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arXiv:cond-mat/0501471 · Physical Review A

Maximal entanglement of two spinor Bose-Einstein condensates

Michael W. Jack, Makoto Yamashita

Published Mar 16, 2005• 12 citations
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Abstract

Starting with two weakly coupled antiferromagnetic spinor condensates, we show that by changing the sign of the coefficient of the spin interaction, ${U}_{2}$, via an optically induced Feshbach resonance, one can create an entangled state consisting of two anticorrelated ferromagnetic condensates. This state is maximally entangled and a generalization of the Bell state from two anticorrelated spin-$1∕2$ particles to two anticorrelated spin-$N∕2$ atomic samples, where $N$ is the total number of atoms.

DOI
10.1103/physreva.71.033619

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The predictions of quantum mechanics often differ from our everyday experiences. In the classical case, the state of a system can be predicted precisely, assuming the exact knowledge of all parameters. This is not possible in quantum mechanics. For example, the spin of one particle can be simultaneously in two different states, until a measurement defines the actual state. If multiple particles are in such superposition states, their spins can be coupled with each other such that the measurement of one particle changes the physical state of the other particles. This coupling effect is a fundamental part of quantum mechanics and is called entanglement. It is a central requirement for applications in the fields of quantum communication, quantum cryptography and quantum computing. One possibility to create entanglement are spin-changing collisions in a spinor Bose-Einstein condensate. These collisions are described by a nonlinear process, which creates non-classical correlations between all atoms of the Bose-Einstein condensate. Within this thesis, 87Rb spinor Bose-Einstein condensates are used to demonstrate Einstein-Podolsky-Rosen entanglement by the generation and analysis of a two-mode entangled state in spin space [A1]. These states are applied in an interferometric measurement with a resolution of 2.05+0.34 -0.37 dB beyond the standard quantum limit [A2]. Depending on the dynamics, the process can also be analogous to the dynamical Casimir effect [A3]. The entanglement between the particles in these publications is strongly connected with their indistinguishability. It is thus possible to make the particles distinguishable again and recover the entanglement between the now separated particles? This question is approached by cutting an entangled state of indistinguishable particles into two spatially separated atomic modes - creating a two-mode entangled state in real space. As shown in Ref. [A4], the entanglement between the two separated clouds of a Bose-Einstein condensate can be measured directly. In the future, the created state can be employed for a test of quantum nonlocality.
We present a theoretical analysis of the experimental scheme for creating maximally entangled states of many atoms in spin-1 Bose-Einstein condensates by driving single atom Raman transition [Li You, Phys. Rev. Lett. 90, 030402 (2003)]. It is shown that, with the help of strong external laser pulses, the model proposed by You can be greatly simplified. Using this simplified interaction, an analytical expression is given for the entangled states between atoms with hyperfine spin $\ensuremath{-}1$ and 1. We also show how to generate the entangled state between atoms with hyperfine spin 0 and 1.
We analyze a scheme for generating entanglement between two spinor Bose-Einstein condensates (BECs). The BECs are off-resonantly coupled to a common photon mode and are controlled by external lasers to induce a SzSz{S}^{z}{S}^{z}SzSz interaction, where Sz{S}^{z}Sz is the total spin of the BEC. We directly simulate the scheme numerically for small systems and show the performance of the scheme. The scaling of the entanglement to large-scale systems under realistic conditions of spontaneous emission and cavity photon loss is analyzed. It is shown that both entanglement in the beyond-continuous-variable regime can be generated, where the entanglement is of the order of the maximal entanglement between the systems.