Journal of Russian Laser Research, Volume 27, Number 5, 2006 SUPERRADIANCE OF TRAPPED ATOMS Igor E. Protsenko P. N. Lebedev Physical Institute, Russian Academy of Sciences Leninskii Prospect 53, Moscow 119991, Russia e-mails: protsen@sci.lebedev.ru Abstract A new method for calculating the total power of the spontaneous emission of a few motionless two- level atoms located at a distance of the order of the resonance-radiation wavelength with dipole–dipole interaction is suggested. The method is based on the Schr¨odinger representation. It is shown, as an example, that two trapped atoms cannot emit a pulse of superradiance under any conditions, while four atoms can emit such a pulse at certain conditions. Different ways of introducing the quasi-stationary states of atoms along with the generalization of the proposed method to other resonance systems are discussed. Keywords: two-level atoms, resonance dipole–dipole interaction, collective spontaneous emission. 1. Introduction The superradiance (SR) or collective spontaneous emission of N two-level atoms was predicted in [1] almost 50 years ago. Experimental and theoretical research of SR are summarized in the reviews [2–4] and the several books (see, for example, [5]. SR is a fundamental physical phenomenon; it can be found in many physical systems [6], and this is why SR still attracts attention even after many years of study. The recent interest in SR is related to new experimental possibilities and novel theoretical methods. In particular, experimental and theoretical researches on SR are carried out for quantum dots [7–9], heterostructures [10, 11], semiconductor lasers [12], molecular aggregates [13], atom Bose– Einstein condensates [14], and atoms near surfaces [15]. Experiments on SR have been suggested for cold atoms in dipole traps [16,17]. The recent interest in systems of particles with a finite number of quantum states coupled by the resonance electromagnetic field (EMF) is related to their potential applications, in particular, in quantum computers [18, 19], single-photon sources [20], amplifiers of “squeezed” EMF [21], nanolasers [22], optical sensors [23], etc. Quasi-monochromatic EMF (including the “near” EMF) is a convenient tool for controlling and coupling quantum nanodevices. The theoretical model of quantum- particle interactions through the resonance EMF is closely related to the Dicke theory of superradiance, especially when the particles are located in a volume of sub-wavelength size such as atoms in dipole traps [16] or ions in linear traps [24]. The study of SR is important for understanding the fundamental aspects of quantum mechanics such as the construction and application of predetermined entangled states of quantum objects with finite quantum states [25–27]. The question how to create a state of quantum objects with a pre-determined “degree” of entanglement is important for quantum information processing [26]. The idea of entanglement 414 Manuscript submitted by the author in English on May 27, 2006. 1573-8760/06/2703-0414 c  2006 Springer Science+Business Media, Inc.