The demonstration of Bose-Einstein condensation in atomic gases at micro-Kelvin temperatures is a striking landmark 1 while its evidence for semiconductor excitons 2-5 still is a longawaited milestone. This situation was not foreseen because excitons are light-mass boson-like particles with a condensation expected to occur around a few Kelvins 6, 7 . An explanation can be found in the underlying fermionic nature of excitons which rules their condensation 8 . Precisely, it was recently predicted that, at accessible experimental conditions, the exciton condensate shall be "gray" with a dominant dark part coherently coupled to a weak bright component through fermion exchanges 9 . This counter-intuitive quantum condensation, since

This corrects the article DOI: 10.1103/PhysRevLett.118.127402.

We study semiconductor excitons confined in an electrostatic trap of a GaAs bilayer heterostructure. We evidence that optically bright excitonic states are strongly depleted while cooling to sub-Kelvin temperatures. In return, the other accessible and optically dark states become macroscopically occupied so that the overall exciton population in the trap is conserved. These combined behaviours constitute the spectroscopic signature for the mostly dark Bose-Einstein condensation of excitons, which in our experiments is restricted to a dilute regime within a narrow range of densities, below a critical temperature of about 1K.Semiconductor excitons, i.e.Coulomb bound electron-hole pairs, constitute a class of composite bosons which has raised a large interest in the context of Bose-Einstein condensation (BEC). This phase transition was originally envisioned in the 1960s [1-3], and fifty years of research were actually necessary to detect anticipated signatures, such as long-range spatial coherence and quantised vortices [4]. The main reason for this unexpectedly long search was given in 2007, when Combescot et al. [5] pointed out that excitons, which exist in either optically bright or optically dark forms, depending on their total spin, always have a dark ground state. Accordingly, BEC is controlled by the macroscopic occupation of dark excitons, a conclusion which stood in striking contrast with previous experimental and theoretical research that had emphasized a condensation dominated by optically bright excitons [6,7].The dark nature of exciton condensation sets strong barriers to evidence the quantum phase transition. Indeed, it impedes direct measurements of the excitons momentum distribution by imaging their photoluminescence in momentum space, as for example employed with atomic gases [8,9] or polaritons [10]. Alternative spectroscopic techniques are thus necessary. We then note that the exciton dark-state condensation leads to a photoluminescence quenching, which is easily identified in principle since it contrasts with the classically expected increase of the optical emission as the exciton temperature is lowered [11,12]. However, relating unambiguously a photoluminescence darkening to BEC is a tedious task since experimental limitations can also induce a photoluminescence bleaching, for example interactions between excitons and excess free carriers [13], or simply non-radiative losses.In this work, we study two-dimensional excitons trapped at a controlled total density, i.e. including bright and dark states, kept constant while the gas is cooled down to sub-Kelvin temperatures. In the dilute regime and for a restricted range of densities only, we evidence quantitatively a photoluminescence darkening of about 30%. By evaluating the strength of non-radiative channels we then show that this pho-toluminescence quenching reveals unambiguously the buildup of a dominant fraction of dark excitons, of around 70% below a critical temperature of around 1 Kelvin. The energy splitting between bright and dark exciton s...

We study the photoluminescence dynamics of ultra-cold indirect excitons optically created in a double quantum well heterostructure. Above a threshold laser excitation, our experiments reveal the apparition of the so-called inner photoluminescence ring. It is characterized by a ring shaped photoluminescence which suddenly collapses once the laser excitation is terminated. We show that the spectrally resolved dynamics is in agreement with an excitonic origin for the inner-ring which is formed due to a local heating of indirect excitons by the laser excitation. To confirm this interpretation and exclude the ionization of indirect excitons, we evaluate the excitonic density that is extracted from the energy of the photoluminescence emission. It is shown that optically injected carriers play a crucial role in that context as these are trapped in our field-effect device and then vary the electrostatic potential controlling the confinement of indirect excitons. This disruptive effect blurs the estimation of the exciton concentration. However, it suppressed by smoothing the electrostatic environment of the double quantum well by placing the latter behind a super-lattice. In this improved geometry, we then estimate that the exciton density remains one order of magnitude smaller than the critical density for the ionization of indirect excitons (or Mott transition) in the regime where the inner-ring is formed.

We study spatially indirect excitons of GaAs quantum wells, confined in a 10  μm electrostatic trap. Below a critical temperature of about 1 K, we detect macroscopic spatial coherence and quantized vortices in the weak photoluminescence emitted from the trap. These quantum signatures are restricted to a narrow range of density, in a dilute regime. They manifest the formation of a four-component superfluid, made by a low population of optically bright excitons coherently coupled to a dominant fraction of optically dark excitons.