# Research

## Putting the "optics" into quantum optics

The study of quantum optics starts, naturally enough, with single mode fields such as are determined by a high-quality cavity. Most experiments, however, use light in propagation and so are, intrinsically, multi-mode or continuum mode. We require the ability to treat, quantum mechanically, multimode (longitudinal and transverse) fields and to incorporate real-world effects such as scattering and losses. This needs to be done, however, without introducing excessive complexity or losing physical insight. The Strathclyde Theoretical Quantum Optics group pioneered the study of quantum fields in realistic media and uses this expertise to extract the physics in experimentally relevant situations and to model them in detail.

The group has interests and expertise that cover all topics in the theoretical and computational study of quantum and nonlinear optics.

Much of classical optics is concerned, naturally enough, with imaging, that is the properties of the optical field in the plane perpendicular to the propagation axis. Quantum optics, however, has historically been more concerned with tests of quantum theory and those effects for which the quantization of the electromagnetic field is required. The two come together in the study of the quantum properties of fields comprised of multiple transverse modes. At Glasgow and Strathclyde, we have concentrated primarily on the study of transverse modes carrying orbital angular momentum, but the principles we have studied, and intend to study, can readily be extended to any sets of transverse modes.

Sets of transverse modes can be engineered to display a range of desired properties. In particular they can be squeezed and very highly entangled states of photon pairs can be prepared (we can readily entangle 50 or more pairs of transverse modes). Such quantum states form a natural and readily accessible “playground” for quantum information processing protocols. We are actively exploring their application to quantum communications (including quantum key distribution) and also to study fundamental tasks such as quantum-limited state-discrimination.

There is a natural link between these ideas and our general theme of quantum-limited metrology. In optical measurements, of course, it is the quantum nature of the electromagnetic field that sets the ultimate limits on the precision of measurements. Simple examples include the smallest displacement, rotation or tilt of an object that can be resolved for the investment of given resources (such as photon number). The design of the best possible observation requires us to consider generalised quantum measurements,that is measurements that cannot be described by the familiar von Neumann projective measurements. At Strathclyde, we have specialised in this problem since the late 1990s and have a wealth of expertise in the optimisation of measurements and also in the design of practical experimental implementations.