arXiv subjects

Edwin Ng

Publications and source records attributed to Edwin Ng.

At least 19 recordsLinked to original sources

arXiv2026

Photonic Ising machines toward and beyond a million spins

Combinatorial optimization problems are central to many challenges in logistics, finance, engineering, and the life sciences, yet they remain among the most computationally demanding. Many of these problems can be mapped onto the Ising model, in which binary spins interact through a network of couplings, and solutions correspond to low-energy, ideally ground-state, spin configurations. Photonic Ising machines have the potential to be fast and energy-efficient heuristic solvers of optimization problems by leveraging the low latency, high bandwidth, and inherent parallelism of optics. However, current photonic implementations remain limited in scalability, connectivity, reconfigurability, and time-to-solution, preventing their use in many practical applications. In this perspective, we examine the current landscape of photonic Ising machines, discuss the challenges and limitations of existing platforms, and identify the scientific and technological advances needed to realize large-scale systems. These developments could establish photonic Ising machines as useful hardware platforms for practical optimization.

physics.optics↗

arXiv2026

Quantum Optical Soliton Dynamics Beyond Linearization: An Open-System Approach

We introduce two approaches to modeling the quantum dynamics of optical $\chi^{(3)}$ solitons. Taking an open-system viewpoint, we project the underlying quantum field into system (soliton) and residual reservoir components. The reservoir is treated as either (i) a discrete ``Lanczos supermode'' (LSM) expansion which localizes dynamics to a few-supermode basis, or (ii) a non-local environment which can be traced out by deriving a Markovian master equation (ME). Using these methods, we analyze and identify the quantum structure of both the soliton's stability and its hierarchy of perturbations. Through numerical simulations, we confirm both methods effectively capture quantum-induced soliton phase shifts in a concise few-mode (single-mode for ME) basis, and the LSM approach also captures photon loss which arises from non-Markovian dispersive couplings. As neither method is limited to the linearized regime, our approaches provide powerful computational tools to analyze complex non-Gaussian quantum dynamics of solitons where other commonly-used methods fail, providing insight into such non-perturbative regimes. We also investigate radiation that occurs in the presence of higher-order dispersion with ultrashort pulses, deriving a ME that predicts photon loss consistent with classical theory, but find that both classical and ME theory dramatically underestimate the actual amount of dissipation, which we explain in terms of dispersive coupling-induced soliton broadening.

quant-ph↗

arXiv2026

Continuum-field quantum optics of frequency comb metrology

Frequency combs enable precision measurements across timekeeping, spectroscopy, ranging and astronomy, and are now extending to integrated and field-deployable platforms. Realizing their full performance demands a comprehensive account of the quantum noise that arises when broadband optical fields are converted into finite-bandwidth electrical signals. Here we present a rigorous first-principles quantum-mechanical framework for optical frequency-comb metrology based on continuous-mode field quantization and a comb-line-resolved description of quantum fluctuations. The theory describes how quantum fluctuations of the comb field are transduced into electrical measurement noise. Formulated at the level of the comb field, the framework unifies the standard quantum limits of optical frequency division (OFD) and dual-comb spectroscopy (DCS) within a single treatment, and provides a general recipe for other comb-based measurements. On this footing, we identify practical, resource-efficient routes to quantum enhancement through engineered comb states, laying a foundation for the design of next-generation frequency combs operating at and beyond standard quantum limits.

quant-ph↗

arXiv2026

Simulation of Hopfield-like Hamiltonians using time-multiplexed photonic networks

We propose a time-multiplexed photonic network architecture based on coupled ring resonators, capable of accurately emulating specific Hamiltonian dynamics. We show that, in the Suzuki-Trotter limit, the resulting stroboscopic evolution reproduces the characteristic dynamics of the bosonized Hopfield model. Furthermore, by incorporating a nonlinear element within the main resonator loop, we outline a scalable route toward optical simulation of both mean-field and quantum nonlinear dynamics associated with the Tavis-Cummings model. Our results establish time-multiplexed resonator networks as a versatile photonic framework for simulating interacting light-matter Hamiltonians and collective many-body phenomena.

physics.optics↗

arXiv2024

Predicting Customer Lifetime Value Using Recurrent Neural Net

This paper introduces a recurrent neural network approach for predicting user lifetime value in Software as a Service (SaaS) applications. The approach accounts for three connected time dimensions. These dimensions are the user cohort (the date the user joined), user age-in-system (the time since the user joined the service) and the calendar date the user is an age-in-system (i.e., contemporaneous information).The recurrent neural networks use a multi-cell architecture, where each cell resembles a long short-term memory neural network. The approach is applied to predicting both acquisition (new users) and rolling (existing user) lifetime values for a variety of time horizons. It is found to significantly improve median absolute percent error versus light gradient boost models and Buy Until You Die models.

