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

TL;DR

This paper demonstrates a physical artificial neuron using four-wave mixing in a Bose-Einstein condensate, showing its potential for neural computation and learning tasks like XOR with high accuracy.

Contribution

It introduces a novel physical implementation of a complex-valued neuron based on four-wave mixing in a BEC, with analytical solutions and learning capabilities.

Findings

Robust Josephson-like oscillations observed in the system

Closed-form solutions match numerical simulations

Neuron successfully trained on XOR problem with high precision

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.