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

TL;DR

This work investigates a photonic dissipative system where robust dissipative causality enables a novel spontaneous symmetry breaking (SSB) mechanism, both theoretically and experimentally. It introduces the full-dissipative connection system (FDCS) and shows how interconnecting multiple FDCS units via optical interference can produce complex, multi-element SSB that maps onto pseudo-spins and an Ising-like energy landscape. The authors propose the SSB machine (SSBM), a solver for combinatorial optimization problems, by encoding pseudo-spin interactions through optical interference and demonstrating, via numerical simulations on a MaxCut3 benchmark, that the system can reach stable Ising-like states with high reliability at low noise. This work highlights a duality-based perspective to tackle hard optimization problems and points toward scalable, causality-driven photonic platforms as alternative computational resources, with experimental demonstration of the SSBM as a future direction.

Abstract

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.

Figures (8)

• Figure 1: Schematic of a dissipative system we focused on. (a) This system maintains a state composed of any one of inflow pulses derived from clock pulses. (b) Clock pulses form $m$ of independent dissipative systems (corresponding to each of connection lines).
• Figure 2: Schematic of a circuit realizing a full-dissipative connection systems (FDCSs). Polarized optical coherent clock pulses (OCPs) $P_{C}(t)$ are supplied from an external input port $\bf{C_{\rm in}}$ to generate the FDCSs and 1$\times$2 MZM is used as a partial inflow gate. Number of the FDCSs and timing of electrical driving pulses to the MZM are tuned by both repetition interval of the OCPs $\Delta t$ and delay time by an optical tunable delay line (OTDL). Furthermore, width of the electrical driving pulses to the MZM are stretched sufficiently wider than the OCP width.
• Figure 3: Convergence characteristics (number of steps needed to reach a threshold) of $\phi_{i}$ with respect to initial values $\phi_{\rm init.}$ and $\gamma$ under a condition of $\theta_{B} = 0$. Color gages for convergence to two attractors :(a) $\phi_{\rm conv.}=0$ and (b) $\phi_{\rm conv.}\ne 0\, (\sim 1)$.
• Figure 4: Pseudo-force ${\mathfrak F}(\phi)$ and pseudo-potential ${\mathfrak V}(\phi)$ defined by Eqs. (5) and (6), respectively ($\phi \in [0, 1]$). Undefined outer region is also drawn mechanically to assist in understanding dissipative causality's behavior under conditions of $\theta_{B} = 0$ and $\gamma = \pi$.
• Figure 5: Experimental system for verifying SSB operation in FDCSs. Number of the generated FDCSs $m = 16$. $P_{C}(t)$:whole width of optical pulse train (OPT) 46.08$\mu s$, the OPT cycle 20kHz, repetition frequency of the optical pulses 39.0625MHz, width of the optical pulse 10$ps$. $P_{I}(t)$:whole width of OPT 409.6$ns$, the OPT cycle 20kHz, repetition frequency of the optical pulses 39.0625MHz, width of the optical pulse 10$ps$. Timing when a peak position of an electrical pulse generated from first optical pulse of the $P_{I}(t)$ reaches a MZM was adjusted so that it coincides with timing when the peak position of the 10th optical pulse from the leading edge of $P_{C}(t)$ reaches the MZM.