3D+1 Quantum Nonlocal Solitons with Gravitational Interaction


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