A Spontaneous Symmetry Breaking Machine -- A Theory for a Novel Type of Spontaneous Symmetry Breaking in a Unique Dissipative System and one Application

We focus on an interesting dissipative system found in a photonics system. In this dissipative system, we theoretically identified that robust causality is generated and as a result, it becomes possible to produce behavior that can be understood as SSB, and, we experimentally demonstrated this finding. Furthermore, we theoretically demonstrated that by combining such dissipative systems as fundamental elements and establishing a certain relationship between them through optical interference, it is possible to create a unique system that generates complex SSB as a whole. This unique SSB can be understood as having a duality with the model of the creation of many-body-like system (MBLS), and by using the correspondence between the many-body-like system and the Ising model, it holds promise as an alternative computational resource for solving combinatorial optimization problems.

💡 Research Summary

The paper introduces a novel class of spontaneous symmetry breaking (SSB) that emerges in a purely dissipative photonic platform, and demonstrates how this phenomenon can be harnessed as a computational resource for combinatorial optimization. The basic building block is the “full‑dissipative connection system” (FDCS). An optical clock pulse train (P C(t)) is fed into a 1×2 Mach‑Zehnder interferometer (MZM) that acts as a variable inflow gate. After passing through a tunable optical delay line, the i‑th pulse influences the (i + m)‑th pulse, where m is an integer defining the number of parallel FDCS channels. Under the hierarchy σ ≪ τ ≪ Δt (optical pulse width ≪ stretched electrical pulse width ≪ pulse repetition interval), the dynamics of each channel reduce to a simple iterative map:

 ϕ_{i+m} = sin²(γ·ϕ_i/2 + θ_B)  (4)

Here ϕ_i denotes the normalized transmission of the i‑th FDCS, γ is a phase‑conversion efficiency, and θ_B is a static MZM phase offset. This map is independent of space‑time coordinates, embodying a “robust causality” where the state of a previous pulse deterministically dictates the next one.

Exploring the map’s parameter space reveals two stable attractors, ϕ = 0 and ϕ ≈ 1, separated by a saddle point at ϕ = ½. When γ≈π a catastrophe creates the second attractor, as shown in the convergence diagrams (Fig. 3). To interpret this behavior, the authors introduce a pseudo‑force

 F(ϕ) = ½ sin