Studies of nonlinear dynamics and quantum and classical coherence are being carried out in a variety of systems in quantum optics. These systems include lasers and nonlinear optical parametric processes such as second harmonic generation and frequency down-conversion. In nonlinear dynamics we have been studying the response of class-B lasers when either the pump or the loss of the laser is modulated. Such systems are capable of exhibiting an interesting sequence of bifurcations involving transitions between multiple steady states, oscillatory states and even chaotic states, depending on the depth and frequency of modulation and the number of modes in the laser. Current experimental efforts are focused on the Ti-sapphire laser, semiconductor lasers, and intracavity second harmonic generation. These studies of nonlinear dynamics have potential for application in laser pulse crafting. For example, carefully crafted waveforms containing time-delayed pulses of different frequencies can be generated for use in time resolved studies of atomic dynamics.

We are also investigating the coherence properties of light generated in optical parametric processes by means of photo-electric counting techniques. These experiments explore the boundary between classical and quantum worlds. Our current interest is focused on nonclassical effects such as photon anti-bunching and sub-Poissonian photon statistics in second harmonic generation and frequency downconversion. Experimental investigations of photon number oscillations in the counting distributions, nonclassical intensity correlations in the homodyne detection of light, and sub-Poissonian photon statistics are underway. The results of these experiments can only be understood quantum mechanically. We are also developing new photodetection techniques based on two-photon absorption of light. These techniques allow us to explore certain higher order photon correlations of microcavity semiconductor lasers which have not been measured with conventional techniques. A variety of experimental techniques relying on fast photon counting and correlation equipment are in use. Nonlinear crystals, carefully designed optical cavities, He:Ne, semiconductor, Ar-ion lasers, an Ar-ion pumped Ti-Sapphire laser, transient digitizers, a host of other state-of-the-art electronic instruments, and several personal computers are available for these experiments.