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Realizing the classical XY Hamiltonian in polariton simulators

Berloff, Natalia G., Silva, Matteo, Kalinin, Kirill, Askitopoulos, Alexis, Töpfer, Julian D., Cilibrizzi, Pasquale, Langbein, Wolfgang and Lagoudakis, Pavlos G. 2017. Realizing the classical XY Hamiltonian in polariton simulators. Nature Materials 16 , pp. 1120-1126. 10.1038/nmat4971

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Abstract

The vast majority of real-life optimization problems with a large number of degrees of freedom are intractable by classical computers, since their complexity grows exponentially fast with the number of variables. Many of these problems can be mapped into classical spin models, such as the Ising, the XY or the Heisenberg models, so that optimization problems are reduced to finding the global minimum of spin models. Here, we propose and investigate the potential of polariton graphs as an efficient analogue simulator for finding the global minimum of the XY model. By imprinting polariton condensate lattices of bespoke geometries we show that we can engineer various coupling strengths between the lattice sites and read out the result of the global minimization through the relative phases. Besides solving optimization problems, polariton graphs can simulate a large variety of systems undergoing the U(1) symmetry-breaking transition. We realize various magnetic phases, such as ferromagnetic, anti-ferromagnetic, and frustrated spin configurations on a linear chain, the unit cells of square and triangular lattices, a disordered graph, and demonstrate the potential for size scalability on an extended square lattice of 45 coherently coupled polariton condensates. Our results provide a route to study unconventional superfluids, spin liquids, Berezinskii–Kosterlitz–Thouless phase transition, and classical magnetism, among the many systems that are described by the XY Hamiltonian.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Physics and Astronomy
Subjects: Q Science > QC Physics
Publisher: Nature
ISSN: 14761122
Date of First Compliant Deposit: 13 October 2017
Date of Acceptance: 19 July 2017
Last Modified: 30 Apr 2018 00:27
URI: http://orca.cf.ac.uk/id/eprint/105520

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