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Communications in Theoretical Physics

Quantum Entanglement of Many Distant Bose—Einstein Condensates in an Optical Lattice by Interference

Ya‐Feng Liu, Xu‐Bo Zou, Guang‐Can Guo

Published Jul 1, 2014• 1 citation
Publisher

Abstract

We propose a scheme to generate maximally entangled states of two distant Bose—Einstein condensates, which are trapped in different potential wells of a one-dimensional optical lattice. We show how such maximally entangled state can be used to test the Bell inequality and realize quantum teleportation of a Bose—Einstein condensate state. The scheme proposed here is based on the interference of Bose—Einstein condensates leaking out from different potential wells of optical lattice. It is briefly pointed out that this scheme can be extended to generate maximally entangled Greenberger—Horne—Zeilinger (GHZ) states of 2m (m > 1) distant Bose—Einstein condensates.

DOI
10.1088/0253-6102/62/1/03

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We propose a scheme to generate maximally entangled states of two distant Bose—Einstein condensates, which are trapped in different potential wells of a one-dimensional optical lattice. We show how such maximally entangled state can be used to test the Bell inequality and realize quantum teleportation of a Bose—Einstein condensate state. The scheme proposed here is based on the interference of Bose—Einstein condensates leaking out from different potential wells of optical lattice. It is briefly pointed out that this scheme can be extended to generate maximally entangled Greenberger—Horne—Zeilinger (GHZ) states of 2m (m > 1) distant Bose—Einstein condensates.
We propose a unified scheme to generate WWW states, Greenberger-Horne-Zeilinger (GHZ) states, and cluster states of four distant atoms, which are trapped separately in leaky cavities. The proposed schemes require linear optical elements and photon detectors with single-photon sensitivity. The quantum noise influences the fidelity of the generated states. Further, based on the four-photon coincidence detection, we propose another scheme to generate the WWW states and GHZ states of four distant atoms. The scheme is insensitive to the quantum noise, but cannot be used to generate the cluster states.
We propose protocols for quantum teleportation of superposed coherent states of atomic Bose—Einstein condensates. We use the photon entanglement states as the quantum channel, which makes it possible to realize the distant teleportation of atomic states. Two robust protocols are introduced: one is a single-photon scheme in which an entangled single-photon state serves as the quantum channel, and the other is a multi-photon scheme where an entangled coherent state of the probe lasers is used as the quantum channel.
Based on the interference effect of polarized photons leaking out of separate cavities, we propose schemes for the generation of the N -atom Greenberger–Horne–Zeilinger (GHZ) state, three-atom W state and a genuine four-atom entangled state |χ⟩. In these schemes, each of the atoms is trapped separately in a remote optical cavity, and the possible spontaneous channels induced by the excited atoms lead to the coherent superposition of the states of the atoms. The desired multipartite entangled states can be generated with a certain success probability by the subsequent detection of the polarized photons in different modes. The schemes would be useful steps towards long-distance quantum communication, distributed quantum computation and constructing remote quantum information processing networks.
We propose a method to generate entangled coherent states between two spatially separated atomic Bose-Einstein condensates (BECs) via the technique of electromagnetically induced transparency (EIT). Two strong coupling laser beams and two entangled probe laser beams are used to cause two distant BECs to be in EIT states and to generate an atom-photon entangled state between probe lasers and distant BECs. The two BECs are initially in unentangled product coherent states while the probe lasers are initially in an entangled state. Entangled states of two distant BECs can be created through the performance of projective measurements upon the two outgoing probe lasers under certain conditions. Concretely, we propose two protocols to show how to generate entangled coherent states of the two distant BECs. One is a single-photon scheme in which an entangled single-photon state is used as the quantum channel to generate entangled distant BECs. The other is a multiphoton scheme where an entangled coherent state of the probe lasers is used as the quantum channel. Additionally, we also obtain some atom-photon entangled states of particular interest such as entangled states between a pair of optical Bell states (or quasi-Bell-states) and a pair of atomic entangled coherent states (or quasi-Bell-states).
Based on the interference effect of polarized photons, we propose a practical scheme for entanglement concentration of unknown atomic entangled states. In the scheme, two λλ-type atoms belonging to different entangled pairs are individually trapped in two spatially separated cavities. By the subsequent detection of the polarized photons leaking out of the separate optical cavities, Alice and Bob as two distant parties can probabilistically extract one maximally entangled four-atom Greenberger–Horne–Zeilinger (GHZ) state from two identical partially entangled Einstein–Podolsky–Rosen (EPR) pairs. We also discuss the influence of cavity decay on the success probability of the scheme. The scheme is feasible and within the reach of current experimental technology.
The unequivocal detection of entanglement between two distinct matter-wave pulses is a significant challenge that has yet to be experimentally demonstrated. We describe a realistic scheme to generate and detect continuous-variable entanglement between two atomic matter-wave pulses produced via degenerate four-wave mixing from an initially trapped Bose-Einstein condensate loaded into a one-dimensional optical lattice. We perform a comprehensive numerical investigation for fixed condensate parameters to determine the maximum violation of separability and Einstein-Podolsky-Rosen inequalities for field quadrature entanglement, and describe and simulate an experimental scheme for measuring the necessary quadratures.