# Research Areas

## Quantum Photosynthesis

We have recently started a collaboration with Graham Fleming's group investigating photosynthesis from the perspective of quantum information processing. Recent experiments in the Fleming group have shown remarkably long-lived quantum coherence among excitons in the early stages of photosynthesis. This suggests that in some sense natural light harvesting may be efficient for similar reasons to the increased speed of quantum computing. In particular, we are examining entanglement, correlated noise, quantum control and quantum walk based models.

## Topological Things

One of the biggest obstacles to quantum information processing is the rapid decay of quantum coherence in most physical systems due to noise and other uncontrolled interactions with the environment. Recently, there have been proposals to circumvent this problem by using states of matter with so-called topological order. Quantum information may be encoded in a topologically ordered phase in non-local, topological degrees of freedom which are inaccessible through local interactions, and hence are practically immune to localized noise sources. Also, certain sufficiently rich topological phases (with quasiparticles that have non-Abelian statistics) support universal quantum computation. We are numerically and theoretically investigating properties of physical models which may display such topological order, and are also formulating experimentally realizable systems in which these models may be implemented physically.

## Optical Lattices

We are studying optical lattice-based implementations of quantum computing. In particular, we are interested in "addressable" optical lattices—those in which the lattice spacing is sufficiently large that individual lattice sites can be addressed with focused laser pulses.

We are also studying photonic crystals of neutral atoms in optical lattices. Optical lattice-based photonic crystals offer a number of advantages over traditional photonic crystals, including the dynamic creation and manipulation of defects. We hope to find ways of using these novel photonic band gap "materials" to store and process photon-based quantum information.

## Quantum Control

The successful construction of quantum devices, especially quantum information processing devices, hinges upon the ability to accurately control quantum systems. This control is essential for operating the devices and also for protecting them from noise and decoherence. The field of quantum control is concerned with modeling and formulating systematic tools for the precise control of quantum systems. We are interested in both the major branches of quantum control, open- loop (where the control signals are predetermined from a model of the system dynamics), and closed-loop (where the control signals are dynamically generated based on information gained from measurements on the system). Some areas we are currently investigating are: questions of optimality for open-loop control sequences in the presence of noise, optimal generation of quantum gates from physical Hamiltonians, modeling of quantum feedback for solid-state quantum devices, and extending classical feedback control theory concepts to the quantum domain.

## Quantum Nanosuperfluids and Bose-Einstein Condensates

Superfluidity and Bose-Einstein condensation are two many-body quantum phases that are not yet fully understood. We investigate the microscopic properties of these interesting phases by conducting simulations of light bosons that are confined by various trapping potentials. We employ a broad range of quantum Monte Carlo techniques to address issues of structure, excitations, spectroscopy, and dynamics, and also explore simple models where relevant.

The relative ease with which Bose condensed gases may be prepared, manipulated, and observed experimentally make these systems very attractive candidates for the detailed study of superfluidity and other coherence properties. One of the most intruiging and possibly useful experimental dials in these systems is the Feshbach resonance -- a phenomena which allows interparticle interactions to be tuned to arbitrary values. Our work focuses on the coherence properties of mesoscopic bose condensed systems in novel geometries. We are especially interested in the interplay between topological constraints imposed by an external potential, interparticle interactions (often in the strongly interacting limit) and coherence. Recent work includes a detailed analysis of the effects of strong interactions on number statistics in a double well condensate and a study of the properties of weakly linked superfluids in both simple and complex (superposition states) of flow in a ring geometry.

Our studies of helium have focused on Van der Waals clusters of these light atoms with a single impurity molecule. Van der Waals clusters are very weakly bonded aggregates of atoms and molecules, which are important in many biological and chemical systems. Helium clusters provide an extreme case of such van der Waals systems, in which quantum mechanics dominates both the structure and properties of the aggregate. The helium displays collective behavior, very weak coupling to embedded molecules, and a number of unusual quantum mechanical effects related to collective manifestations of permutation symmetry. These cluster features are related to the unique superfluid behavior of bulk helium: clusters of helium thus offer a fascinating potential for the study of intra- and inter-molecular chemical dynamics of molecules in both a superfluid and, more generally, a low temperature quantum environment.