ua nt - p h / 02 07 00 6 v 1 1 J ul 2 00 2 DURABLE ENTANGLEMENT IN ATOMIC SYSTEMS


We discuss the generation and monitoring of durable atomic entangled state via Raman-type process, which can be used in the quantum information processing. PACS number(s): 03.65.Ud, 32.80.-t Typeset using REVTEX 1 The problem of creation of entangled states in atomic systems has attracted a great deal of interest (see and references therein). In particular, the entangled states were engineered through the use of cavity QED and technique of ion traps. An interesting proposal has been made recently (for further discussion, see Refs. 5 and 6). It was shown that a pure entangled state of two atoms in an optical resonator can be obtained through the exchange by a single photon. Since the excitation of the system either is carried by a cavity photon or is shared between the atoms, the absence of the photon leakage from the resonator can be associated with the presence of atomic entanglement. This entanglement can be observed in the process of continuous monitoring of the cavity decay. The importance of this scheme is caused by the fact that its realization seems to be easy available with present experimental technique. The result can also be generalized on the multi-atom systems. In view of the practical realization, it seems to be more convenient if the existence of atomic entanglement would manifest itself via a certain signal photon rather than via the absence of photons as in Ref. 4. This implies that there should be at least two different modes interacting with the atoms such that the photon of one of them provides the correlation between the atoms, while the photon of the other mode can freely leave the resonator to signalize the rise of atomic entanglement. In this note we discuss a way how to obtain a durable maximum entangled state of atoms in an optical resonator which can be monitored through the detection of signal photons. Consider the Raman-type process in a three-level atom shown in Fig. 1. Here 1 ↔ 2 and 2 ↔ 3 are the dipole transitions corresponding to the pump and Stokes modes, while the dipole transition between the levels 1 and 3 is forbidden because of the parity conservation. We assume that the two identical atoms of this type are located in a high-quality cavity tuned to resonance with 1 ↔ 2 transition, while the Stokes photons can leak away freely (Fig. 2). Assume that initially both atoms are in the ground state (level 1) and there is a single cavity photon, so that the initial state is 2 |ψ0〉 = |1, 1〉|1P 〉|VS〉. (1) Here |nP 〉 denotes the n-photon state of the cavity (pump) mode and |VS〉 denotes the vacuum state of the Stokes field. Then, the absorption of the cavity photon by atomic system should lead to the state |ψ1〉 = 1 √ 2 (|2, 1〉+ |1, 2〉)|0P 〉|VS〉, (2) which manifests the entanglement of atoms excited to the level 2. This atomic entanglement is similar to that discussed in Ref. 4 and has a very short lifetime defined by the atom-field coupling constants for the allowed transitions. The decay of the excited atomic state (2) can either return the system into the initial state (1) or turn (2) into the state |ψk〉 = 1 √ 2 (|3, 1〉+ |1, 3〉)|0P 〉|1Sk〉, (3) where |nSk〉 denotes the state of n Stokes photons with frequency ωSk. This state again manifests the maximum atomic entanglement. Since the cavity walls are supposed to be transparent for the Stokes photons and 3 ↔ 1 is the dipole-forbidden transition, the atomic entanglement described by (3) would exist for a very long time determined by the weak interaction between the atoms excited to the level 3 and a certain dissipative environment. The creation of this atomic entanglement manifests itself by the Stokes photon that can be detected outside the cavity. It should be noted that, in addition to |ψ1〉 and |ψk〉, the following maximum entangled states |φ1〉 = 1 √ 2 (|2, 1〉 − |1, 2〉)|0P 〉|VS〉, |φk〉 = 1 √ 2 (|3, 1〉 − |1, 3〉)|0P 〉|1Sk〉 also contribute into the base states of the system under consideration. Both of them are stabile states but they cannot be achieved in the process of evolution beginning with the initial state (1) (see Ref. 6). Therefore, they can be discarded.

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@inproceedings{Can2002uaN, title={ua nt - p h / 02 07 00 6 v 1 1 J ul 2 00 2 DURABLE ENTANGLEMENT IN ATOMIC SYSTEMS}, author={Muhammet Ali Can and A. A. Klyachko and Alexander S. Shumovsky}, year={2002} }