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It is found that the thermalization of triplet spin-flip magneto-excitons in a quantum Hall dielectric is an unprecedentedly long process for translation-invariant nonequilibrium electronic systems. It is shown that a magneto-fermionic condensate, a state characterized by the ability to rapidly transfer spin over macroscopic distances, is formed by spin-flip excitons with generalized momenta on the order of the reciprocal magnetic length.

We discuss spin excitations in a degenerate 2D electron gas in a perpendicular quantizing magnetic field: spin-wave and ‘Goldstone’ excitons in a quantum Hall ferromagnetic (filling factor ν = 1), and spin-cyclotron excitons in a quantum Hall insulator (ν = 2). The latter exhibit record-setting long lifetimes, up to 1 ms, owing to which a transition to a basically new collective state, a magnetofermionic condensate, is observable at temperatures T < 1 K. The condensate’s properties may be explained in terms of a coherent state being formed due to the emergence of a dense ensemble of photoexcited long-lived spin-cyclotron excitons obeying Bose statistics in a nonequilibrium system of 2D fermions.

In a dilute gas of triplet magnetoexcitons, complete thermalization does not occur because the energy and momentum cannot be conserved simultaneously. Relaxation to the lowest energy state becomes possible owing to exciton—exciton scattering upon reaching a certain critical exciton density. Since thermalization times are extremely large, ensembles of magnetoexcitons are substantially nonequilibrium and consist of above-condensate magnetoexcitons with generalized momenta close to zero and magnetoexcitons at the energy minimum with momenta about the inverse magnetic length. It has been shown experimentally that the magnetoexciton density is transferred to long distances not by all magnetoexcitons, but by those whose momentum is close to the inverse magnetic length, ∼106 cm−1, and these magnetoexcitons form a magnetofermionic condensate.

A fundamentally new collective state, namely, the magnetofermionic condensate, is discovered during photoexcitation of a sufficiently dense gas of long-lived triplet cyclotron magnetoexcitons in a twodimensional Hall insulator with a high electron mobility, a filling factor of ν = 2, and temperatures of T < 1 K. The condensed phase coherently interacts with an external electromagnetic field, exhibits superradiant properties in the recombination of correlated condensate electrons with heavy holes in the valence band, and spreads nondissipatively in the layer of a two-dimensional electron gas to macroscopical large distances, transferring an integer spin. The observed effects are explained in terms of a coherent condensate in a nonequilibrium system of two-dimensional fermions with a fully quantized energy spectrum, in which a degenerate ensemble of long-lived triplet magnetoexcitons obeying the Bose statistics is present.

Excitation of long-lived triplet magnetoexcitons in a Hall insulator (filling factor ν = 2) with a high mobility of electrons, at low temperatures, Т < 1 K, enabled to discover a new collective state − magnetofermionic condensate, that interacts coherently with an external electromagnetic field, exhibits superradiant properties and, owing to its low viscosity, spreads over the surface of the two-dimensional structure for macroscopically large distances.

The possibility of creating dense ensembles of spin excitons, transferring them to macroscopic distances on the order of hundreds of microns, and recording the appearance of these excitons in the region spatially remote from the excitation point by means of simple techniques of photoexcitation and space-resolved detection of photoluminescence of a two-dimensional electron gas in a GaAs/AlGaAs quantum well has been demonstrated.

An experimental technique is developed to perform photoexcitation of an ensemble of translationinvariant triplet excitons, to manipulate this ensemble, and to detect the properties of its components. In particular, the influence of temperature on the radiationless decay during the relaxation of an exciton spin into the ground state of a Hall insulator at a filling factor ν = 2 is studied. The generation of photoexcited electrons and holes is controlled using photoinduced resonance reflection spectra, which makes it possible to estimate the density of light-generated electron–hole pairs and to independently control the self-consistent generation of electrons at the first Landau level and holes (vacancies) at the ground (zero) cyclotron electronic level. The existence of triplet excitons is established from inelastic light scattering spectra, which are used to determine the singlet–triplet exciton splitting. The lifetimes of triplet excitons, which are closely related to the relaxation time of an electron spin, are extremely long: they reach 100 μs in perfect GaAs/AlGaAs heterostructures with a high mobility of two-dimensional electrons at low temperatures. These long spin relaxation times are qualitatively explained, and the expected collective behavior of high-density triplet magnetoexcitons at sufficiently low temperatures, which is related to their Bose nature, is discussed.

We report on optical visualization of spin propagation more than 100 µm. We present an electronic system in a new state of aggregation, the magnetofermionic condensate, in which the lowest-energy spin excitations − photoexcited spin-triplet magnetoexcitons – freely propagate over long distances, in the order of a millimeter, which implies non-diffusion spin transport. Our results open up a completely new system suitable for spintronic devices.

