P HYSICAL R EVIEW LETTERS VOLUME 79 7 JULY 1997 NUMBER 1 Generation of Einstein-Podolsky-Rosen Pairs of Atoms E. Hagley, X. Maı ˆtre, G. Nogues, C. Wunderlich, M. Brune, J. M. Raimond, and S. Haroche Laboratoire Kastler Brossel,* Département de Physique de l’Ecole Normale Supérieure, 24 rue Lhomond, F-75231 Paris Cedex 05, France (Received 6 March 1997) Pairs of atoms have been prepared in an entangled state of the Einstein-Podolsky-Rosen ( EPR) type. They were produced by the exchange of a single photon between the atoms in a high Q cavity. The atoms, entangled in a superposition involving two different circular Rydberg states, were separated by a distance of the order of 1 cm. At variance with most previous EPR experiments, this one involves massive particles. It can be generalized to three or more atoms and opens the way to new tests of nonlocality in mesoscopic quantum systems. [S0031-9007(97)03502-3] PACS numbers: 03.65. – w, 32.80. – t, 42.50. – p One of the most puzzling aspects of quantum mechan- ics, its nonseparability, is illustrated vividly by the famous Einstein-Podolsky-Rosen ( EPR) paradox [1]. A pair of particles flying apart from each other is predicted by quantum mechanics to yield measurement results incom- patible with our intuitive conceptions about locality and reality. Such a nonclassical behavior is expected from any system made of two parts whose wave function can- not be written, in any basis, as a direct product of inde- pendent substates. The system parts are then said to be entangled. The study of entanglement has been given a firm conceptual ground by Bell who derived inequalities that Nature should obey if locality and reality were re- spected and which are violated by quantum mechanics [2]. Many experiments since Bell’s paper have demonstrated violations of these inequalities and have vindicated quan- tum theory [3–7]. In most EPR experiments so far [3,4,6,7], pairs of pho- tons flying apart are created in a correlated state by a ra- diative process (spontaneous emission cascade in an atom or down-conversion in a nonlinear medium). Entangled protons have also been studied in an early experiment [5]. All these studies have dealt with very simple elementary particle systems, in which the entanglement mechanism is imposed by spontaneous processes. Entangling more complex systems in a controlled way is a challenging goal, which has been discussed in many recent proposals. The generation of EPR pairs of mas- sive atoms instead of massless photons has been considered [8–11]. Ideas to generalize entanglement to larger num- bers of particles have also been analyzed [8,10,12]. The “manipulation” of entanglement is another impor- tant aspect of the new EPR experiment proposals. The idea is to apply a set of well-controlled interactions to the particles of the system in order to bring them into a “tailored” entangled state. In this context, the physics of entanglement meets the theory of quantum informa- tion processing. Teleportation of quantum states could in principle be achieved [13] as well as quantum cryptogra- phy [14]. Simple quantum computation steps could also be carried out. Particles can then be viewed as carriers of quantum bits of information and the realization of “engi- neered” entanglement is closely related to the building of gates acting on these bits [15]. We describe here an experiment in which we have entangled two initially independent atoms and analyzed their correlations. The entanglement procedure involves the resonant coupling, one by one, of the atoms to a high Q microwave superconducting cavity C. The atoms, prepared in circular Rydberg states [16], exchange a single photon in the cavity and become entangled by this indirect interaction. We have demonstrated the effect with pairs of atoms separated by centimetric distances and we have measured their correlations at a distance by a Ramsey interferometric method. This experiment can be generalized to atomic triplets or to larger numbers of 0031-9007 97 79(1) 1(5)$10.00 © 1997 The American Physical Society 1