arXiv 1204.26802012-04-12quant-ph

扩展的双参数Fock空间中相干态和压缩态的表示

Representations of Coherent and Squeezed States in an Extended Two-parameters Fock Space

M K Tavassoly, M H Lake

备注：: 14 pages, accepted in Chinees Physics C

摘要：

最近引入了一个由$|n>_λ$张成的$f$变形Fock空间.这些基确实是变形的非厄米哈密顿量的本征态。在这篇文章中，我们将使用一种新的非正交基矢来构造相干态和压缩态，在特殊情况下，这将导致早期已知的状态。为此，我们首先推广以前介绍的Fock空间的$|n>_λ$基，到一个新的，由一个扩展的双参数基$|n>_{λ_{1},λ_{2}}$。这些基底现在是非厄米哈密顿$H_{λ_{1},λ_{2}}=a^{\dagger}_{λ_{1},λ_{2}}a+1/2$的本征态，其中$a^{\dagger}_{λ_{1},λ_{2}}=a^{\dagger}+λ_{1}a + λ_{2}$和$a$分别是变形的产生算符和普通的玻色子湮灭算符。基$|n>_{λ_{1},λ_{2}}$是非正交的（压缩态），但可归一化。然后，在我们的双参数Fock空间中，推导出相干态和压缩态的新的表示。最后，我们讨论了量子统计特性，以及所获得的状态的非经典特性，数值。

英文摘要：

Recently a $f$-deformed Fock space which is spanned by $|n>_λ$ has been introduced. These bases are indeed the eigen-states of a deformed non-Hermitian Hamiltonian. In this contribution, we will use a rather new non-orthogonal basis vectors for the construction of coherent and squeezed states, which in special case lead to the earlier known states. For this purpose, we first generalize the previously introduced Fock space spanned by $|n>_λ$ bases, to a new one, spanned by an extended two-parameters bases $|n>_{λ_{1},λ_{2}}$. These bases are now the eigen-states of a non-Hermitian Hamiltonian $H_{λ_{1},λ_{2}}=a^{\dagger}_{λ_{1},λ_{2}}a+1/2$, where $a^{\dagger}_{λ_{1},λ_{2}}=a^{\dagger}+λ_{1}a + λ_{2}$ and $a$ are respectively, the deformed creation and ordinary bosonic annihilation operators. The bases $|n>_{λ_{1},λ_{2}}$ are non-orthogonal (squeezed states), but normalizable. Then, we deduce the new representations of coherent and squeezed states, in our two-parameters Fock space. Finally, we discuss the quantum statistical properties, as well as the non-classical properties of the obtained states, numerically.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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