Spatial modes of light directly give the most easily accessible degree of freedom that span an infinite dimensional Hilbert space. The higher dimensional spatial mode entanglement realized using spontaneous parametric down conversion (SPDC) process is generally restricted to the subspace defined by a single spatial mode in pump. Access to other modal subspaces can be realized by pumping beams carrying several easily tunable transverse modes. As a proof-to-principle experiment, we generate twin-photon states in a nonlinear SPDC process with pump as a superposition of first order Laguerre-Gaussian (or Hermite-Gaussian) modes. We show that the generated states can be easily tuned between different subspaces by controlling the respective modal content in the pump superposition.

中文翻译：

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在用光的空间模式编码的状态中希尔伯特空间的选择性调谐

光的空间模式直接给出了跨越无限维希尔伯特空间的最容易获得的自由度。使用自发参数下变频 (SPDC) 过程实现的高维空间模式纠缠通常限于由泵中的单个空间模式定义的子空间。可以通过泵浦携带几个易于调谐的横向模式的光束来实现对其他模态子空间的访问。作为原理验证实验，我们在非线性 SPDC 过程中生成双光子状态，泵浦作为一阶拉盖尔-高斯（或厄米-高斯）模式的叠加。我们表明，通过控制泵叠加中的相应模态内容，可以轻松地在不同子空间之间调整生成的状态。