Realizing the $XY$ Hamiltonian in polariton simulators (1607.06065v1)

Abstract: Several platforms are currently being explored for simulating physical systems whose complexity increases faster than polynomially with the number of particles or degrees of freedom in the system. Defects and vacancies in semiconductors or dielectric materials, magnetic impurities embedded in solid helium \cite{lemeshko13}, atoms in optical lattices, photons, trapped ions and superconducting q-bits are among the candidates for predicting the behaviour of spin glasses, spin-liquids, and classical magnetism among other phenomena with practical technological applications. Here we investigate the potential of polariton graphs as an efficient simulator for finding the global minimum of the $XY$ Hamiltonian. By imprinting polariton condensate lattices of bespoke geometries we show that we can simulate a large variety of systems undergoing the U(1) symmetry breaking transitions. We realise various magnetic phases, such as ferromagnetic, anti-ferromagnetic, and frustrated spin configurations on unit cells of various lattices: square, triangular, linear and a disordered graph. Our results provide a route to study unconventional superfluids, spin-liquids, Berezinskii-Kosterlitz-Thouless phase transition, classical magnetism among the many systems that are described by the $XY$ Hamiltonian.

• The paper shows that polariton condensate lattices can simulate the XY Hamiltonian, enabling controlled studies of magnetic phases and symmetry-breaking transitions.
• Experimental results reveal that coupling strength oscillates with the product k₍c₎d, effectively toggling between ferromagnetic and anti-ferromagnetic interactions.
• The research establishes a scalable platform for probing topological order and quantum phase transitions, paving the way for polariton-based quantum simulation devices.

Realizing the $XY$ Hamiltonian in Polariton Simulators: A New Approach to Quantum Simulation

The paper examines the feasibility of leveraging polariton graphs as simulators for finding the global minimum of the $XY$ Hamiltonian. By utilizing imprinted polariton condensate lattices of specific geometries, the authors have successfully simulated a broad spectrum of systems that undergo U(1) symmetry breaking transitions. The results indicate potential pathways for investigating phenomena such as unconventional superfluids, spin-liquids, the Berezinskii-Kosterlitz-Thouless (BKT) phase transition, and classical magnetism among others described by the $XY$ Hamiltonian.

Key Findings and Numerical Results

A major contribution of this paper is the realization of various magnetic phases—including ferromagnetic, anti-ferromagnetic, and frustrated spin configurations—on unit cells of square, triangular, and disordered lattices. Particularly, the coupling strength between polariton nodes was found to be dictated by parameters such as lattice geometry and the outflow wavevector, making it possible to toggle between ferromagnetic and anti-ferromagnetic interactions.

In experiments, different configurations such as an Ising chain, a square lattice, and a triangular lattice were realized and studied. The coupling strength in these lattices exhibited periodic oscillations depending on the product $k_c d$, where $k_c$ is the outflow wavevector and $d$ is the distance between nodes. For instance, $\cos(k_c d + \phi)$ governed the switching mechanism between coupling phases, with $\phi$ contextualized by system parameters.

Implications and Future Development

The polariton-based approximation to the $XY$ Hamiltonian opens avenues for investigation in various condensed matter physics domains and beyond. One practical implication of this research is the potential to develop polariton condensate-based devices for topological quantum computation. The experiments indicate that polariton graphs can be used to simulate and explore various XY Hamiltonian-related phenomena such as topological order and phase transitions beyond the Berezinskii-Kosterlitz-Thouless transition. Furthermore, the ability to induce precise coupling interactions offers a scalable and flexible platform for exploring complex disordered systems.

Potential advancements in this domain could focus on enhancing both the spatial and dynamic control of the polariton condensates, which could improve our understanding and predictive capabilities regarding quantum phase transitions and complex exciton condensate dynamics. Room temperature operations and electrical pump-mediated exciton condensation are foreseeable future steps that would enhance the practical feasibility of polariton graph-based simulations.

The research lays a promising groundwork for future explorations in quantum simulations using polariton lattices. The rigor in parametrically controlling the lattice dimensions, separation, and wavevector suggests a novel route for resolving complex computational challenges with potentially significant ramifications across both theoretical research and technological innovation.