For a Schottky-diode structure containing two narrow GaAs (3.5 nm) and AlAs (5 nm) heterolayers, the photoluminescence properties of long-living dipolar excitons, indirect in both real and momentum space, are studied in perpendicular magnetic fields in the Faraday configuration of measurements. With an external perpendicular electric field, the lifetimes of such excitons can be extended to ∼1 μs. Nevertheless the exciton spin subsystem remains nonequilibrium: the exciton spin-relaxation time is even longer. The degree of circular polarization of the photoluminescence attains 80% in a field of 6 T. With an electric field, it is possible to control the degree and sign of the circular polarization.

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.

Coherent condensate states of particles obeying either Bose or Fermi statistics are in the focus of interest in modern physics. Here we report on condensation of collective excitations with Bose statistics, cyclotron magnetoexcitons, in a high-mobility two-dimensional electron system in a magnetic field. At low temperatures, the dense non-equilibrium ensemble of long-lived triplet magnetoexcitons exhibits both a drastic reduction in the viscosity and a steep enhancement in the response to the external electromagnetic field. The observed effects are related to formation of a super-absorbing state interacting coherently with the electromagnetic field. Simultaneously, the electrons below the Fermi level form a super-emitting state. The effects are explicable from the viewpoint of a coherent condensate phase in a non-equilibrium system of two-dimensional fermions with a fully quantized energy spectrum. The condensation occurs in the space of vectors of magnetic translations, a property providing a completely new landscape for future physical investigations., The motion of particles in a quantum condensate state are described by a single macroscopic wave function, leading to a host of unusual properties. Here, the authors generate such a condensation of magnetically induced excitons, known as cyclotron magnetoexcitons, in a high-mobility quantum well.

An electro-optical trap for spatially indirect dipolar excitons is implemented in a GaAs/AlAs Schottky diode with a 400-A-wide GaAs single quantum well. In the presence of bias voltage applied to the gate, the trap for excitons appears upon annular 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 due to screening of the applied electric field by nonequilibrium charge carriers within the excitation region. Excitons are collected inside the ring due to the ambipolar drift of carriers and the dipole-dipole repulsion of excitons in the optically pumped region. For dipolar excitons thus accumulated in the middle of the ring-shaped electro-optical trap, significant narrowing of the luminescence line is observed with increasing excitation density, which indicates the collective behavior of the excitons.

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.

An electro-optical trap for spatially indirect dipolar excitons has been implemented in a GaAs/AlAs Schottky diode with a 400-A-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.

The phase diagram of Bose-Einstein condensates of dipolar excitons accumulated in lateral electrostatic traps is determined. Spatially periodic luminescence structures of the exciton Bose condensate and their critical dependence on pump level and temperature are observed. Coherence in the dipolar exciton Bose-Einstein condensates is studied by direct measurement of the 1-st and 2-nd order correlators with variations in pump level and temperature. These results are indicative of large-scale coherence of the exciton Bose condensate.

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The construction of a helium cryostat with pumping of 3He vapors designed for optical measurements with a high spatial resolution in the temperature range 0.45–4.20 K. The cryostat is equipped with four windows made from fused silica. A studied sample is mounted inside a reservoir filled with liquid 3He in a holder minimizing the influence of both vibrations and thermal drifts and can stay in the chamber at T = 0.45 K for >20 h. The cryostat was used to study photoluminescence of GaAs/AlGaAs semiconductor heterostructures. It was revealed that, in a structure with two tunnel-coupled GaAs quantum wells with a width of 120 A, the threshold pumping power required for the appearance of a narrow spectral line, which corresponds to the Bose condensate of spatially indirect dipolar excitons, decreases by a factor of 6, as the temperature falls from 1.50 to 0.45 K. In a sample with a single wide (250 A) GaAs quantum well, the distribution patterns of the luminescence of dipolar excitons inside a 5-µm circular potential trap were obtained at T = 0.45 K. The spatial resolution of the distributions is no worse than 1.5 µm.

