Realizing the classical XY Hamiltonian in polariton simulators

Area of Science:

• Quantum simulation
• Condensed matter physics
• Computational optimization

Background:

• Classical computers struggle with complex optimization problems due to exponential scaling.
• Many optimization problems map to finding the ground state of spin models like the XY model.
• Analogue simulators offer a potential solution for intractable computational problems.

Purpose of the Study:

• Investigate polariton graphs as an efficient analogue simulator for the XY model.
• Demonstrate the use of polariton graphs for solving optimization problems.
• Explore the simulation of various physical systems described by the XY Hamiltonian.

Main Methods:

• Fabrication of polariton condensate lattices with engineered geometries.
• Control of coupling strengths between lattice sites.
• Readout of global minimization results via relative phases of polaritons.
• Realization of different magnetic phases and lattice structures.

Main Results:

• Successfully used polariton graphs to find the global minimum of the XY model.
• Engineered bespoke lattice geometries to control coupling strengths.
• Demonstrated the simulation of ferromagnetic, anti-ferromagnetic, and frustrated spin configurations.
• Showcased scalability on a 45-site extended square lattice.

Conclusions:

• Polariton graphs are a promising analogue simulator for the XY model and optimization problems.
• This approach enables the study of diverse physical phenomena, including unconventional superfluids and classical magnetism.
• The method offers a scalable route for simulating complex quantum and classical systems.