Since the beginning of my Physics research career, I have had a variety of research interests. These include:

• working on one of the earliest theoretical proposals for experimentally realizing a quantum logic gate, involving cavity quantum-electrodynamics
• the theoretical investigation of the problems of quantum state synthesis, quantum measurement, and quantum chaotic dynamics, along with ideas for their experimental implementation in a single trapped ion configuration;
• theoretical investigation on the nonlinear and possibly chaotic dynamics of atomic Bose-Einstein condensates subjected to a chaos-inducing external potential, particularly driven Bose-Einstein condensates;
• theoretical investigation of the possibility of optical-cavity-mediated dissipative dynamics of atomic Bose-Einstein condensates;
• theoretical determination of the properties of mixtures of ultra-cold bosonic and fermionic atomic gases;
• and the theoretical interpretation of quantum chaotic dynamics observed in an atom-optical system, in particular actively collaborating with the experimental effort in Oxford led by Dr Gil Summy (now relocated to Oklahoma State University in Stillwater; the experimental effort, and my collaboration with it, continues in Oxford under the direction of Dr Michael d'Arcy) in analyzing the novel phenomenon of quantum accelerator modes.

Recently, my major research interests have been the properties and dynamics of ultracold, quantum-degenerate atomic gases, particularly atomic Bose-Einstein condensates, and quantum chaotic dynamics, as observed in atomic-optical systems. Combining this, I have also been studying the possibility of observing quantum-chaotic dynamics when a Bose-Einstein condensate is taken as the initial condition of the atomic ensemble.

I am presently particularly interested in the effect on and growth of dynamical instabilities and excitations of Bose- Einstein condensates, when initially Bose condensed systems are manipulated and strongly perturbed by applied external fields. This now has real experimental relevance, in view of such currently active experimental investigations considering, for example: the use of Feshbach resonances, controlled using magnetic fields, to tune atom-atom interactions and produce atom-molecule oscillations; the use of optical lattice potentials to observe Bloch oscillations; and the tuning of the lattice potential depth in order to observe the superfluid-Mott insulator phase transition. Each of these examples involves putting the condensate into a dynamical, non-equilibrium situation, where excitations and dynamical instabilities must be considered. In the cases of tuning to very large scattering lengths, and superfluid-Mott insulator phase transitions, a simple mean-field description is in any case manifestly inadequate. There is also the potential for the controlled manipulation of instabilities in a Bose-Einstein condensate; by feeding quasiparticle excitations one can for example think of the creation of a source of of entangled pairs of atoms of opposite momentum. I am interested in trying to develop useful methodologies to understand the issues involved in such comparatively dramatic dynamical experimental situations, and applying them to real experimental examples.