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

Kai Niklas Hansmann; Reinhold Walser

doi:10.1103/physreva.109.013302

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arXiv · 2309.16302

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

Kai Niklas Hansmann·Reinhold Walser

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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.

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BibTeX RIS

Kai Niklas Hansmann, Reinhold Walser. 2023-09-28. Forming complex neurons by four-wave mixing in a Bose-Einstein condensate. https://doi.org/10.1103/physreva.109.013302

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