中国物理B ›› 2005, Vol. 14 ›› Issue (7): 1307-1312.doi: 10.1088/1009-1963/14/7/007

• GENERAL • 上一篇    下一篇

Application of new entangled state representation to a two-coupled oscillator system

庞乾骏   

  1. Department of Physics, Shanghai Jiaotong University,Shanghai 200030, China
  • 收稿日期:2004-10-09 修回日期:2005-03-04 出版日期:2005-06-20 发布日期:2005-06-20

Application of new entangled state representation to a two-coupled oscillator system

Pang Qian-Jun (庞乾骏)   

  1. Department of Physics, Shanghai Jiaotong University,Shanghai 200030, China
  • Received:2004-10-09 Revised:2005-03-04 Online:2005-06-20 Published:2005-06-20

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摘要： We study the eigenstate problem of a two-coupled oscillator system. A new entangled state representation $\left\vert \gamma \right\rangle $ composed of the common eigenvectors of operators $% (x_{1}+p_{2})$ and $(p_{1}+x_{2})$ is established. Eigenvalues and eigenvectors of the Hamiltonian are obtained in $\left\vert \gamma \right\rangle $ representations. The same problem is studied in the second-quantization representation. We find that the second-quantization representation can be used to derive the normally ordered product expression of eigenvector in Fock space. In particular, we find that the ground state of the Hamiltonian is a kind of generalized two-mode squeezed state.

Abstract: We study the eigenstate problem of a two-coupled oscillator system. A new entangled state representation $\left\vert \gamma \right\rangle $ composed of the common eigenvectors of operators $% (x_{1}+p_{2})$ and $(p_{1}+x_{2})$ is established. Eigenvalues and eigenvectors of the Hamiltonian are obtained in $\left\vert \gamma \right\rangle $ representations. The same problem is studied in the second-quantization representation. We find that the second-quantization representation can be used to derive the normally ordered product expression of eigenvector in Fock space. In particular, we find that the ground state of the Hamiltonian is a kind of generalized two-mode squeezed state.

Key words: entangled state, two coupled oscillator system

中图分类号:  (Entanglement and quantum nonlocality)

  • 03.65.Ud
02.10.Ud (Linear algebra)