The ability to create and manipulate strongly correlated quantum many-body states is of central importance to the study of collective phenomena in several condensed-matter systems. In the last decades, a great amount of work has been focused on ultracold atoms in optical lattices, which provide a flexible platform to simulate peculiar phases of matter both for fermionic and bosonic particles. The recent experimental demonstration of Bose-Einstein condensation (BEC) of light in dye-filled microcavities has opened the intriguing possibility to build photonic simulators of solid-state systems, with potential advantages over their atomic counterpart. A distinctive feature of photon BEC is the thermo-optical nature of the effective photon-photon interaction, which is intrinsically nonlocal and can thus induce interactions of arbitrary range. This offers the opportunity to systematically study the collective behavior of many-body systems with tunable interaction range. In this paper, we theoretically study the effect of nonlocal interactions in photon BEC. We first present numerical results of BEC in a double-well potential, and then extend our analysis to a short one-dimensional lattice with open boundaries. By resorting to a numerical procedure inspired by the Newton-Raphson method, we simulate the time-independent Gross-Pitaevskii equation and provide evidence of surface localization induced by nonlocality, where the condensate density is localized at the boundaries of the potential. Our work paves the way toward the realization of synthetic matter with photons, where the interplay between long-range interactions and low dimensionality can lead to the emergence of unexplored nontrivial collective phenomena.
From condensed matter to quantum chromodynamics, multidimensional spins are a fundamental paradigm, with a pivotal role in combinatorial optimization and machine learning. Machines formed by coupled parametric oscillators can simulate spin models, but only for Ising or low-dimensional spins. Currently, machines implementing arbitrary dimensions remain a challenge. Here, we introduce and validate a hyperspin machine to simulate multidimensional continuous spin models. We realize high-dimensional spins by pumping groups of parametric oscillators, and study NP-hard graphs of hyperspins. The hyperspin machine can interpolate between different dimensions by tuning the coupling topology, a strategy that we call “dimensional annealing”. When interpolating between the XY and the Ising model, the dimensional annealing impressively increases the success probability compared to conventional Ising simulators. Hyperspin machines are a new computational model for combinatorial optimization. They can be realized by off-the-shelf hardware for ultrafast, large-scale applications in classical and quantum computing, condensed-matter physics, and fundamental studies.
Nonlocal quantum fluids emerge as dark-matter models and tools for quantum simulations and technologies. However, strongly nonlinear regimes, like those involving multi-dimensional self-localized solitary waves (nonlocal solitons), are marginally explored for what concerns quantum features. We study the dynamics of 3D+1 solitons in the second-quantized nonlocal nonlinear Schroedinger equation. We theoretically investigate the quantum diffusion of the soliton center of mass and other parameters, varying the interaction length. 3D+1 simulations of the Ito partial differential equations arising from the positive P-representation of the density matrix validate the theoretical analysis. The numerical results unveil the onset of non-Gaussian statistics of the soliton, which may signal quantum-gravitational effects and be a resource for quantum computing. The non-Gaussianity arises from the interplay of the quantum diffusion of the soliton parameters and the stable invariant propagation. The fluctuations and the non-Gaussianity are universal effects expected for any nonlocality and dimensiona