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

Selective tuning of Hilbert spaces in states encoded with spatial modes of light