Realization of some unitary transformations and generation of entanglement between different degrees of freedom of light
ABSTRACT :
In this talk, I will begin by introducing first-order optical systems (FOOS) [1]. An optical system is said to be of first-order, provided it transforms the Wigner-Wolf function linearly. These FOOS can be realized in a lab using elementary optical transformations such as free propagation and thin lenses. While overviewing the recent advancements in realizing a FOOS which could require arbitrarily large free propagation distances, I will explore our recently proposed gadget which realizes a given FOOS using 5 spatial light modulators (SLMs) and 4 units of free propagation distance [2]. As an application of this proposed gadget, I will explain its usage in generating entanglement between polarization and spatial degrees of freedom (DoF) of a light field passing through the proposed optical setup. In the second part, I will talk about a device called ‘Polarization selective Dove prism’ (PSDP) which can couple orbital angular momentum (OAM) – with azimuthal indices ±1 – and polarization DoF without resorting to SLMs or interferometric methods [3]. I will also demonstrate its applications in performing generalized X operations and sorting of OAM states of light. In the third part, I will explain a method based on quantum walks to hyperentangle a single photon in three DoF: polarization, OAM, and path [4]. A passive optical setup using polarization beamsplitters and J-plates which can hyperentangle an input single photon has been proposed. The amount of entanglement between different DoF can be controlled by varying the J-plate parameters. Finally, I will briefly discuss my ongoing research problems.