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We present a scheme to generate maximally entangled states of two three-level atoms with a nonresonant cavity by cavity-assisted collisions. Since the cavity field is only virtually excited no quantum information will be transferred from the atoms to the cavity. Entangled states of quantum particles give the possibility to test quantum mechanics against a local hidden variable theory [1,2,3]. They also have practical applications in quantum cryptography [4], quantum dense coding [5] and quantum teleportation [6]. Most of the research in quantum information processing is based on entanglement generation of quantum two-level systems (Qubits), which represent the information. Recently, there is much interest in N -level quantum systems (N ≥ 3) to represent information. It was demonstrated that key distributions based on three-level quantum systems are more secure against eavesdropping than those based on two-level systems [7]. Key distribution protocols based on entangled three-level systems were also proposed [8]. The security of these protocols is related to the violation of the Bell inequality. Recently, it was shown that the quantum prediction differs more radically from classical physics in the case of three-level systems than in the case of two-level systems. The three-level system provides in this context a much smaller level of noise [9]. The proof of Bell's theorem without the inequalities by Greenberger, Horne, and Zeilinger (GHZ) was extended to multiparticle multi-level systems [10]. One way to generate multiqubit entanglement of N -level quantum systems is to use higher order parametric down conversion [11]. A more direct way is to use multilevel quantum systems. In this context entanglement generation of N -level quantum systems was reported [12,13]. Rydberg atoms which cross superconductive cavities are an almost ideal system to generate entangled states and to perform small scale quantum information processing [14]. A number of schemes were proposed in the context of cavity QED. In particular EPR pairs [15] and GHZ states [16] were successfully generated by a successive interaction of a series of atoms in a cavity field. In these schemes cavities act as memories, which store the information of an electric system and transfer it back to the electric system. Thus, the decoherence of the cavity field becomes one of the main obstacles for the implementation of quantum information in cavity QED. Recently, significant progress was made by proposals for atoms, which interact with a nonresonant cavity [17]. In this theoretical scheme it is suggested to use a dynamic, which involves a virtual exchange of a photon with the field. To the first order of the approximation the scheme is insensitive to cavity losses or to the presence of a stray of a thermal field in the mode. Recently, this process was also suggested to generate GHZ states [19] and to implement the quantum search algorithm [20]. Following the proposal of Ref [17] an experiment was performed in which two Rydberg atoms cross a nonresonant cavity. T...

We present a scheme to generate arbitrary superpositions of Dicke states of excitons in optically driven quantum dots. The proposal is based on a sequence of laser pulses to control transitions between the nearestneighbor Dicke states appropriately. It is shown that only N laser pulses are needed to generate arbitrary superpositions of Dicke states of N quantum dots.Quantum entanglement is one of the most striking features of quantum mechanics ͓1,2͔. The recent progress in quantum information theory allows one to regard it as an essential resource for many ingenious applications, e.g., quantum cryptography ͓3͔, quantum dense coding ͓4͔ and quantum teleportation ͓5͔. Since the Greenberger-Horne-Zeilinger ͑GHZ͒ state gives a prospect to test quantum nonlocality without an inequality ͓6͔, there is much interest in applications of multiparticle entangled states ͓6-9͔. In Ref.͓10͔ the existence of two inequivalent classes of three-qubit entangled states was shown, namely, the GHZ class and the W class. These two classes are inequivalent because states from one class cannot be transformed to states of the other class by local operations and classical communication ͓10͔. It was also shown that the correlation between two qubits, which are selected from a trio prepared in a W state, violates the Clauser-Horne-Shimony-Holt inequality more than the correlation between two qubits in any other quantum state ͓11͔. The W state was used to realize the teleportation of an unknown state probability ͓12͔. In Ref. ͓13͔ the quantum key distribution was proposed with W states. In Ref. ͓14͔, Cabello presented the Bell inequality involving the tripartite and bipartite correlations PHYSICAL REVIEW A 68, 034306 ͑2003͒

We present a scheme to generate an arbitrary two-dimensional quantum state of motion of a trapped ion. This proposal is based on a sequence of laser pulses, which are tuned appropriately to control transitions on the sidebands of two modes of vibration. Not more than (M + 1)(N + 1) laser pulses are needed to generate a pure state with a phonon number limit M and N.PACS number:42.50.Dv, 42.50.CtThe generation of nonclassical states was studied in the past theoretically and experimentally. The first significant advances were made in quantum optics by demonstrating antibunched light [1] and squeezed light [2]. Various optical schemes for generating Schrödinger cat states were studied [3], which led to an experimental realization in a quantized cavity field [4]. Several schemes were proposed to generate any single-mode quantum state of a cavity field [5,6,7] and traveling laser field [8]. Recently, possible ways of generating various two-mode entangled field states were proposed. For example, it was shown [9] that entangled coherent states, which can be a superposition of two-mode coherent states [9,10] can be produced using the nonlinear Mach-Zehnder interferometer. These quantum states can be considered as a two(multi)-mode generalization of single-mode Schrödinger cat states [11]. A method to generate another type of two-mode Schrödinger cat states, which are known as SU(2) Schrödinger cat states, was proposed [13,14]. These quantum states result when two different SU(2) coherent states [12,13,14] are superposed. It was also shown that two-mode entangled number states can be generated by using nonlinear optical interactions [15], which may then be used to obtain the maximum sensitivity in phase measurements set by the Heisenberg limit [16] . In general, however, an experimental realization of nonclassical field states is difficult, because the quantum coherence can be destroyed easily by the interaction with the environment. Recent advances in ion cooling and trapping have opened new prospects in nonclassical state generation. An ion confined in an electromagnetic trap can be described approximately as a particle in a harmonic potential. Its center of mass (c.m.) exhibits 1

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