Phase diagram of the bose condensation of dipolar excitons in GaAs/AlGaAs quantum-well heterostructures

Experimental studies of the phase diagram of Bose condensation in a system of spatially indirect dipolar excitons in GaAs/AlGaAs quantum wells are reviewed. The properties of spatially periodic patterns arising in the luminescence of the exciton Bose condensate in a ring-shaped potential trap and the coherence of the condensate luminescence are discussed.     

Two-photon correlations of luminescence at the Bose-Einstein condensation of dipolar excitons

Correlations of the luminescence intensity (the second-order correlation function g ⁽²⁾(τ)), where τ is the delay time between the photons detected in pairs) under the conditions of the Bose-Einstein condensation (BEC) of dipolar excitons has been studied in a temperature range of 0.45–4.2 K. Photoexcited dipolar excitons have been accumulated in a lateral trap in a GaAs/AlGaAs Schottky diode with a 25-nm wide single quantum well with an electric bias applied across the heterolayers. Two-photon correlations have been measured with the use of a two-beam intensity interferometer with a time resolution of }~0.4 ns according to the well-known classical Hanbury-Brown-Twiss scheme. The photon bunching has been observed at the onset of Bose-Einstein condensation manifested by the appearance of a narrow exciton condensate line in the luminescence spectrum at an increase in the optical pumping (the line width near the threshold is ?200 μeV). At the same time, the two-photon correlation function itself obeys the super-Poisson distribution, g ⁽²⁾(τ) > 1, at time scale τ_c ? 1 ns of the system coherence. The photon bunching is absent at a pumping level substantially below the condensation threshold. The effect of bunching also decreases at pumping significantly above the threshold, when the narrow exciton condensate line starts to dominate in the luminescence spectra, and finally disappears with the further increase in the optical excitation. In this region, the distribution of pair photon correlations is a Poisson distribution manifesting the united quantum coherent state of the exciton condensate. Under the same conditions, the first-order spatial correlation function g ⁽¹⁾(r) determined from the interference pattern of the luminescence signals from the spatially separated parts of the condensate at constant pumping remains noticeable at distances of no less than 4 μm. The discovered effect of photon bunching is very sensitive to temperature and decreases by several times with a temperature increase in the range of 0.45–4.2 K. Assuming that the luminescence of the dipolar excitons directly reflects the coherence properties of the gas of interacting excitons, the discovered photon bunching at the onset of condensation, where the fluctuations of the exciton density and, consequently, of the luminescence intensity are most significant, indicates a phase transition in the interacting Bose gas of excitons, which is an independent way of detecting the Bose-Einstein condensation of excitons.     

Collective state in a bose gas of interacting interwell excitons

Experiments associated with direct observations of a collective state in a gas of interacting interwell excitons in GaAs/AlGaAs double quantum wells are discussed. The structures constitute Schottky photodiodes. In a metallic gate, circular windows of various sizes (diameters of 2 to 20 μm) are etched by means of electronic-beam lithography. Through these windows, the photoluminescence of interwell and intrawell excitons is excited and detected. A microscopic device allows the observation of the spatial structure of luminescence with a resolution of 1 μm through the windows of a sample placed in superfluid helium. Using optical interference filters, the spatial structure of the luminescence is analyzed selectively in the spectrum for interwell and intrawell excitons under the same experimental conditions. It is found that the photoluminescence of interwell excitons under certain conditions exhibits an axisymmetric spatial structure: along the perimeter of the windows through which the photoluminescence is observed, a regular ring pattern of equidistant bright spots of the luminescence of interwell excitons appears. This structure appears only above the photoexcitation power threshold and the number of equidistant bright spots in the ring increases with the pumping power. At high pumping powers, the structure of distinct periodic luminescence spots is smeared. At a fixed pumping power, the phenomenon exhibits explicit critical temperature dependence: the structure of regularly located luminescence spots is smeared at T > 4 K. Axisymmetric spatial configurations of equidistant luminescence spots are observed in windows of the diameters 2, 5, and 10 μm. For intrawell excitons, the spatial structure of luminescence is not observed under similar experimental conditions: the luminescence of intrawell excitons is spatially uniform in all the windows under investigation. The effect is a result of the collective behavior of interacting interwell excitons.     

