Open RQC colloquium. Lecture 37

Abstract

Recently we proposed and experimentally realised polariton graphs as a novel platform for solving hard optimization problems that can be mapped into the XY model. Polariton condensates can be imprinted into any two-dimensional graph by spatial modulation of the pumping laser as Fig. 1 illustrates. By controlling the pumping intensity and profile, the graph geometry and the separation distance between the lattice sites one can control the couplings between the sites and realise various phase configurations that minimize the XY model. This gives rise to the use of the polariton graph as an analogue XY Hamiltonian simulator. The search for the global minimum of the XY Hamiltonian is via a bottom-up approach which has an advantage over classical or quantum annealing techniques, where the global ground state is reached through either a transition over metastable excited states or via tunnelling between the states in time that depends on the size of the system. In my talk I will discuss the range of optimization problems that can be efficiently solved by polariton graphs. In particular, I will elucidate a relationship between the energy spectrum of the XY Hamiltonian and the total number of condensed polariton particles. 

Biography

Natalia Berloff is a Professor of Applied Mathematics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK and a Professor of Skolkovo Institute of Science and Technology, Russia. She received her BS (1991)and MS (1992) degree from the Department of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, and PhD in Mathematics (1997) from the  Department of Mathematics, Florida State University, USA. In  1997  she was a recipient of  the UC Presidents Postdoctoral Fellowship and worked at Department of Mathematics, University of California, Los Angeles, USA (1997-1999), where she later became an Assistant Professor (1999-2002). Since 2002 Natalia has been a faculty member at University of Cambridge and Fellow of Jesus College. Her research interests are in quantum fluids, superfluid turbulence, coherence in nonequilibrium quantum systems: Bose Condensation of excitons and polaritons, magnons, atomic gases, superfluid helium, strong light-matter coupling in solid-state and atomic systems and driven quantum systems.

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