Forming complex neurons by four-wave mixing in a Bose-Einstein condensate

Abstract

A physical artificial complex-valued neuron is formed by four-wave mixing in a homogeneous three-dimensional Bose-Einstein condensate. Bragg beamsplitter pulses prepare superpositions of three plane-waves states as an input- and the fourth wave as an output signal. The nonlinear dynamics of the non-degenerate four-wave mixing process leads to Josephson-like oscillations within the closed four-dimensional subspace and defines the activation function of a neuron. Due to the high number of symmetries, closed form solutions can be found by quadrature and agree with numerical simulation. The ideal behaviour of an isolated four-wave mixing setup is compared to a situation with additional population of rogue states. We observe a robust persistence of the main oscillation. As an application for neural learning of this physical system, we train it on the XOR problem. After $100$ training epochs, the neuron responds to input data correctly at the $10^{-5}$ error level.

References in corpus (16)

• Deep Learning with Coherent Nanophotonic Circuits
• Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates
• Neuromorphic Silicon Photonic Networks
• Single-chip photonic deep neural network for instantaneous image classification
• All Optical Neural Network with Nonlinear Activation Functions
• Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate
• Generation of macroscopic pair-correlated atomic beams by four-wave mixing in Bose-Einstein condensates
• Free-space optical neural network based on thermal atomic nonlinearity
• Evolution of a spinor condensate: coherent dynamics, dephasing and revivals
• Theory of four-wave mixing of matter waves from a Bose-Einstein condensate
• Operationally meaningful representations of physical systems in neural networks
• Semifluxons in Superconductivity and Cold Atomic Gases
• Aberrations in (3+1)D Bragg diffraction using pulsed Gaussian laser beams
• Predicting the motion of a high-Q pendulum subject to seismic perturbations using machine learning
• Dressed state approach to matter wave mixing of bosons
• The emergence of atomic semifluxons in optical Josephson junctions