This project studies new forms of imaging by exploiting the quantum entanglement of light. This is done by producing new spatial modes of light that are common to two beams of light but not to any one individually. Since spatial modes are the building blocks of images this research promises the development of new types of images that are common to light photons traveling in different directions. These images may be of higher resolution than the ones carried by the individual photons.
The broader impact of this project is that it advances our understanding of quantum information and imaging by involving only undergraduate researchers working with a faculty mentor. The students will be exposed to a vanguard technology early on in their studies at the same time that this technology is being developed. This program has been very successful in involving women and ethnic minorities. Other impacts include the development of new materials and laboratories for a modern way to teach quantum mechanics, which prepares students to the rising field of quantum information.
This project involved the research on the use of spatial modes of light, the fundamental blocks of images, to encode quantum information onto photons. The significance is that with spatial modes we can create many quantum bits of information for photons to carry, and for use in either quantum computing or quantum communication. Our initial efforts concentrated on the measurement of images carried with single photons, and we performed the first measurements of the helical mode of single photons. The first figure shows images taken one photon at a time of a photon in two spatial modes and how by interference we can see the different images (modes) that the photon can take. A second part of our research involves creating entangled states of spatial modes. This work is still ongoing, but it is important because it can be used to encode more quantum bits of information per photon. A third part of our research was a spinoff of our efforts to understand and create states of photons that were "entangled" in polarization and spatial mode. We found that such a situation with classical beams of light gives rise to beams with a mode that we call "Poincare," because it is related to the Poincare sphere, which assigns each point on the surface of a sphere to a unique elliptic, circular or linear state of polarization. The second figure shows one of the Poincare modes that we created, which carries a distinct state of polarization in each point of the beam. The color labels the orientation of the axis of the state of polarization, and the color saturation is proportional to the intensity of light. This work is important because opens a new type of studies with optical beams of light, which can have inherent fundamental interest as well as practical applications. Our research involves only undergraduate researchers. In the span of this grant, we have had 12 undergraduates participate, of which 6 already appear as coauthors in 4 research publications. In addition, we have embarked in a project to disseminate undergraduate experiments with photons, which are uniquely suited to teach the fundamentals of quantum mechanics. Our dissemination efforts in the last two years involved offering hands-on workshops to faculty interested for implementing the experiments as advanced laboratories in their home institutions. We have also created a unique laboratory component for a course on quantum mechanics that is based on photons. We have published, in a second edition of an introductory physics textbook, two new chapters devoted to the fundamentals of photons, quantum interference and quantum entanglement.
