作为辛群表示的压缩态
Squeezed States as Representations of Symplectic Groups
摘要：
研究表明，类SU（1，1）和类SU（2）双光子相干态可以组合成类O（3，2）双光子态.由于O（3，2）群有许多子群，所以也有许多新的有趣的新相干和压缩双光子态。其中，双光子剪切态的对称性与二维欧氏群的对称性相似。现在有双声子相干态，它们可能表现出光子尚未观察到的对称性，包括剪切态。让我们注意到SU（1，1）和S（3，2）分别同构于辛群Sp（2）和Sp（4），辛变换包括旋转和压缩变换。
英文摘要：
It is shown that the SU(1,1)-like and SU(2)-like two-photon coherent states can be combined to form a O(3,2)-like two-photon states. Since the O(3,2) group has many subgroups, there are also many new interesting new coherent and squeezed two-photon states. Among them is the two-photon sheared state whose symmetry property is like that for the two-dimensional Euclidean group. There are now two-phonon coherent states which may exhibit symmetries not yet observed for photons, including sheared states. Let us note that both SU(1,1) and S(3,2) are isomorphic to the symplectic groups Sp(2) and Sp(4) respectively, and that symplectic transformations consist of rotations and squeeze transformations.
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