Electro-optical trap for dipolar excitons in a GaAs/AlAs Schottky diode with a single quantum well

An electro-optical trap for spatially indirect dipolar excitons has been implemented in a GaAs/AlAs Schottky diode with a 400-Å-wide single quantum well. In the presence of a bias voltage applied to a gate, the trap for excitons appears upon ring illumination of the structure by a continuous-wave or pulsed laser generating hot electron-hole pairs in the quantum well. A barrier for excitons collected inside the illuminated ring appears because of the screening of the applied electric field by nonequilibrium carriers directly in the excitation region. Excitons are collected inside the ring owing to the ambipolar drift of carriers and dipole-dipole exciton repulsion in the optical pump region. For dipolar excitons thus collected in the center of the ring electrooptical trap, a significant narrowing of the luminescence line that accompanies an increase in the density of excitations indicates the collective behavior of dipolar excitons.     

Dipolar excitons in a potential trap in a magnetic field

The conditions for observing the Zeeman spin splitting compensation in an exciton Bose gas have been investigated. The magnetoluminescence of spatially indirect, dipolar excitons in a 25-nm-wide GaAs/AlGaAs quantum well upon their accumulation in a lateral electrostatic trap has been studied in the Faraday geometry. The critical magnetic field B _cr below which the spin (paramagnetic) splitting of the luminescence line for a heavy-hole exciton at the trap center is almost completely compensated due to the exchange interaction in a dense Bose gas has been found to increase linearly with exciton concentration in qualitative agreement with the theory. Using a potential trap is fundamentally important. Incomplete compensation is observed in a homogeneous photoexcitation spot for dipolar excitons: the splitting is considerably smaller than that for a spatially direct exciton but differs noticeably from zero. The spin splitting compensation effect is observed only under neutral charge balance conditions—there is no Zeeman splitting suppression in a charged quantum well.     

Bose–Einstei condensation of dipolar excitons in a ring trap

The temperature of Bose–Einstein condensation and the fraction of particles in a condensate for a system of spatially indirect dipole excitons in an electrostatic ring trap have been found. If only levels of the radial motion close to the bottom of the potential well of the trap are populated considerably, the oscillatory model of the single-particle spectrum is applicable. In this case, even the strong exciton–exciton interaction can be taken into account.     

Bose condensation of two-dimensional dipolar excitons: Simulation by the quantum Monte Carlo method

The Bose condensation of two-dimensional dipolar excitons in quantum wells is numerically studied by the diffusion Monte Carlo simulation method. The correlation, microscopic, thermodynamic, and spectral characteristics are calculated. It is shown that, in structures of coupled quantum wells, in which low-temperature features of exciton luminescence have presently been observed, dipolar excitons form a strongly correlated system.     

Angular distribution of photoluminescence as a probe of bose condensation of trapped excitons

Recent experiments on two-dimensional exciton systems have shown that excitons collect in shallow in-plane traps. We find that Bose condensation in a trap results in a dramatic change of the exciton photoluminescence (PL) angular distribution. The long-range coherence of the condensed state gives rise to a sharply focused peak of radiation in the direction normal to the plane. By comparing the PL profile with and without Bose condensation, we provide a simple diagnostic for the existence of a Bose condensate. The PL peak has strong temperature dependence due to the thermal order parameter phase fluctuations across the system. The angular PL distribution can also be used for imaging vortices in the trapped condensate. Vortex phase spatial variation leads to destructive interference of PL radiation in certain directions, creating nodes in the PL distribution that imprint the vortex configuration.     

Lasing threshold in traps for Bose-condensation of dipolar excitons

We consider exciton recombination lasing in heterostructure traps for Bose–Einstein condensation of dipolar excitons. We show that such structures suit well for class D lasers where cavity decay strongly exceeds polarization decay. We evaluate lasing threshold taking into account specific inhomogeneous broadening of the exciton spectral line owing to Bose–Einstein condensation phenomenon under quasi-equilibrium conditions.It is found that narrowing of the exciton momentum distribution just before the condensation onset considerably lowers lasing threshold. At the same time, it is pointed out that a subsequent formation of condensate itself does not help lasing much. We conclude that it is possible to achieve lasing on polariton modes in nowadays experiments aimed on Bose–Einstein condensation of excitons.     

