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Chinese Physics Letters

Generation of Entangled Coherent States in Raman-Coupled Bose-Einstein Condensates

KUANGLe-Man, ZENGAi-Hua, KUANGZhen-Hua

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

A method for producing entangled coherent states (ECSs) for atomic Bose-Einstein condensates (BECs) ispresented. The proposed method involves a BEC with three internal states and two classical laser beams ina three-level Lambda configuration. We show how to generate multi-state ECSs through properly manipulatingstrengths of these interactions and laser detunings. A maximally entangled coherent state is obtained explicitly.

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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).
We propose a direct, coherent coupling scheme that can create massively entangled states of Bose-Einstein-condensed atoms. Our idea is based on an effective interaction between two atoms from coherent Raman processes through a (two-atom) molecular intermediate state. We compare our scheme with other recent proposals for generation of massive entanglement of Bose-Einstein-condensed atoms. We also present explicit calculations that support the possibility of detecting maximally entangled states without requiring single-atom resolved measurements.
We outline a procedure for Heisenberg-limited phase resolution between two Bose-Einstien condensates (BECs) defined as different hyperfine levels. The method involves first establishing a maximally entangled state using the ideas of nonlinear interferometry previously discussed in the optical domain [C. C. Gerry et al., Phys. Rev. A 66, 013804 (2002)]. In the case of the condensates, the nonlinear interactions are realized by the interatomic interactions within each condensate. Quarter cycle Raman pulses between hyperfine levels act as beam splitters. Parity measurements of one of the components of the BEC resolve the phase at the Heisenberg limit. We point out that parity measurements can be made by coupling the mode of interest with a third condensate where both components evolve under nonlinear interatomic interactions. After another Raman pulse, the components are populated according to parity. One need only determine which component is populated to determine the parity.
We propose a scheme for generating many-atom maximal entanglement states in spin-1 Bose-Einstein condensates. By applying a far-off-resonate blue-detuned linear-polarized laser to the condensates, the hyperfine level F=1,m=0F=1,m=0F=1,m=0 ground state and the hyperfine F=0F=0F=0 excited state are conveniently coupled. Such a configuration is more efficient and provides a fast implementation of the maximally entangled GHZ state, using only half of the time that is required in single-atom Raman-transition-based schemes [You, Phys. Rev. Lett. 90, 030402 (2003)].