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Protected Polarization Symmetry Breaking in Kerr Resonators for Random Number Generation and Photonic Ising Machines

Liam Quinn

Published Jan 1, 2024• 0 citations
OpenAlex

Abstract

This thesis experimentally and theoretically investigates the applications of spontaneous symmetry breaking in nonlinear resonators. Symmetry breaking refers to the transition of an initially symmetric system into a pair of asymmetric states. In a resonator with two equally driven polarization components, the intensities of the two fields would typically be expected to remain equal. However, this symmetry can spontaneously break as a result of small changes to the input conditions, causing one polarization component to increase in intensity while the other decreases. In practice, the selection enacted by symmetry-breaking is not entirely random, due to experimental asymmetries that bias the outcome. In this thesis we will experimentally and numerically explore a remarkable technique which can eliminate said biases through a nonlinear symmetry protection mechanism. Operation in this symmetry protected regime allows for a truly random selection of states, even in the presence of experimental imperfections. We experimentally verified the efficacy of the symmetry-protection mechanism by constructing an all-optical random number generator. Using an optical fiber resonator coherently driven with a train of pulses, we have achieved optical random bit generation at rates exceeding 3 Mbit/s without post-processing. We evaluated the randomness of the system with a variety of metrics, demonstrating the high fidelity of the random number generator. We extended this platform further to develop a novel optical Ising machine, a computational platform demonstrated to offer efficient solutions to combinatorial optimization problems which arise in a variety of contexts. Our proof-of-concept experimental results demonstrate continuous operation with up to 100 coupled spins for over an hour, enabled by the symmetry-protection protocol that ensures highly robust operation. Furthermore, the ability to measure artificial spins through optical intensity offers advantages over existing phase-based Ising implementations. We support our experimental findings with numerical simulations, which highlight the platform’s future potential for scaling to larger systems, with all-to-all coupling.

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This thesis experimentally and theoretically investigates the applications of spontaneous symmetry breaking in nonlinear resonators. Symmetry breaking refers to the transition of an initially symmetric system into a pair of asymmetric states. In a resonator with two equally driven polarization components, the intensities of the two fields would typically be expected to remain equal. However, this symmetry can spontaneously break as a result of small changes to the input conditions, causing one polarization component to increase in intensity while the other decreases. In practice, the selection enacted by symmetry-breaking is not entirely random, due to experimental asymmetries that bias the outcome. In this thesis we will experimentally and numerically explore a remarkable technique which can eliminate said biases through a nonlinear symmetry protection mechanism. Operation in this symmetry protected regime allows for a truly random selection of states, even in the presence of experimental imperfections. We experimentally verified the efficacy of the symmetry-protection mechanism by constructing an all-optical random number generator. Using an optical fiber resonator coherently driven with a train of pulses, we have achieved optical random bit generation at rates exceeding 3 Mbit/s without post-processing. We evaluated the randomness of the system with a variety of metrics, demonstrating the high fidelity of the random number generator. We extended this platform further to develop a novel optical Ising machine, a computational platform demonstrated to offer efficient solutions to combinatorial optimization problems which arise in a variety of contexts. Our proof-of-concept experimental results demonstrate continuous operation with up to 100 coupled spins for over an hour, enabled by the symmetry-protection protocol that ensures highly robust operation. Furthermore, the ability to measure artificial spins through optical intensity offers advantages over existing phase-based Ising implementations. We support our experimental findings with numerical simulations, which highlight the platform’s future potential for scaling to larger systems, with all-to-all coupling.
Time-multiplexed networks of degenerate optical parametric oscillators have demonstrated remarkable success in simulating coupled Ising spins, thus providing a promising route to solving complex combinatorial optimization problems. In these systems, referred to as coherent Ising machines, spins are encoded in the oscillator phases, and measured at the system output using phase-sensitive techniques, making intricate phase stabilization necessary. Here, we introduce an optical Ising machine based on spontaneous polarization symmetry breaking in a coherently driven fiber Kerr nonlinear resonator. In our architecture, the spins are encoded in the polarization state, allowing robust, all-intensity readout with off-the-shelf telecom components. By operating in a newly-discovered regime where nonlinearity and topology lock the system's symmetry, we eliminate drift and bias, enabling uninterrupted Ising trials at optical speeds for over an hour, without manual intervention. This all-fiber platform not only simplifies the hardware but also opens a path to more stable, high-throughput coherent optical optimization devices for applications from finance to drug design and beyond.
We demonstrate an all-optical random number generator based on spontaneous symmetry breaking in a coherently driven Kerr resonator. Random bit sequences are generated by repeatedly tuning a control parameter across a symmetry-breaking bifurcation that enacts random selection between two possible steady-states of the system. Experiments are performed in a fiber ring resonator, where the two symmetry-broken steady-states are associated with orthogonal polarization modes. Detrimental biases due to system asymmetries are suppressed by leveraging a recently discovered self-symmetrization phenomenon that ensures the symmetry-breaking dynamics act as an unbiased coin toss, with a genuinely random selection between the two available steady-states. We optically generate bits at a rate of 3 MHz without post-processing and verify their randomness using the National Institute of Standards and Technology and Dieharder statistical test suites.
Time-multiplexed networks of degenerate optical parametric oscillators have demonstrated remarkable success in simulating coupled Ising spins, thus providing a promising route to solving complex combinatorial optimization problems. In these systems $\unicode{x2014}$ referred to as coherent Ising machines $\unicode{x2014}$ the spins are encoded in the phases of the oscillators, and spin states are measured at the system output using phase-sensitive techniques. Here, we present an experimental demonstration of a conceptually new optical Ising machine based upon spontaneous polarization symmetry breaking within a coherently-driven optical fibre Kerr nonlinear resonator. In our scheme, the spin states are encoded using polarization, which allows the state of the network to be robustly read out using straightforward intensity measurements. Furthermore, by operating within a recently-discovered regime where the interplay between nonlinearity and topology fundamentally safeguards the system's symmetry, we ensure that our spins evolve without unwanted biases. This enables continuous Ising machine trials at optical data rates for up to an hour without resetting or manual adjustments. With an all-fibre implementation that relies solely on standard telecommunications components, we believe our work paves the way for substantial advances in the performance and stability of coherent optical Ising machines for applications ranging from financial modeling to drug discovery and machine learning.
We exploit polarization self-rotation in atomic rubidium vapor to observe spontaneous symmetry breaking and bistability of polarization patterns. We pump the vapor cell with horizontally polarized light while the vertical polarization, which is initially in the vacuum state, is resonated in a ring cavity. Vacuum fluctuations in this mode experience cumulative gain due to the compound action of amplification due to the self-rotation and feedback through the resonator, eventually acquiring a macroscopic magnitude akin to an optical parametric oscillator. The randomness of these fluctuations results in a bistable, random macroscopic polarization pattern at the output. We propose utilizing this mechanism to simulate Ising-like interaction between multiple spatial modes and as a basis for a fully optical coherent Ising machine.