ISSN 1063-7761, Journal of Experimental and Theoretical Physics, 2006, Vol. 103, No. 2, pp. 167–182. © Pleiades Publishing, Inc., 2006. Original Russian Text © I.E. Protsenko, 2006, published in Zhurnal Éksperimental’noœ i Teoreticheskoœ Fiziki, 2006, Vol. 130, No. 2, pp. 195–211. 167 1. INTRODUCTION The phenomenon of superradiance or collective spontaneous emission in a system of N two-level atoms has been known for more than 50 years beginning with Dicke’s work [1]. Since that time, numerous experi- mental and theoretical works have been reported and summarized in, e.g., [2– 4] and [5]. Superradiance is an interesting, complex, and fundamental physical phe- nomenon beyond the scope of quantum electrodynam- ics [6]. For this reason, it attracts attention despite a long period of investigations. Current interest in super- radiance is stimulated by new experimental capabilities and new applications of theoretical methods of its anal- ysis. In particular, theoretical investigations are per- formed and various experiments are proposed and conducted on studying superradiance and related phe- nomena in quantum-dot systems [7–9], heterostruc- tures [10, 11], semiconductor lasers [12], molecular groups (aggregates) [13], cold atoms in dipole traps [14, 15], atomic Bose condensates [16], and atoms near surfaces [17]. Interest in systems consisting of particles that have several quantum states (“finite-size” systems such as two-level atoms, quantum dots, etc.) and inter- act with each other and with the environment through the resonant electromagnetic field is associated with plans for using them as a basis for creating elementary logical cells for quantum computers [18, 19] and other ultraminiature quantum nanodevices, e.g., sources of single photons for uneavesdroppable optical communi- cation lines (quantum cryptography) [20], amplifiers for “squeezed” electromagnetic fields [21], nanolasers [22], and sensors [23]. It is convenient to control quan- tum nanodevices, to realize the interaction between their components, and to acquire information on their state by means of quasimonochromatic electromag- netic fields emitted and absorbed by quantum particles. The theoretical description of the interaction between quantum particles through the resonant electromag- netic field is closely related to the theory developed on the basis of Dicke’s idea, particularly when the interac- tion can be described in the dipole approximation and particles are located in a volume with characteristic sizes of about the wavelength of resonance radiation. The latter condition is satisfied in many applied situa- tions, e.g., for cold atoms in dipole traps [14] or ions in linear traps [24]. Continuation of investigations of superradiance is necessary for solving a number of fundamental prob- lems of quantum mechanics. One of them is the cre- ation and use of given mixed [25] (entangled [26, 27]) states of quantum objects that interact with each other and have a finite number of basis quantum states. The problem of obtaining quantum states with a certain degree of entanglement is closely related to problems of quantum information processing [26], but it is also considered independently beginning with [28] and the discovery of Bell inequalities [29], which have now been replaced by other criteria (e.g., concurrence [30]) characterizing the “degree of entanglement” of sates and the “quantum level” of noise in the system. Under actual conditions, finite-level quantum systems do not exist, because any quantum object (atom, quantum dot, etc.) interacts with an environment (thermostat) for which the number of degrees of freedom is infinite; in particular, a two-level atom interacts with electromag- netic field modes in the process of spontaneous emis- sion [31]. The thermostat affects finite-level systems, not only inducing spontaneous transitions in them, but also changing the energies and matrix elements of tran- sitions between their states. An important example (see below) is presented by mixed states of dipole–dipole interacting atoms for which the degree of entanglement criterion [30] is defined in [32]. Spontaneous emission and resonant dipole–dipole interaction between two- Superradiance of Several Cold Atoms I. E. Protsenko Lebedev Physical Institute, Russian Academy of Sciences, Leninskiœ pr. 53, Moscow, 119991 Russia e-mail: protsen@sci.lebedev.ru Received December 26, 2005 Abstract—A method for calculating the spontaneous emission power of several immobile dipole-interacting two-level atoms located in a volume of about the wavelength of resonance radiation has been proposed in the Schrödinger representation. It has been shown that two atoms cannot, but four atoms can, emit a superradiance pulse under the conditions corresponding to experiments with cold atoms in dipole traps. Various methods for determining the quasistationary mixed atomic states, as well as the generalization of this method to other reso- nance emitting systems, are discussed. PACS numbers: 42.50.Fx, 32.80.Pj, 31.70.Hq DOI: 10.1134/S1063776106080012 ATOMS, MOLECULES, OPTICS