Theoretical Methods in Quantum Optics
The origin of "modern" Quantum Optics can be associated with the development of the laser in the 1950's and the subsequent need for a careful exposition of the statistical properties of laser light and, in particular, a quantum theory of optical coherence. It is for the development of such a theory in the early 1960's that Roy Glauber was awarded the Nobel Prize in Physics in 2005. With this theoretical foundation laid, it also became possible to define a clear boundary between light fields that could, or could not, be described in classical terms. Subsequently, tremendous interest grew in uniquely quantum mechanical states of light fields, such as "squeezed" states and "antibunched" states, and practical means of producing these states. Through interactions of laser fields with atoms and nonlinear optical materials, experiments in the 1970's and 1980's were eventually successful in generating and observing these manifestly non-classical states. However, these seminal results in the laboratory demanded further theoretical developments in order to accurately model the open, dissipative quantum systems that experimenters actually deal with in practice. In addition, remarkable recent experiments are able to isolate individual quantum systems, such as single atoms, and implement strong interactions with single photons, thereby realising systems where quantum fluctuations are dominant, and perturbative theoretical models are inadequate. Significantly, this experimental progress has also enabled a wide range of advances in the coherent quantum control of the states of both light and matter.
All of these developments have contributed to establishing Quantum Optics as an exciting and fruitful testbed for fundamental issues in quantum mechanics, such as decoherence, measurement and entanglement, as well as a leading field of research into quantum information science. In these lectures I discuss some of the key theoretical methods that have been developed in connection with the description of fundamental systems in Quantum Optics. These include phase-space representations, quantum mechanical master equations, stochastic differential equations, and quantum trajectories. The methods are illustrated with both classic and currently-topical examples, such as the interaction of simple atomic systems with laser fields and, in the context of so-called "cavity QED", with single-photon light fields, where a full quantum mechanical treatment of both light fields and atoms is necessary. I will also describe some potential applications of such systems in quantum information processing, including recent results for cavity QED with lithographically-fabricated toroidal microresonators.
Lecture Notes from Scott Parkin´s lectures can be found here:
Lecture Notes:
Download