Nonlinear Atomic-Optics and Generation of Two-Component Entangled Atom Lasers

Two-component entangled atom laser is obtained via quantum state transfer technique from lights to matter waves in a five-level M -type system. The considered atom-atom collisions can yield an effective Kerr susceptibility for this system and lead to the selfand crossphase modulation between the two output atom lasers. This effect results in generation of entangled states of output atom lasers. Furthermore, based on the Bell-state measurement, an useful scheme is proposed to spatially separate the generated entangled atom lasers. PACS numbers: 03.75.-b, 03.67.-a, 42.50.Gy Quantum entanglement has always attracted great interest as it is one of the key differences between quantum and classical physics. Since it can be exploited for various novel applications such as quantum computation and precision measurements, there has been a continuing effort to engineer the robust quantum entangled states in different systems. Since the experimental realization of Bose-Einstein Condensation (BEC) in dilute atomic clouds in 1995, much efforts have been taken in preparing a continuous atom laser [1] and exploring its potential applications in, e.g., gravity measurements through atom interferometry [2]. The method for creating two correlated matter waves has been proposed via four-wave mixing using BECs several years ago [3], and the large amplification of the generated correlated matter waves was also achieved [4]. Entanglement between the generated matter waves is possible when consider the coherent collisions between condensate atoms, which has been observed before [5]. Here we propose a technique to generate two-component entangled atom lasers from a five-level M -type system, with coherent collisions between atoms considered. This technique is based on the physical mechanism of Electromagnetically Induced Transparency (EIT) [6] which has attracted much attention in both experimental and theoretical aspects [7, 8, 9, 10], especially for the rapid developments of quantum memory technique [11], i.e., transferring the quantum states of photon wave-packet to collective Raman excitations in a loss-free and reversible manner. The quantum state transfer technique via EIT provides a new optical technique to generate continuous atom laser with extra quantum states [12, 13]. Very recently, consider the nonlinear effect in the EIT quantum state transfer process, many intriguing applications were discovered by a series publications, such as the solitons formed by dark-state polaritons in the EIT Kerr medium [9], generation of quantum phase gate for photons [14] and nonclassical soliton atom laser [15] by considering the coherent atom-atom collisions. In the following we investigate how to generate two-component entangled atom laser by considering the atom-atom collisions in the quantum state transfer technique from lights to matter waves in a fivelevel M -type system. The considered atom-atom collisions can yield an effective Kerr susceptibility for the probe lights and lead to the selfand cross-phase modulation between the two output atom lasers. This effect is useful for generation of entangled states. Furthermore, we propose a scheme to spatially separate the generated entangled atom lasers via entanglement swapping technique [16]. The system we considered is shown in Fig.1. A beam of five-level M type atoms moving in the z direction interact with two quantized probe and two classical control Stokes fields [12, 13], and the former fields are taken to be much weaker than the later ones. Atoms in different internal states are described by five bosonic fields Ψ̂μ(r, t)(μ = b, q1, q2, e1, e2). The two Stokes fields coupling the transitions from the state |qj〉 to excited one |ej〉 (j = 1, 2) can be described by the Rabifrequencies Ωcj = Ω0j(z)e −iωs(t−z/cj), respectively, with Ω0j being taken as real, and cj denoting the Electronic address: [email protected]