Realizing spin-Hamiltonians in nanoscale active photonic lattices

Abstract

Spin models arise in the microscopic description of magnetic materials, where the macroscopic characteristics are governed by exchange interactions among the constituent magnetic moments. Recently, there has been a growing interest in complex systems with spin Hamiltonians, largely due to the rich behaviors exhibited by such interactions at the macroscale. Along these lines, it has been shown that certain classes of optimization problems involving large degrees of freedom can be effectively mapped into classical spin models. In this vein, the respective extremum can be found by identifying the ground state of the associated spin Hamiltonian. Here, we show both theoretically and experimentally, that the cooperative interplay among vectorial electromagnetic modes in coupled metallic nanolasers can be utilized as a means to emulate certain types of spin-like systems. The ensuing spin exchange interactions are in general anisotropic, in a way similar to that encountered in magnetic materials involving spin-orbit coupling. For some topologies, we find that these active nanophotonic structures are governed by a classical XY Hamiltonian that exhibits two phases akin to those associated with ferromagnetic (FM) and antiferromagnetic (AF) materials. In addition, we show that in certain configurations, the electromagnetic field distribution can undergo geometrical frustration, depending on the lattice shape and the transverse resonant modes supported by the individual cavity elements. Our results could pave the way towards a new scalable nanophotonic platform to study spin exchange interactions, that can in turn be potentially exploited to investigate more large-scale networks, emulate some magnetic materials, or to address a variety of optimization problems.

arXiv comment30 pages

References in corpus (16)

• Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
• Quantum simulation of frustrated magnetism in triangular optical lattices
• Thresholdless Nanoscale Coaxial Lasers
• Network of Time-Multiplexed Optical Parametric Oscillators as a Coherent Ising Machine
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Engineering Ising-XY spin models in a triangular lattice via tunable artificial gauge fields
• Realizing the $XY$ Hamiltonian in polariton simulators
• Large-scale Ising spin network based on degenerate optical parametric oscillators
• Phase Diagram for the Winfree Model of Coupled Nonlinear Oscillators
• Orbital ordering and frustration of $p$-band Mott-insulators
• Octupolar ordering of classical kagome antiferromagnets in two and three dimensions
• Simple universal models capture all classical spin physics
• Dissipative Topological Defects in Coupled Laser Networks
• A Polariton Graph Simulator
• Optical Phase Transitions in Photonic Networks: A Spin System Formulation
• Boltzmann sampling for an XY model using a non-degenerate optical parametric oscillator network

Cited by in corpus (14)

• Non-reciprocal phase transitions
• Scalable spin-glass optical simulator
• Experimental Observation of Phase Transitions in Spatial Photonic Ising Machine
• Biasing the quantum vacuum to control macroscopic probability distributions
• Wavelength-division multiplexing optical Ising simulator enabling fully programmable spin couplings and external magnetic fields
• Mapping the XY Hamiltonian onto a Network of Coupled Lasers
• Ising Hamiltonian Minimization: Gain-Based Computing with Manifold Reduction of Soft-Spins vs Quantum Annealing
• Self-organized vortex and antivortex patterns in laser arrays
• Artificial polariton molecules
• Adiabatic evolution on a spatial-photonic Ising machine
• Spin Hamiltonians in the Modulated Momenta of Light
• Large-scale Sustainable Search on Unconventional Computing Hardware
• Adiabaticity enhancement in the classical transverse field Ising chain, and its effective non-Hermitian description
• Polaritonic XY-Ising Machine