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

TL;DR

This paper demonstrates a method to selectively tune the spatial mode subspaces of entangled photon pairs generated via SPDC by controlling the modal content of the pump beam, enabling flexible access to different Hilbert space regions.

Contribution

It introduces a technique to control and access various spatial mode subspaces in entangled photon states through pump beam superpositions in SPDC.

Findings

Generated states can be tuned between different modal subspaces.

Control over pump modal content allows selective access to Hilbert space regions.

Proof-of-principle experiment confirms tunability of spatial mode entanglement.

Abstract

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.