Generation and manipulation of classically entangled spin-orbit modes of photons via classical and quantum interference

Cody Leary

A classically entangled spin-orbit mode of a photon. The polarization distribution is spatially varying, and may be controllably rotated by means of a relatively simple optical transformation.

Photons have four internal degrees of freedom (DOFs), in addition to external attributes such as their direction of travel, or momentum. These may be described as one energy (or wavelength) DOF, one polarization (or spin) DOF, and two “orbital” DOFs associated with the beam’s spatial intensity distribution in the plane perpendicular to its motion. Although in many physical situations (and almost all textbook situations) these four degrees of freedom are independent of one another, it is possible to realize states of light in which they become become mixed up — or nonseparable — with respect to one another. A particularly interesting example of this are the so-called “spin-orbit”‘ modes of photons, in which their spin and orbital degrees of freedom are nonseparable. This means that the photon’s state of polarization varies spatially across its wavefunction, in the direction transverse to the photon’s motion (an example is shown in the figure). This situation provides an example of “classical entanglement”, which occurs whenever the photon’s electric field cannot be expressed in the form of a product between the field’s complex amplitude E(r) and a constant unit polarization vector. This concept differs from that of quantum entanglement, in that the latter term applies to the relationship between photons at two distinct points in space, while the former applies only to two distinct degrees of freedom of light at the same spatial location. Classically entangled modes have potential applications ranging from efficient position measurements of high speed objects to the distribution of quantum entanglement to ensembles of atoms for the purposes of secure communication and computation. In this project, we will continue the pioneering work of several recent Wooster graduates in understanding spin-orbit modes theoretically, generating them experimentally, and working out the details of their potential applications to the fields of classical and quantum information science. We have succeeded creating a novel class of spin-orbit modes of light such as the one shown in the figure, and have achieved control over the spatial distribution of both the polarization and intensity distributions of a subset of such beams. Possible future directions in this project include: 1) Enlarge our experimental parameter space to verify the full range of our theoretical predictions regarding the creation and manipulation of these modes. 2) Extend the existing experiments to the quantum optical regime through the creation of correlated photon pairs that are simultaneously exhibit both classical and quantum entanglement via quantum interference. Extensive experimental labwork and theoretical modeling via Mathematica will be required for this project.