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Realizing the classical XY Hamiltonian in polariton simulators.

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Berloff, Natalia G 
Silva, Matteo 
Askitopoulos, Alexis 
Töpfer, Julian D 

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.

Description

Keywords

cond-mat.mes-hall, cond-mat.mes-hall, cond-mat.quant-gas, quant-ph

Journal Title

Nat Mater

Conference Name

Journal ISSN

1476-1122
1476-4660

Volume Title

16

Publisher

Springer Science and Business Media LLC

Rights

All rights reserved