-wave scattering channels, and particularly focus on paraexciton-paraexciton scattering and paraexciton-orthoexciton scattering. Furthermore, the two-body decay is briefly discussed in context with the conversion of resonantly excited paraexcitons to orthoexcitons.
Finally, in Chapter 6, some conclusions are drawn from the pre- sented results, and an outlook is given on further experiments on BEC of 1S excitons that combine high resolution spectroscopy with previous attempts in strain-induced traps.
Autor*in
Jan Christopher Brandt
Themen in »Interactions of 1S Excitons in Cu2O: A High Resolution Spectroscopy Study«
pump probe absorption spectroscopy bose-einstein condensation cuprous oxide exciton-exciton interaction exciton-phonon coupling laser spectroscopy polariton propagation beats semiconducto opties