Quantum Information in Many-Particle Systems

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My programme of research will be to explore the relationships between the fields of condensed matter physics and quantum information theory, linked through the concept of quantum correlations. The activities described in this proposal centre on understanding the properties of various correlated condensed matter systems, and how these correlations can be manipulated and consumed in order to perform useful quantum tasks. An important aspect of this theoretical programme will be to propose feasible experiments, as well as to interpret the results of on-going experimental work; in this context my research will primarily focus on ultracold atomic systems and cavity quantum electrodynamics (QED) in atomic systems. The strong interactions between photons and atoms in cavity QED affords unique opportunities to generate strongly correlated states in a highly controllable environment, and experiments have only just begun to explore this possibility. I will focus on schemes to generate (a) frustrated magnets via cavity-mediated long-range interactions, (b) topological states (such as quantum Hall insulators) by cavity-tailored band structure, and (c) strongly correlated superfluid states (such as those in high-temperature superconductors) in coupled-cavity geometries. To characterize the resulting states, I will employ sophisticated analytical approaches in addition to developing new tools based on powerful graph theory methods, and perform numerical calculations on state-of-the-art computer clusters. The particles comprising these states are usually highly entangled, potentially allowing them to be resources for the implementation of quantum algorithms. I will explore approaches to universal quantum computing with strongly correlated states, either by making sequential measurements of the particles or by allowing the system to dynamically evolve. I expect the results of this research to not only provide insights into strongly correlated states in other condensed matter systems, but also to inspire new experimental strategies for fault-tolerant quantum computation.