Direct and spatially indirect excitons in GaAs/AlGaAs superlattices in strong magnetic fields

Luminescence and luminescence excitation spectra are used to study the energy spectrum and binding energies of direct and spatially indirect excitons in GaAs/AlGaAs superlattices having different electron and hole miniband widths in high magnetic fields perpendicular to the heterolayers. The ground state of the indirect excitons formed by electrons and holes which are spatially distributed among neighboring quantum wells is found to lie between the ground 1s state of the direct excitons and the threshold of the continuum of dissociated exciton states in the minibands. The indirect excitons have a substantial oscillator strength when the binding energy of the exciton exceeds the scale of the width of the resulting miniband. It is shown that a high magnetic field shifts a system of symmetrically bound quantum wells toward weaker bonding. At high exciton concentrations, spatially indirect excitons are converted into direct excitons through exciton-exciton collisions. Fiz. Tverd. Tela (St. Petersburg) 40, 833–836 (May 1998)     

Conditions and features of the lasing in traps for the bose condensation of dipolar excitons

We study the conditions and features of the polariton mode lasing in traps for the Bose condensation of dipolar excitons. We discuss the spectral linewidth of lasing modes and the effects of spatial and spectral inhomogeneity of the exciton distribution. We study in detail the possibility of the polariton mode lasing in the vicinity of the Bose condensation threshold. We analyze the impact of the inhomogeneous broadening of the exciton line on the stability of stationary lasing. We also propose additional experiments aimed at obtaining more information on the polariton mode lasing in semiconductor structures for the Bose condensation of excitons.     

Direct and spatially indirect excitons in GaAs/AlGaAs superlattices in strong magnetic fields

Luminescence and luminescence excitation spectra are used to study the energy spectrum and binding energies of direct and spatially indirect excitons in GaAs/AlaAs superlattices, with different widths of the electron and hole minibands, located in a high magnetic field perpendicular to the heterolayers. It is found that the ground state of the indirect excitons formed by electrons and holes and spatially separated between neighboring quantum wells lies between the ls ground state of the direct excitons and the continuum threshold for dissociated exciton states in the minibands. Indirect excitons in superlattices have a significant oscillator strength when the binding energy of the exciton exceeds the order of the width of the resulting miniband. The behavior of the binding energy of direct and indirect heavy hole excitons during changes in the tunneling coupling between the quantum wells is established. It is shown that a strong magnetic field, which intensifies the Coulomb interaction between the electron and hole in an exciton, weakens the bond in a system of symmetrically bound quantum wells. The spatially indirect excitons studied here are analogous to first order Wannier-Stark localized excitons in superlattices with inclined bands (when an electrical bias is applied), but in the present case the localization is of purely Coulomb origin. Zh. éksp. Teor. Fiz. 112, 1106–1118 (September 1997)     

Polariton-mode lasing and Bose condensate of dipolar excitons in heterostructures

The analysis of the polariton modes in 2D traps based on heterostructures with quantum wells for Bose-Einstein condensation of dipolar excitons is presented. The characteristic equation of such modes is derived with allowance for the polarization relaxation of excitons and radiative losses from the trap. The spectrum and structure of high-quality modes are analytically and numerically studied. It is demonstrated that several modes become unstable at a high enough density of excitons and a long relaxation time of the exciton polarization. In accordance with the estimations, such an instability can be reached in the experiments on the Bose-Einstein condensation of dipolar excitons and can be used to interpret the corresponding coherent emission.     

Gas–crystal phase transition in a 2D dipolar exciton system

A system of dipolar excitons at temperatures exceeding the expected Bose–Einstein condensation temperature is considered. It is shown that a first-order phase transition with the formation of a phase close to the crystal of such excitons is possible at such temperatures. The phase diagram in the range of low concentrations and temperatures is constructed. The effect of this transition on the luminescence spectrum of the system is analyzed.     

