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Physical Review A

二重井戸Bose‐Einstein凝縮体の量子コヒーレンス:Su(2)コヒーレント状態経路積分アプローチ

You Zhou, Hui Zhai, Lue R, Xu Zi-Zhong, Lei Chang

Published Jan 1, 2003• 4 citations
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Standing on the results for the minimum weight states obtained in the previous paper (I), an idea how to construct the linearly independent basis is proposed for the su(n)-Lipkin model. This idea starts in setting up m independent su(2)-subalgebras in the cases with n=2m and n=2m+1 (m=2,3,4,...). The original representation is re-formed in terms of the spherical tensors for the su(n)-generators built under the su(2)-subalgebras. Through this re-formation, the su(m)-subalgebra can be found. For constructing the linearly independent basis, not only the su(2)-algebras but also the su(m)-subalgebra play a central role. Some concrete results in the cases with n=2, 3, 4 and 5 are presented.

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Entangled SU (2) and SU (1,1) coherent states are developed as superpositions of multiparticle SU (2) and SU (1,1) coherent states. As a special example of entangled SU (2) coherent states, entangled binomial states are introduced and these entangled binomial states enable the contraction from entangled SU (2) coherent states to entangled harmonic oscillator coherent states. Entangled SU (2) coherent states are discussed in the context of pairs of qubits. We also introduce the entangled negative binomial states and entangled squeezed states as examples of entangled SU (1,1) coherent states. A method for generating the entangled SU (2) and SU (1,1) coherent states is discussed and degrees of entanglement calculated. Two types of SU (1,1) coherent states are discussed in each case: Perelomov coherent states and Barut-Girardello coherent states.

arXiv:quant-ph/0001073•Journal of Physics A Mathematical and General•Oct 5, 2000•112 citations
Standing on the results for the minimum weight states obtained in the previous paper (I), an idea how to construct the linearly independent basis is proposed for the su(n)-Lipkin model. This idea starts in setting up m independent su(2)-subalgebras in the cases with n=2m and n=2m+1 (m=2,3,4,...). The original representation is re-formed in terms of the spherical tensors for the su(n)-generators built under the su(2)-subalgebras. Through this re-formation, the su(m)-subalgebra can be found. For constructing the linearly independent basis, not only the su(2)-algebras but also the su(m)-subalgebra play a central role. Some concrete results in the cases with n=2, 3, 4 and 5 are presented.
Entangled SU (2) and SU (1,1) coherent states are developed as superpositions of multiparticle SU (2) and SU (1,1) coherent states. As a special example of entangled SU (2) coherent states, entangled binomial states are introduced and these entangled binomial states enable the contraction from entangled SU (2) coherent states to entangled harmonic oscillator coherent states. Entangled SU (2) coherent states are discussed in the context of pairs of qubits. We also introduce the entangled negative binomial states and entangled squeezed states as examples of entangled SU (1,1) coherent states. A method for generating the entangled SU (2) and SU (1,1) coherent states is discussed and degrees of entanglement calculated. Two types of SU (1,1) coherent states are discussed in each case: Perelomov coherent states and Barut-Girardello coherent states.