Dense Exciton Gas Research Articles

Evidence for a Bose-Einstein condensate of excitons

We report compelling evidence for a “gray” condensate of dipolar excitons, electrically polarised in a 25 nm wide GaAs quantum well. The condensate is composed by a macroscopic population of dark excitons coherently coupled to a lower population of bright excitons. To create the exciton condensate we use an all-optical approach in order to produce microscopic traps which confine a dense exciton gas that yet exhibits an anomalously weak photoemission at sub-kelvin temperatures. This is the first fingerprint for the “gray” condensate. It is then confirmed by the macroscopic spatial coherence and the linear polarization of the weak excitonic photoluminescence emitted from the trap, as theoretically predicted.

Exciton Gas versus Electron Hole Liquid in the Double Quantum Wells

ABSTRACTThe many-body correlation effects in the spatially separated electron and hole layers in the coupled quantum wells (CQW) are investigated. A special case of the many-component electron-hole system is considered, ν>>1 being the number of the components. Keeping the main diagrams in the parameter 1/ν allows us to justify the selection of the RPA diagrams. The ground state of the system is found to be the electron-hole liquid with the energy smaller than the dense exciton gas phase. The possible connection is discussed between the results obtained and the experiments in which the inhomogeneous state in the CQW is found.

Excitation energy dependence of the exciton inner ring

We report on the excitation energy dependence of the inner ring in the exciton emission pattern. The contrast of the inner ring is found to decrease with lowering excitation energy. Excitation by light tuned to the direct exciton resonance is found to effectively suppress excitation-induced heating of indirect excitons and facilitate the realization of a cold and dense exciton gas. The excitation energy dependence of the inner ring is explained in terms of exciton transport and cooling.

Electrostatically trapping indirect excitons in coupled InxGa1−xAs quantum wells

We report on photoluminescence experiments on spatially indirect excitons in an InGaAs coupled double quantum well device in which semitransparent gates are employed to tune the in-plane potential landscape. We introduce a trapping configuration in which exciton generation is spatially separated from the excitonic trapping potential. Suitably biased gates control the flow of indirect dipolar excitons from the generation area to the electrostatically defined trap. Thus the trap is filled only with indirect excitons precooled to the lattice temperature. Using a confocal microscope at liquid helium temperatures we map the in-plane distribution of excitons at various gate voltages and illumination conditions. Our small and strongly confining traps with precooled excitons demonstrate interesting many-body effects which can be interpreted in terms of the electrostatic screening, the Coulomb binding, and excitonic flows. Gate voltage dependencies of PL energy in our samples are not monotonic and can be explained by considering the nonlinear exciton flows between the elements of our structure. At strong illumination hysteretic switching of the trapped exciton population reflects a nonlinear character of the self-consistent trapping potential. An unusual nonlinear increase of the emission of the trap is likely coming from the many-body interactions in a dense exciton gas in the presence of a disorder potential at high light intensity. The designs of electrostatic traps proposed and realized here allow for stronger confinements and lower temperatures and will be used to search for coherent phenomena in dense exciton gases.

Stimulated Emission from Wide-Gap Semiconductors

Stimulated emission and optical gain problems are reviewed on the basis of analysis of highly photoexcited III-Nitride and ZnO wide-gap materials. Spontaneous and stimulated emission along with optical gain of these materials in UV region is analyzed. The possible mechanisms of inverted population in In-containing materials and ZnO semiconductors are discussed involving mechanisms of dense electron-hole plasma, carrier (exciton) localization, as well as various interaction processes in dense exciton gas.

Trapping Indirect Excitons in a GaAs Quantum-Well Structure with a Diamond-Shaped Electrostatic Trap

We report on the principle and realization of a new trap for excitons--the diamond electrostatic trap--which uses a single electrode to create a confining potential for excitons. We also create elevated diamond traps which permit evaporative cooling of the exciton gas. We observe the collection of excitons towards the trap center with increasing exciton density. This effect is due to screening of disorder in the trap by the excitons. As a result, the diamond trap behaves as a smooth parabolic potential which realizes a cold and dense exciton gas at the trap center.

Kinetics of indirect excitons in an optically induced trap in GaAs quantum wells

We report on the kinetics of a low-temperature gas of indirect excitons in the optically-induced exciton trap. The excitons in the region of laser excitation are found to rapidly -- within 4 ns -- cool to the lattice temperature T = 1.4 K, while the excitons at the trap center are found to be cold -- essentially at the lattice temperature -- even during the excitation pulse. The loading time of excitons to the trap center is found to be about 40 ns, longer than the cooling time yet shorter than the lifetime of the indirect excitons. The observed time hierarchy is favorable for creating a dense and cold exciton gas in optically-induced traps and for in situ control of the gas by varying the excitation profile in space and time before the excitons recombine.