Direct imaging of anisotropic exciton diffusion and triplet diffusion length in rubrene single crystals

We visualize exciton diffusion in rubrene single crystals using localized photoexcitation and spatially resolved detection of excitonic luminescence. We show that the exciton mobility in this material is strongly anisotropic with long-range diffusion by several micrometers associated only with the direction of molecular stacking in the crystal, along the b axis. We determine a triplet exciton diffusion length of 4.0 ± 0.4 μm from the spatial exponential decay of the photoluminescence that originates from singlet excitons formed by triplet-triplet fusion.     

Exciton-exciton interaction in coupled quantum wells

The exciton-exciton interaction is investigated for spatially indirect excitons in coupled quantum wells. The Hartree-Fock and Heitler-London approaches are improved by a full two-exciton calculation including the van der Waals effect. Using these potentials for the singlet and triplet channel, the two-body scattering matrix is calculated and employed to derive a modified relation between exciton density and blue shift. Such a relation is of central importance for gauging exciton densities on the way toward Bose condensation.     

Bose condensation of interwell excitons in double quantum wells

The luminescence of interwell excitons in double quantum wells GaAs/AlGaAs (n-i-n heterostructures) with large-scale fluctuations of random potential in the heteroboundary planes was studied. The properties of excitons whose photoexcited electron and hole are spatially separated in the neighboring quantum wells were studied as functions of density and temperature within the domains on the scale less than one micron. For this purpose, the surfaces of the samples were coated with a metallic mask containing specially prepared holes (windows) of a micron size an less for the photoexcitation and observation of luminescence. For weak pumping (less than 50 μW), the interwell excitons are strongly localized because of small-scale fluctuations of a random potential, and the corresponding photoluminescence line is inhomogeneously broadened (up to 2.5 meV). As the resonant excitation power increases, the line due to the delocalized excitons arises in a thresholdlike manner, after which its intensity linearly increases with increasing pump power, narrows (the smallest width is 350 μeV), and undergoes a shift (of about 0.5 μeV) to lower energies, in accordance with the filling of the lowest state in the domain. With a rise in temperature, this line disappears from the spectrum (T _c ≤ 3.4 K). The observed phenomenon is attributed to Bose-Einstein condensation in a quasi-two-dimensional system of interwell excitons. In the temperature range studied (1.5–3.4 K), the critical exciton density and temperature increase almost linearly with temperature.     

Acousto-exciton interaction in a gas of 2D indirect dipolar excitons in the presence of disorder

A theory for the linear and quadratic responses of a 2D gas of indirect dipolar excitons to an external surface acoustic wave perturbation in the presence of a static random potential is considered. The theory is constructed both for high temperatures, definitely greater than the exciton gas condensation temperature, and at zero temperature by taking into account the Bose–Einstein condensation effects. The particle Green functions, the density–density correlation function, and the quadratic response function are calculated by the “cross” diagram technique. The results obtained are used to calculate the absorption of Rayleigh surface waves and the acoustic exciton gas drag by a Rayleigh wave. The damping of Bogoliubov excitations in an exciton condensate due to theirs scattering by a random potential has also been determined.     

Collective phenomena in cold indirect excitons

Due to their long lifetimes, indirect excitons can cool to below the temperature of quantum degeneracy. This gives an opportunity to experimentally study cold composite bosons. Both theoretically predicted phenomena and phenomena that have not been anticipated were observed in a cold gas of indirect excitons. In this contribution, we overview our studies of cold indirect excitons over the past decade, presenting spontaneous coherence and condensation of excitons, spatially modulated exciton state, long-range spin currents and spin textures, and exciton localization–delocalization transitions.     

耦合量子阱中激子凝聚的研究进展

近年来，半导体量子阱中激子的玻色一爱因斯坦凝聚研究取得了很大进展．实验上利用耦合量子阱间接激子中电子和空穴在空间上的分离，显著提高了激子的冷却速度和寿命，成功地把激子冷却到1K以下，观察到了激子的准凝聚状态，并且在强激光照射下，发现了随光照强度增强而增大的激子发光环和环上形成的有规则斑点图案，引起了广泛的兴趣和重视．理论研究表明，发光环的出现是电子和空穴在量子阱中的反常输运行为造成的，但环上形成规则斑点的物理机理目前尚不清楚．文章介绍了这方面的实验背景和形成激子环的物理图像，指出了理论研究中存在的问题，并对解决问题的方案进行了讨论．