Correlations of luminescence intensity have been studied under Bose-Einstein condensation of dipolar excitons in the temperature range of 0.45-4.2 K. Photoexcited dipolar excitons were collected in a lateral trap in GaAs/AlGaAs Schottky-diode heterostructure with single wide (25 nm) quantum well under applied electric bias. Two-photon correlations were measured with the use of a classical Hanbury Brown - Twiss intensity interferometer (time resolution ~0.4 ns). Photon "bunching" has been observed near the Bose condensation threshold of dipolar excitons determined by the appearance of a narrow luminescence line of exciton condensate at optical pumping increase. The two-photon correlation function shows super-poissonian distribution at time scales of system coherence (, Comment: 6 pages, 5 figures

The linear polarization of luminescence from the Bose-Einstein condensate of dipolar (indirect) excitons accumulated in the ring lateral traps in GaAs/AlGaAs Schottky-diode heterostructures with a wide single quantum well has been observed. Luminescence from direct excitons remains unpolarized under the same experimental conditions. It has been shown that the linear polarization of the exciton condensate may arise from the anisotropic electron-hole (e–h) exchange interaction associated with the lateral anisotropy of the confining potential. The interaction mixes and splits the ground state of optically active excitons on heavy holes (with angular momentum projections of m=±1). The split spectral components from the corresponding angular momentum projections are linearly polarized in mutually orthogonal directions. Under this e–h exchange, the condensate component of excitons should appear in the lowest of the split states and luminescence from the Bose-Einstein condensate of excitons in such a split state becomes linearly polarized along the 〈110〉 crystallographic direction in the quantum well plane. The observed effect is a manifestation of spontaneous symmetry breaking in Bose-Einstein condensation of excitons.

Experiments connected with dipolar exciton Bose-Einstein condensation in ring lateral traps in GaAs/AlGaAs Schottky- diode heterostructures with double and single quantum wells are presented. The observed behaviour of luminescence spectra and patterned luminescence structure in circular ring traps, as well as linear polarization of luminescence and long-range spatial coherence of Bose condensate are discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The kinetics of the luminescence spectra of dipolar excitons accumulated in circular traps under pulsed off-resonance laser photoexcitation is investigated. The temperature of the exciton gas is determined.

An experimental technique for the indirect manipulation and detection of electron spins entangled in two-dimensional magnetoexcitons has been developed. The kinetics of the spin relaxation has been investigated. Photoexcited spin-magnetoexcitons were found to exhibit extremely slow relaxation in specific quantum Hall systems, fabricated in high mobility GaAs/AlGaAs structures, namely, the relaxation time reaches values over one hundred microseconds. A qualitative explanation of this spin-relaxation kinetics is presented. Its temperature and magnetic field dependencies are discussed within the available theoretical framework., 5 pages, 3 figures

The Bose condensation of spatially indirect (dipolar) excitons in a wide single quantum well in an electric field transverse to the heterolayers is analyzed. Voltage is applied between a metallic film on the surface (Schottky gate) and a conducting electron layer inside a heterostructure (integrated electrode). The excitation of dipolar excitons and observation of their luminescence are performed through circle windows in a metallic mask 5 μm in diameter. Excitons are collected in a ring lateral trap, which is formed along the window perimeter owing to the strongly inhomogeneous electric field. When the critical condensation conditions in pump and temperature are reached, a narrow line of dipolar excitons corresponding to the exciton condensate appears stepwise in the luminescence spectrum. Under these conditions, a spatially periodic structure of equidistant luminescence spots appears in the luminescence pattern that is observed through a window with a resolution of about 1 μm and is selected by means of an interference filter. An in situ optical Fourier transform of spatially periodic structures from the real space to the k space is derived. The resulting Fourier transforms reproducing the pattern of the luminescence intensity distribution in the far field exhibit the result of the destructive and constructive interference, as well as the fact that the luminescence is directed along the normal to the heterolayers. These results are consequences of the large-scale coherence of the condensed exciton state in the ring lateral trap. Direct measurements of double-beam interference from pairs of luminescence spots in the ring show that the spatial coherence length is no less than 4 μm. Such a large scale means that the experimentally observed periodic luminescence structures are described by a common wavefunction under the condition of the Bose condensation of dipolar 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.

Photoluminescence of interwell excitons in GaAs/AlGaAs double quantum wells (n-i-n heterostructure) containing large-scale random potential fluctuations in the planes of heteroboundaries is studied. The properties of excitons, in which a photoexcited electron and a hole are spatially separated in neighboring quantum wells, were investigated upon variation of the power density of off-resonance laser excitation and temperature (1.5–4.2 K), both under lateral (in the heteroboundary plane) confinement of the excitation region to a few micrometers and without such a limitation (directly from the region of laser-induced photoexcitation focused to a spot not exceeding 30 μ. Under low pumping (with a power smaller than a microwatt), interwell excitons are strongly localized due to small-scale random potential fluctuations and the corresponding photoluminescence line is nonhomogeneously broadened to 2.5–3.0 meV. With increasing pumping power, the narrow line of delocalized excitons with a width of approximately 1 meV emerges in a threshold manner (the intensity of this line increases superlinearly near the threshold with increasing pumping). For a fixed pumping, the intensity of this line decreases linearly upon heating until it completely vanishes from the spectrum. The observed effect is attributed to Bose condensation in a quasi-two-dimensional system of interwell excitons. Within the proposed model, we show that the linear mode in the behavior of the luminescence intensity until its disappearance in the continuum of the photoluminescence spectrum upon a change in temperature is observed only for the condensed part of interwell excitons. At the same time, the luminescence of the above-the-condensate part of excitons is almost insensitive to temperature variations in the temperature range studied.

