Nonlinear optical phenomena in coherent phase of 2D exciton system Yu.E. Lozovik, I.L. Kurbakov, I.V. Ovchinnikov * Laboratory for Nanophysics, Institute of Spectroscopy RAN, 142190 Troitsk, Moscow region, Russian Federation Received 5 December 2002; accepted 3 February 2003 by E.L. Ivchenko Abstract We show that spatial many-particle coherence of condensed 2D exciton system, which is represented by anomalous averages k ^ a † k 1 ··· ^ a † k N l; can be transferred to exciton luminescence via the processes of coherent (simultaneous) recombination of many correlated excitons with production of the same number of correlated photons ( ^ a † k is exciton creation operator). In high-quality samples 2D momentum conservation dictates the requirement P i k i ¼ 0 for 2D exciton momenta. Due to momentum conservation, the photons coherently produced in such a process possess zero sum 2D momentum as well. Analyzing such a many-photon spatial coherence of the luminescence we predict new nonlinear optical effects in a coherent phase of 2D exciton system. The effects are the above-mentioned processes stimulated by external laser beams. They effectively look as if the stimulated exciton system irradiates a unidirectional beam with recoil momentum. ‘Recoil’ beams constitute a photon ‘fan’ in case of single stimulating laser beam and a photon ‘lattice’ in case of two stimulating laser beams. Quantitative estimations for exciton system in GaAs/AlGaAs double quantum wells point to possible experimental observability of the effects. q 2003 Elsevier Science Ltd. All rights reserved. PACS: 71.35.Lk; 78.45. þ h; 42.65. 2 k Keywords: A. Nanostructures; A. Quantum wells; D. Radiation effects The progress in manufacturing heterostructures, in particu- lar of double quantum wells (DQW), has considerably intensified the search of coherent exciton phase. The point is that the systems of quasi-2D spatially indirect excitons in DQW (with spatially separated electrons and holes) have several virtues for exciton condensation such as long exciton lifetimes, effective inter-exciton dipole– dipole repulsion or easy controllability of such systems’ properties (e.g. by external electric or magnetic fields). A number of phenom- ena has been predicted to exist in the system of excitons in DQW [1–7] (see also 3D exciton phases in Ref. [8]). The system of indirect excitons in DQW has been paid much attention especially for the last decade (see e.g. Ref. [9]) what resulted in recent convincing evidences of formation of exciton coherent phase [10]. In all the experiments researches mainly focused on one-photon property of exciton luminescence such as spectral line shape which is determined by one-exciton coherence of exciton system. Condensed exciton system, however, must possess many-particle coherent correlations as well. It is natural that many-exciton coherence must be transferred in some way to exciton luminescence [11]. In this letter, we analyze the processes of transfer of exciton coherence to exciton luminescence induced by laser beam(s) in 2D exciton system. We show that stimulation by a single laser beam must lead to appearance of several unidirectional beams constituting a photon fan and stimulation by two laser beams must lead to a photon lattice. These effects look very different from analogous effects in 3D exciton system considered in Ref. [12]. Before we proceed with analysis of spatial nonlinear properties of exciton luminescence let us discuss briefly what many-exciton spatial coherence is. In coherent phase 0038-1098/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0038-1098(03)00128-5 Solid State Communications 126 (2003) 269–273 www.elsevier.com/locate/ssc * Corresponding author. Tel.: þ7-095-334-0881; fax: þ 7-095- 334-0886. E-mail addresses: ovchinnikov@isan.troitsk.ru (I.V. Ovchinnikov), lozovik@isan.troitsk.ru (Y.E. Lozovik).