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.