Realizing the classical XY Hamiltonian in polariton simulators
| Autor: | Wolfgang Werner Langbein, Natalia G. Berloff, Pasquale Cilibrizzi, Kirill P. Kalinin, Julian D. Töpfer, Matteo Silva, Alexis Askitopoulos, Pavlos G. Lagoudakis |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Phase transition
Optimization problem 02 engineering and technology 01 natural sciences symbols.namesake quant-ph Lattice (order) 0103 physical sciences cond-mat.mes-hall Polariton General Materials Science Statistical physics 010306 general physics QC Physics Condensed Matter::Quantum Gases Mechanical Engineering General Chemistry 021001 nanoscience & nanotechnology Condensed Matter Physics Classical XY model Square lattice Mechanics of Materials symbols Ising model 0210 nano-technology Hamiltonian (quantum mechanics) cond-mat.quant-gas |
| ISSN: | 1476-1122 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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