Luminescence rings in coupled quantum wells

Coupled quantum wells are attractive for superfluidity of excitons, because exciton lifetime can be extended by applying an electric field normal to the planes of the wells. With increasing electric field, an indirect exciton, formed from an electron in one well and a hole in the adjacent well, shifts to lower energy. We have fabricated I%,,Gao,&s coupled wells which have a confined state below the GaAs-substrate, and we create a high density of excitons in the wells with a very efficient way: illuminate the system with red light(600-650nm) well above the substrate band-gap. Carriers generated in the substrate will fall into excitonic states in the wells, which are the lowest excited state in the system. We find that above a critical density, the indirect exciton luminescence exhibits a ring structure of hundreds of micrometers radius centered on the laser spot[l]. Fig.1 shows a typical image from our experimental data with an intensified CCD-camera. The radius of the ring changes when any one of the following is adjusted: laser intensity, applied voltage, temperature, laser photon energy, applied magnetic field and stress. The most surprising thing is that no luminescence appears in the intervening region. This implies that the excitons must travel in some dark states until they reach some critical distance at which they collectively revert to luminescent states, which is unprecedented in other excitonic systems. As seen in Fig.2, the critical excitation density at which the ring appears depends on the temperature. Although the critical-density is expected to be directly proportional to the temperature for a Kosterlitz-Thouless transition to a superfluid state in two dimensions[2], we observe a superlinear dependence. At high temperature, however, the number of excitons is not directly proportional to the number of laser photons. An increasing fraction of the photons will create free electrons and holes. The solid line in Fig.2 is a fit to the Kosterlitz-Thouless critical-density, using a mass-action equation for the number of excitons in equilibrium as a function of temperature[3]. Fig. 3 shows the ring intensity versus time after a laser pulse, for a ring of radius 500pn, when the excitons are created by laser pulses with 260ns period. The exciton lifetime is consistent with travel over such long distances. Immediately after the laser pulse, the recorded luminescence intensity drops, then recovers its steady-state value. We interpret this as motion of the ring in response to the laser pulse. The response of the ring within about lOns, shown in Fig.3, corresponds to a velocity of approximately 5x106cm/s, which is much faster than the speed of sound in GaAs. This indicates wavelike propagation of energy through the dark intervening region. These data also rule out the possibility of a radiative re-absorption effect, because the luminescence from the ring has a much longer lifetime than that from the laser spot. Although it is not clear whether ths effect is related to superfluidity, the long lifetime and distance traveled by the excitons makes it possible to imagine “excitonic circuits” in which excitons are moved from one place to another