Stimulated emission due to spatially separated electron-hole plasma and exciton system in homoepitaxial GaN

Stimulated emission under quasi-resonant photoexcitation was studied in high-quality homoepitaxial GaN layers. Emission escaping perpendicular to the excited surface as well as propagating along the surface was analyzed as a function of the excitation power density in the temperature range from 8 to $600\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Contributions of stimulated emission due to inelastic exciton\char21{}exciton/carrier interaction and recombination in electron-hole plasma (EHP) were revealed and simultaneously observed from the sample edge. The concurrent action of two mechanisms of stimulated emission was interpreted to be caused mainly by spatially inhomogeneous Mott transition due to separation of EHP located at the very surface of the layer and dense exciton gas located deeper in the layer. The separation is facilitated by high carrier diffusion length in homoepitaxial GaN. Stimulated emission due to inelastic exciton\char21{}exciton/carrier interaction was unambiguously traced up to the temperature of $440\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.

Creation of supercooled exciton gas and transformation to electron-hole droplets in diamond

We investigated the formation dynamics of electron-hole droplets in a high-purity single crystal diamond under photoexcitation near the band gap using time-resolved emission spectroscopy. Below the exciton Mott transition density, photogenerated carriers are cooled, and exciton emission appears within 30 ps. A broad emission band of droplets rises slowly, accompanied with a reduction in the exciton emission intensity in the next hundred picoseconds. This spectral change indicates the initial formation of low-temperature supersaturated exciton gas and subsequent spatial condensation of dense exciton gas into electron-hole droplets.

Relaxation kinetics of excitons in cuprous oxide

Due to a simple band structure, the excitons in cuprous oxide $({\mathrm{Cu}}_{2}\mathrm{O})$ are a model system for kinetic studies. Cuprous oxide appeared to be a host for a Bose-Einstein condensate of excitons, as the excitons showed transient kinetic energy distributions which matched those expected for a Bose gas near the critical density for Bose-Einstein condensation. However, recent absolute measurements of the exciton density made it clear that two-exciton annihilation is limiting the exciton density to far below the quantum density. This paper reconciles the measured exciton density with the observed exciton energy distributions by using a Boltzmann equation approach. We include experimentally determined rates for acoustic- and optical-phonon emission, conversion between exciton spin states, and two-exciton annihiliation, and use recent diffusion-Monte-Carlo estimates of the exciton-exciton elastic scattering cross section. Many experiments intending to produce a dense exciton gas in ${\mathrm{Cu}}_{2}\mathrm{O}$ used surface photoexcitation, and we found it important to include the resulting spatial inhomogeneities in the model by following the exciton occupation numbers as functions of space as well as momentum and time. A detailed but straightforward numerical integration of the resulting Boltzmann equation does in fact match the experimental results, without the assumption of quantum statistics for the excitons.

One-Dimensional Model of Many-Exciton Effects in Photoluminescence Spectra

We solve numerically in one dimension and in the self-consistent ladder approximation the many-body problem of interacting electrons and holes. The model contains the minimal ingredients allowing to take into account the coexistence of a population of bound excitonic states with weakly correlated e-h pairs. A simplified contact potential for the Coulomb interaction is used. The strong e-h correlation leads to asymmetric single particle spectral functions with structures related to bound excitonic states. This asymmetry becomes more pronounced at low temperature when the formation of a dense exciton gas occurs. We discuss the role of the many-exciton effects by comparing the photoluminescence peak energies obtained in the ladder and Hartree-Fock approximation.

Electric-Field Tuning of Spin-Dependent Exciton-Exciton Interactions in Coupled Quantum Wells

We have shown experimentally that an electric field decreases the energy separation between the two components of a dense spin-polarized exciton gas in a coupled double quantum well, from a maximum splitting of $\sim 4$ meV to zero, at a field of $\sim $35 kV/cm. This decrease, due to the field-induced deformation of the exciton wavefunction, is explained by an existing calculation of the change in the spin-dependent exciton-exciton interaction with the electron-hole separation. However, a new theory that considers the modification of screening with that separation is needed to account for the observed dependence on excitation power of the individual energies of the two exciton components.

Dynamics of dense exciton gas in semiconductor nanocrystals

The nonlinear absorption of CuBr nanocrystals embedded in a transparent glass matrix was investigated by using the excite-and-probe method. The luminescence properties of samples with different average nanocrystal radii were also studied. A fast-decaying damping of exciton absorption band was observed, and interpreted as being mainly caused by elastic collisions between excitons. The relationship between the photoinduced changes of the absorption and the exciton density was established. Radiative exciton - exciton interaction and surface recombination were revealed as the main recombination processes governing the decay of excitons in CuBr nanocrystals, and the relevant rate constants were evaluated.