The luminescence of interwell excitons laterally confined by long range potential fluctuations and with the use of inhomogeneous electric field in n-i-n GaAs/AlGaAs heterostructures double quantum wells has been investigated under variation of excitation power and temperature. Above mobility threshold very narrow interwell exciton line has been observed and its intensity decrease is linearly dependent on temperature growth. The observed phenomena, which were critical to exciton density and temperature, are attributed to the Bose-condensation in laterally confined quasi-two dimensional system of interwell excitons. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The luminescence of interwell excitons in double quantum wells based on GaAs/AlGaAs semiconductor heterostructures (n-i-n structures) in a lateral trap prepared with the use of an inhomogeneous electric field was studied at helium temperatures. A rather strong and inhomogeneous electric field occurred in the depth of the heterostructure when a current passed through the contact between the conducting tip of a tunneling microscope and the heterostructure surface to the bulk region containing a built-in gate. Because of the Stark shift of energy bands in the electric field, the photoexcited electrons and holes are spatially separated in neighboring quantum wells by a tunnel-transparent barrier and are bound into interwell quasi-two-dimensional excitons. These excitons have a dipole moment even in the ground state. Therefore, electrostatic forces in the inhomogeneous electric field cause the excitons to move in the plane of quantum wells toward the maximum field region and eventually accumulate in the lateral trap artificially prepared in such a way. The maximum trap depth achieved through the inhomogeneous electric field was 13.5 meV, and its lateral size was about 10 μm. It is shown that, in the traps prepared in this way, photoexcited interwell excitons behave with increasing concentration at sufficiently low temperatures (T=2K) in the same fashion as in the lateral traps caused by large-scale fluctuations of the random potential. At concentrations exceeding the percolation threshold, the interwell excitons condense into the lowest energy state in the trap.

The luminescence of interwell excitons in GaAs/AlGaAs double quantum wells (n-i-n heterostructures) with large-scale fluctuations of random potential in the heteroboundary planes was studied at low temperatures down to 0.5 K. The properties of excitons whose photoexcited electron and hole are spatially separated in the neighboring quantum wells by a tunneling barrier were studied as functions of density and temperature. The studies were performed within domains about one micron in size, which played the role of macroscopic traps for interwell excitons. For this purpose, the sample surface was coated with a metal mask containing special openings (windows) of a micron size or smaller. Both photoexcitation and observation of luminescence were performed through these windows by the fiber optic technique. At low pumping powers, the interwell excitons were strongly localized because of the residual charged impurities, and the corresponding photoluminescence line was nonuniformly broadened. As the laser excitation power increased, a narrow line due to delocalized excitons arose in a threshold-like manner, after which its intensity rapidly increased with growing pumping and the line itself narrowed (to a linewidth less than 1 meV) and shifted toward lower energies (by about 0.5 meV) in accordance with the filling of the lowest exciton state in the domain. An increase in temperature was accompanied by the disappearance of the line from the spectrum in a nonactivation manner. The phenomenon observed in the experiment was attributed to Bose-Einstein condensation in a quasi-two-dimensional system of interwell excitons. In the temperature interval studied (0.5–3.6) K, the critical exciton density and temperature were determined and a phase diagram outlining the exciton condensate region was constructed.

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.

The time evolution and kinetics of photoluminescence (PL) spectra of interwell excitons in double GaAs/AlGaAs quantum wells (n-i-n structures) have been investigated under the pulse resonance excitation of intrawell 1sHH excitons using a pulsed tunable laser. It is found that the collective exciton phase arises with a time delay relative to the exciting pulse (several nanoseconds), which is due to density and temperature relaxation to the equilibrium values. The origination of the collective phase of interwell excitons is accompanied by a strong narrowing of the corresponding photoluminescence line (the line width is about 1.1 meV), a superlinear rise in its intensity, a long time in the change of the degree of circular polarization, a displacement of the PL spectrum toward lower energies (about 1.5 meV) in accordance with the filling of the lowest state with the exciton Bose condensate, and a significant increase in the radiative decay rate of the condensed phase. The collective exciton phase arises at temperatures T

Supplementary papers for this conference are available at Chernogolovka 2000: Mesoscopic and strongly correlated electron systems

Experimental observations of the collective behavior of interwell excitons in the binary quantum wells with inclined bands under bias are discussed.

