INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF OPTICS B: QUANTUM AND SEMICLASSICAL OPTICS J. Opt. B: Quantum Semiclass. Opt. 6 (2004) S610–S617 PII: S1464-4266(04)72641-5 Stationary two-atom entanglement induced by nonclassical two-photon correlations R Tana´ s 1 and Z Ficek 2 1 Nonlinear Optics Division, Institute of Physics, Adam Mickiewicz University, Pozna´ n, Poland 2 Department of Physics, School of Physical Sciences, The University of Queensland, Brisbane, QLD 4072, Australia E-mail: tanas@kielich.amu.edu.pl Received 26 September 2003, accepted for publication 6 January 2004 Published 28 May 2004 Online at stacks.iop.org/JOptB/6/S610 DOI: 10.1088/1464-4266/6/6/022 Abstract A system of two two-level atoms interacting with a squeezed vacuum field can exhibit stationary entanglement associated with nonclassical two-photon correlations characteristic of the squeezed vacuum field. The amount of entanglement present in the system is quantified by the well known measure of entanglement called concurrence. We find analytical formulae describing the concurrence for two identical and nonidentical atoms and show that it is possible to obtain a large degree of steady-state entanglement in the system. Necessary conditions for the entanglement are nonclassical two-photon correlations and nonzero collective decay. It is shown that nonidentical atoms are a better source of stationary entanglement than identical atoms. We discuss the optimal physical conditions for creating entanglement in the system; in particular, it is shown that there is an optimal and rather small value of the mean photon number required for creating entanglement. Keywords: entanglement, squeezing, superpositions 1. Introduction Entanglement between separate quantum systems is one of the key problems in quantum mechanics. A number of interesting concepts and methods for creating entanglement have been proposed involving trapped and cooled ions or neutral atoms [1–8]. Of particular interest is generation of entangled states in two-atom systems, since they can represent two qubits, the building blocks of the quantum gates that are essential to implement quantum protocols in quantum information processing. It has been shown that entangled states in a two-atom system can be created by a continuous driving of the atoms with a coherent or chaotic thermal field [5, 9–12], or by a pulse excitation followed by a continuous observation of radiative decay [13–15]. Moreover, the effect of spontaneous emission on initially prepared entangled state has also been discussed [16–19]. These studies, however, have been limited to the small sample (Dicke) model [20] or the situation involving noninteracting atoms strongly coupled to a cavity mode. The difficulty of the Dicke model is that it does not include the dipole–dipole interaction among the atoms and does not correspond to realistic experimental situations of atoms located (trapped) at different positions. In fact, the model corresponds to a very specific geometrical configuration of the atoms confined to a volume much smaller compared with the atomic resonant wavelength (the small-sample model). The present atom trapping and cooling techniques can trap two atoms at distances of order of a resonant wavelength [21–23], which makes questionable the applicability of the Dicke model to physical systems. Recently, we have shown [24] that spontaneous emission from two spatially separated atoms can lead to a transient entanglement of initially unentangled atoms. This result contrasts with the Dicke model where spontaneous emission cannot produce entanglement from initially unentangled atoms [10, 18]. We have also found [25] analytical results for 1464-4266/04/060610+08$30.00 © 2004 IOP Publishing Ltd Printed in the UK S610