Theory of the optical properties of excitons in a homogeneous magnetic field

Abstract We derive the semiconductor Bloch equations for magnetoexcitons in real space. By means of the Laguerre-Fourier transform, an equivalent formulation can be given which uses Landau orbitals and plane waves as a basis set. The linear optical absorption is calculated using the real-space formulation. A transition is performed from a three-dimensional (zero magnetic field) to a one-dimensional (high magnetic field) semiconductor. A gap equation for a dense exciton gas is deduced, which contradicts previous results.

Photoluminescence excitation spectroscopy of the dense exciton gas involved in the lasing transition in ZnSe epitaxial layers

The lasing transition in ZnSe epitaxial layers has been investigated at 77 K. The lowest lasing threshold (I/sub th/) was achieved when the layers were resonantly excited at the photon energy of the exciton level. It was found that the exciton level at the excitation intensity just above the I/sub th/ was red-shifted by about 16 meV compared with the free exciton line (2.792 eV) under weak excitation condition. The energy difference between the exciton line and the lasing peak was about 19 meV at I=I/sub th/ and increased with increasing excitation intensity up to I=8/spl times/I/sub th/. This suggests that the stimulated emission occurs due to the inelastic exciton-exciton scattering process at this temperature. >

Many‐Body Theory for the Dense Exciton Gas of Direct Semiconductors. III. Response of the Many‐Exciton System on an Externally Driven Light Field

AbstractThe nonlinear response of a dense exciton gas in a platelet on an externally driven field is discussed using non equilibrium Green's function technique. A generalized Boltzmann‐equation of excitons containing many‐particle corrections in the diffusion‐, drift‐ and collision‐term is derived. Using a relaxed distribution (Boltzmann‐distribution) and an unrelaxed distribution (macro‐occupation) of ls‐excitons a bistability in exciton density as well as in the transmitted light intensity is obtained for a nearly resonant and stationary applied pump‐field of intensity 0.1 and 10kW/cm2, respectively. The bistability is obtained as a pure excitonic effect below the Mott‐transition.

Many‐Body Theory for the Dense Exciton Gas of Direct Semiconductors II. Calculation of Exciton Level Shift and Damping in Dependence on Exciton Density

AbstractThe spectral properties of a dense exciton gas are discussed using an exciton self‐energy in second collisional Born approximation with respect to exciton‐exciton interaction. The shift of the continuum edge and the ls exciton as well as the increase of the damping of the ls exciton are calculated linearly in the exciton density. The distribution of ls excitons is assumed to be either a macro‐occupation of the k = 0 state or a Boltzmann distribution with effective temperature varying between 10 and 60 K. A weakening of the level shift is obtained with increasing temperature. In the case of macro‐occupation damping is calculated self‐consistently resulting in a sublinear dependence on density.

Many‐Body Theory for the Dense Exciton Gas of Direct Semiconductors I. General Considerations

AbstractThe dense exciton gas is studied theoretically using the two‐time electron–hole pair propagator. The equation of motion for the propagator and an expression for the electron–hole pair selfenergy are transformed to a picture in which electron–hole pairs are mapped on bosons. The lowest decoupling of the selfenergy provides contributions of first and second order concerning the interaction between electron–hole pairs including electron–electron, hole–hole, and electron–hole pair exchange. It is shown that only the direct interaction between electron–hole pairs can be screened by a dielectric function. The connection with results obtained on the basis of an effective Hamiltonian for bosonic electron–hole pairs is discussed.

Stimulated radiation emitted from zinc selenide single crystals under streamer excitation conditions

A study was made of stimulated emission of radiation and lasing in zinc selenide single crystals subjected to a transverse streamer discharge (T = 294 and 77 K). The stimulated radiation observed in the 448–449 nm range at 77 K was attributed to radiative recombination in a dense exciton gas, whereas that observed at room temperature originated from an electron–hole plasma. The threshold density of nonequilibrium carriers needed for the generation of light at 77 K did not exceed 1018 cm−3 .

Transient Light‐Induced Gratings Due to Excitons in CdSe

AbstractTransient light‐induced gratings due to free carriers and excitons are created in CdSe in a medium density range of 1015 to 1017 cm−3 by two coherent intense (ns) IR‐pump beams. Detailed investigations of probe‐beam diffraction due to thin excitonic gratings in the spectral region just below the An = 1 ‐exciton line at 85 K and its dependence on sample temperature and on the excitation level are presented. First‐order diffraction efficiences up to 5% and a nonlinear dependence of diffraction on the excitation level can be observed. For the first time numerical calculations of probe‐beam diffraction due to excitonic phase and amplitude gratings are presented. The comparison with the experiment shows, that the damping of a dense exciton gas increases proportional to the excitation intensity in the case of two‐photon interband excitation, and that the light‐induced absorptive changes Δ due to dense excitons dominate over the dispersive changes Δn in the spectral region under consideration.