Dirk Semkat

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.

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.

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.

Comment on "condensation of excitons in a trap".

C of excitons is still a fascinating topic of solid state physics. In a recent Letter “Condensation of Excitons in a Trap”, High et al. claim to have observed a condensed state in a system of indirect excitons in double quantum well structures within an electrostatic potential trap. As in every Bose−Einstein condensate, spontaneous coherence of matter waves should emerge in the exciton system. This coherence is transferred to the decay luminescence and thus should be observable in the light emission from the exciton cloud. Indeed, the authors have observed in a series of experiments a pronounced increase of the coherence of the light emitted from the excitons either by lowering the temperature or by increasing the power of the laser exciting the excitons (compare Figures 3d,e, 4, and 5 of ref 1). The coherence properties of the emitted light were measured with the well-known technique of shift interferometry. Here two images of the same object, shifted by a small amount of δ, are superimposed, and by varying the phase delay between the two light paths, interference fringes are generated (see Figure 2 of ref 1). To determine the interference contrast, the authors use the simple formula C = (I12 − I1 − I2)/2(I1I2). Further support for the interpretation of the occurrence of a “condensate” is derived by the authors from a simple ideal Boson model for the excitons captured in a harmonic trap from the critical temperature Tc = (6 )/(π)ħω2d with ω2d = (ωxωy) 1/2 being the 2d oscillator frequency. With the assumptions for the trap oscillator frequencies the authors give, this indeed would lead to a critical temperature for BEC for N ≃ 3 × 10 excitons in the trap of 2 K. As will be shown in this comment, there are several objections against the statements in ref 1 based on a rigorous theory of shift interferometry as well as on the thermodynamic properties of a dense interacting exciton gas in a potential trap. Theory of Shift Interferometry. We start with a single point emitter at position xo,yo in the object plane at −d1, which is imaged by a lens. The amplitude of the light field at a point (xi,yi) in the image plane at d2 is then given by 3

Unique signatures for Bose-Einstein condensation in the decay luminescence lineshape of weakly interacting excitons in a potential trap

We calculate the spatially resolved optical emission spectrum of a weakly interacting Bose gas of excitons confined in a three dimensional potential trap due to interband transitions involving weak direct and phonon mediated exciton-photon interactions. Applying the local-density approximation, we show that for a noncondensed system the spatiospectral lineshape of the direct process reflects directly the shape of the potential. The existence of a Bose-Einstein condensate changes the spectrum in a characteristic way so that it directly reflects the constant chemical potential of the excitons and the renormalization of the quasiparticle excitation spectrum. Typical examples are given for parameters of the lowest yellow excitons in

Interacting multicomponent exciton gases in a potential trap: Phase separation and Bose-Einstein condensation

{\text{Cu}}_{2}\text{O}

Mott transition versus Bose-Einstein condensation of excitons

.

Imaging interferometry of excitons in two-dimensional structures: can it detect exciton coherence

The system under consideration is a multicomponent gas of interacting paraexcitons and orthoexcitons confined in a three-dimensional potential trap. We calculate the spatially resolved optical emission spectrum due to interband transitions involving weak direct and phonon-mediated exciton-photon interactions. For each component, the occurrence of a Bose-Einstein condensate changes the spectrum in a characteristic way so that it directly reflects the constant chemical potential of the excitons and the renormalization of the quasiparticle excitation spectrum. Moreover, the interaction between the components leads, in dependence on temperature and particle number, to modifications of the spectra indicating phase separation of the subsystems. Typical examples of density profiles and luminescence spectra of ground-state paraexcitons and orthoexcitons in

Multicomponent exciton gas in cuprous oxide: cooling behaviour and the role of Auger decay

{\text{Cu}}_{2}\text{O}

Phase separation of multicomponent excitonic Bose–Einstein condensates

are given.