Studying bi-partite entangled state representations via the integration over ket-bra operators in 详细信息    查看全文

• 作者：Hong-Yi Fan ; Sen-Yue Lou
• 关键词：integration over ket ; bra operators ; $\mathfrak{Q}$ ; ordering ; $\mathfrak{P}$ ; ordering ; entangled state representation
• 刊名：Frontiers of Physics
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：9
• 期：4
• 页码：460-464
• 全文大小：178 KB
• 参考文献：1. A. Einstein, B. Podolsky, and N. Rosen, Can quantummechanical description of physical reality be considered complete? / Phys. Rev., 1935, 47(10): 777 CrossRef
  2. H. Y. Fan and J. R. Klauder, Eigenvectors of two particles-relative position and total momentum., / Phys. Rev. A, 1994, 49(2): 704 CrossRef
  3. H. Y. Fan and Y. Fan, Dual eigenkets of the Susskind-Glogower phase operator, / Phys. Rev. A, 1996, 54(6): 5295 CrossRef
  4. P. A. M. Dirac, The Principles of Quantum Mechanics, Oxford: Clarendon Press, 1930
  5. H. Y. Fan and J. Zhou, Coherent state and normal ordering method for transiting Hermite polynomials to Laguerre polynomials, / Science China: Physics, Mechanics & Astronomy, 2012, 55(4): 605
  6. H. Y. Fan, New fundamental quantum mechanical operatorordering identities for the coordinate and momentum operators, / Science China: Physics, Mechanics & Astronomy, 2012, 55(5): 762 CrossRef
  7. H. Y. Fan and S. Y. Lou, / Science China: Physics, Mechanics and Astronomy, 2013 (to appear)
  8. H. Weyl, Quantenmechanik und gruppentheorie, / Z. Phys., 1927, 46(1-): 1 CrossRef
  9. E. Wigner, On the quantum correction for thermodynamic equilibrium, / Phys. Rev., 1932, 40(5): 749 CrossRef
  10. H. Y. Fan, S. Wang, and L. Y. Hu, Evolution of the singlemode squeezed vacuum state in amplitude dissipative channel, / Front. Phys., DOI 10.1007/s11467-013-0367-z
  11. H. Y. Fan, Squeezed states: Operators for two types of one- and two-mode squeezing transformations, / Phys. Rev. A, 1990, 41(3): 1526 CrossRef
  12. H. Y. Fan, H. L. Lu, and Y. Fan, Newton-Leibniz integration for ket-bra operators in quantum mechanics and derivation of entangled state representations, / Ann. Phys., 2006, 321(2): 480 CrossRef
  13. H. Y. Fan, Operator ordering in quantum optics theory and the development of Dirac’s symbolic method, / J. Opt. B, 2003, 5(4): R147 CrossRef
  14. H. Y. Fan, H. C. Yuan, and N. Q. Jiang, Deriving new operator identities by alternately using normally, antinormally, and Weyl ordered integration technique, / Science China: Phys Mechanics & Astronomy, 2010, 53(9): 1626
  
• 作者单位：Hong-Yi Fan (1)
  Sen-Yue Lou (1)
  
  1. Department of Physics, Ningbo University, Ningbo, 315211, China
  
• ISSN：2095-0470

文摘

For two particles-relative position and total momentum we have introduced the entangled state representation |η? and its conjugate state |ξ? In this work, for the first time, we study them via the integration over ket-bra operators in \(\mathfrak{Q}\) -ordering or \(\mathfrak{P}\) -ordering, where \(\mathfrak{Q}\) -ordering means all Qs are to the left of all Ps and \(\mathfrak{P}\) -ordering means all Ps are to the left of all Qs. In this way we newly derive \(\mathfrak{P}\) -ordered (or \(\mathfrak{Q}\) -ordered) expansion formulas of the two-mode squeezing operator which can show the squeezing effect on both the two-mode coordinate and momentum eigenstates. This tells that not only the integration over ket-bra operators within normally ordered, but also within \(\mathfrak{P}\) -ordered (or \(\mathfrak{Q}\) -ordered) are feasible and useful in developing quantum mechanical representation and transformation theory.