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Realizing the classical XY Hamiltonian in polariton simulators

Realizing the classical XY Hamiltonian in polariton simulators
Realizing the classical XY Hamiltonian in polariton simulators
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.
1476-1122
1120-1126
Berloff, N.G.
fefc15e9-ddda-4726-ac1a-3fb18db995d3
Silva, Matteo
a200bb38-2c5f-4c66-9b75-e79bf2685dd7
Kalinin, Kirill
6e4d1521-96b9-4b3d-a9f1-b7be13481456
Askitopoulos, Alexis
2365a936-bc12-47bc-94aa-e186b2bc0390
Topfer, Julian D
dafe018b-4c32-4d82-af51-e2f86ba5db32
CILIBRIZZI, PASQUALE
9734aced-5f2d-42a5-91fa-6f5be3bd2429
Langbein, Wolfgang
6ee2fdee-4357-44ba-a063-d2822d9018cc
Lagoudakis, Pavlos
ea50c228-f006-4edf-8459-60015d961bbf
Berloff, N.G.
fefc15e9-ddda-4726-ac1a-3fb18db995d3
Silva, Matteo
a200bb38-2c5f-4c66-9b75-e79bf2685dd7
Kalinin, Kirill
6e4d1521-96b9-4b3d-a9f1-b7be13481456
Askitopoulos, Alexis
2365a936-bc12-47bc-94aa-e186b2bc0390
Topfer, Julian D
dafe018b-4c32-4d82-af51-e2f86ba5db32
CILIBRIZZI, PASQUALE
9734aced-5f2d-42a5-91fa-6f5be3bd2429
Langbein, Wolfgang
6ee2fdee-4357-44ba-a063-d2822d9018cc
Lagoudakis, Pavlos
ea50c228-f006-4edf-8459-60015d961bbf

Berloff, N.G., Silva, Matteo, Kalinin, Kirill, Askitopoulos, Alexis, Topfer, Julian D, CILIBRIZZI, PASQUALE, Langbein, Wolfgang and Lagoudakis, Pavlos (2017) Realizing the classical XY Hamiltonian in polariton simulators. Nature Materials, 16 (11), 1120-1126. (doi:10.1038/NMAT4971).

Record type: Article

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.

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Realizing the classical XY Hamiltonian in polariton simulators - Accepted Manuscript
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Accepted/In Press date: 19 July 2017
e-pub ahead of print date: 25 September 2017
Published date: 1 November 2017

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Local EPrints ID: 415651
URI: http://eprints.soton.ac.uk/id/eprint/415651
ISSN: 1476-1122
PURE UUID: 6fd0f01a-8339-4e2a-a682-f0b5c826d395

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Date deposited: 17 Nov 2017 17:30
Last modified: 10 Oct 2020 04:02

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Contributors

Author: N.G. Berloff
Author: Matteo Silva
Author: Kirill Kalinin
Author: Alexis Askitopoulos
Author: Julian D Topfer
Author: PASQUALE CILIBRIZZI
Author: Wolfgang Langbein

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