Abrupt changes in the capacitance between the p and n regions were observed in a planar p-i-n GaAs/AlGaAs heterostructure with two tunneling-coupled quantum wells exposed to laser irradiation (λ=633 nm). These changes can be caused by variations in both temperature (in the vicinity of T∼2 K) and the dc voltage applied to the structure. A memory effect was detected; this effect manifested itself in the long lifetime of anomalies observed after the illumination had been turned off. Self-consistent calculations of distributions of charge and electric field were performed for the structures that contained a donor impurity in AlGaAs layers; this impurity is responsible for origination of DX centers that give rise to persistent photoconductivity. It is demonstrated that abrupt changes in capacitance can occur in such a structure, and the values of the parameters required for origination of these jumps are determined.

A strong increase in the intensity of the peaks of excited magnetoexciton (ME) states in the photoluminescence excitation (PLE) spectra recorded for the ground heavy-hole magnetoexcitons (of the $1s\mathrm{HH}$ type) has been found in a $\mathrm{GaAs}/{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ superlattice in strong magnetic field B applied normal to the sample layers. While varying B, the intensities of the PLE peaks have been measured as functions of energy separation $\ensuremath{\Delta}E$ between excited ME peaks and the ground state of the system. The resonance profiles have been found to have maxima at $\ensuremath{\Delta}{E}_{\mathrm{max}}$ close to the energy of the GaAs LO phonon. However, the value of $\ensuremath{\Delta}{E}_{\mathrm{max}}$ depends on quantum numbers of the excited ME state. The revealed very low quantum efficiency of the investigated sample allows us to ascribe the observed resonance to the enhancement of the nonradiative magnetoexciton relaxation rate arising due to LO-phonon emission. The presented theoretical model, being in a good agreement with experimental observations, provides a method to extract 1sHH magnetoexciton ``in-plane'' dispersion from the dependence of $\ensuremath{\Delta}{E}_{\mathrm{max}}$ on the excited ME state quantum numbers.

Photoluminescence (PL) and PL excitation (PLE) measurements have been performed in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ biased double quantum well heterostructures. The recombination of electrons, e, with holes, h, located in the same or in two adjacent wells, has been investigated for different exciting power densities, P, and temperatures, T. For increasing P or decreasing T, a sharp transition from two gases of photoexcited electrons and holes, spatially separated and confined in the two wells, to two two-dimensional (2D) liquids has been observed. The gas-to-2D-liquid transition is evidenced by a strong screening of applied biases and by major changes in the optical spectra. The phase diagram in the $(P,T)$ plane of the $e\ensuremath{-}h$ system has been determined. Time-resolved PL, cw PL, and PLE in the presence of a magnetic field normal to the quantum wells support the presence of e- and h-liquid phases in the two wells with a critical density equal to $8.8\ifmmode\times\else\texttimes\fi{}{10}^{10} {\mathrm{cm}}^{\ensuremath{-}2}$ and a binding energy of 2.5 meV.

Photoluminescence spectra of interwell excitons in double GaAs/AlGaAs quantum wells (n-i-n structures) have been investigated (an interwell exciton in these systems is an electron-hole pair spatially separated by a narrow AlAs barrier). Under resonance excitation by circularly polarized light, the luminescence line of interwell excitons exhibits a significant narrowing and a drastic increase in the degree of circular polarization of photoluminescence with increasing exciton concentration. It is found that the radiative recombination rate significantly increases under these conditions. This phenomenon is observed at temperatures lower than the critical point and can be interpreted in terms of the collective behavior of interwell excitons.

Photoluminescence (PL) and PL excitation measurements (PLE) have been performed in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ double quantum well (QW) structures under different applied electric fields. An emission due to charged excitons (trions) has been identified in the PL spectra $\ensuremath{\sim}3$ meV below the heavy-hole exciton emission. These trions are localized by random potential fluctuations, at the interfaces or in the QW, as shown by the saturation of their emission intensity with respect to that of the heavy-hole excitons. Trions are positively charged, namely, they are made by two holes and one electron, as shown by (i) an analysis of the PL polarization for resonant excitation of the heavy- and the light-exciton ground state, and (ii) the analysis of the Zeeman effect for the trion PL band in the Faraday geometry, i.e., for a magnetic field normal to the QW's.