stat.AP↗

arXiv2024

Hybrid AM/FM Mode-Locking of Singly-Resonant OPOs

We investigate a new mode-locking regime in the singly-resonant OPO employing simultaneous amplitude- and frequency-modulation of the intracavity field. This OPO exhibits deterministic, "turn-key" formation of a stable, broadband, chirped frequency comb with high conversion efficiency. Comb-forming dynamics follow a simple phase-space dynamical model, governed by cavity dispersion and modulator chirp, which agrees closely with full numerical simulations. The comb exhibits fast, mode-hop-free tuning over the full gain window of the OPA crystal, controlled by the modulator frequency. Conditions for comb stability, and techniques to enhance comb bandwidth through intentional phase-mismatch and chirping, are investigated.

physics.optics↗

arXiv2024

Skew-Gaussian model of small-photon-number coherent Ising machines

A Gaussian quantum theory of bosonic modes has been widely used to describe quantum optical systems, including coherent Ising machines (CIMs) that consist of $\chi^{(2)}$ degenerate optical parametric oscillators (DOPOs) as nonlinear elements. However, Gaussian models have been thought to be invalid in the extremely strong-gain-saturation limit. Here, we develop an extended Gaussian model including two third-order fluctuation products, $\langle \delta \hat{X}^3\rangle$ and $\langle \delta \hat{X}\delta \hat{P}^2\rangle$, which we call self-skewness and cross-skewness, respectively. This new model which we call skew-Gaussian model more precisely replicates the success probability predicted by the quantum master equation (QME), relative to Gaussian models. We also discuss the impact of skew variables on the performance of CIMs.

quant-ph↗

arXiv2024

Ultrafast second-order nonlinear photonics -- from classical physics to non-Gaussian quantum dynamics

Photonic integrated circuits with second-order ($\chi^{(2)}$) nonlinearities are rapidly scaling to remarkably low powers. At this time, state-of-the-art devices achieve saturated nonlinear interactions with thousands of photons when driven by continuous-wave lasers, and further reductions in these energy requirements enabled by the use of ultrafast pulses may soon push nonlinear optics into the realm of single-photon nonlinearities. This tutorial reviews these recent developments in ultrafast nonlinear photonics, discusses design strategies for realizing few-photon nonlinear interactions, and presents a unified treatment of ultrafast quantum nonlinear optics using a framework that smoothly interpolates from classical behaviors to the few-photon scale. These emerging platforms for quantum optics fundamentally differ from typical realizations in cavity quantum electrodynamics due to the large number of coupled optical modes. Classically, multimode behaviors have been well studied in nonlinear optics, with famous examples including soliton formation and supercontinuum generation. In contrast, multimode quantum systems exhibit a far greater variety of behaviors, and yet closed-form solutions are even sparser than their classical counterparts. In developing a framework for ultrafast quantum optics, we will identify what behaviors carry over from classical to quantum devices, what intuition must be abandoned, and what new opportunities exist at the intersection of ultrafast and quantum nonlinear optics. While this article focuses on establishing connections between the classical and quantum behaviors of devices with $\chi^{(2)}$ nonlinearities, the frameworks developed here are general and are readily extended to the description of dynamical processes based on third-order ($\chi^{(3)}$) nonlinearities.

physics.optics↗

arXiv2023

Mesoscopic ultrafast nonlinear optics -- The emergence of multimode quantum non-Gaussian physics

Over the last few decades, nonlinear optics has become significantly more nonlinear, traversing nearly a billionfold improvement in energy efficiency, with ultrafast nonlinear nanophotonics in particular emerging as a frontier for combining both spatial and temporal engineering. At present, cutting-edge experiments in nonlinear nanophotonics place us just above the mesoscopic regime, where a few hundred photons suffice to trigger nonlinear saturation. In contrast to classical or deep-quantum optics, the mesoscale is characterized by dynamical interactions between mean-field, Gaussian, and non-Gaussian quantum features, all within a close hierarchy of scales. When combined with the inherent multimode complexity of optical fields, such hybrid quantum-classical dynamics present theoretical, experimental, and engineering challenges to the contemporary framework of quantum optics. In this review, we highlight the unique physics that emerges in multimode nonlinear optics at the mesoscale and outline key principles for exploiting both classical and quantum features to engineer novel functionalities. We briefly survey the experimental landscape and draw attention to outstanding technical challenges in materials, dispersion engineering, and device design for accessing mesoscopic operation. Finally, we speculate on how these capabilities might usher in some new paradigms in quantum photonics, from quantum-augmented information processing to nonclassical-light-driven dynamics and phenomena to all-optical non-Gaussian measurement and sensing. The physics unlocked at the mesoscale present significant challenges and opportunities in theory and experiment alike, and this review is intended to serve as a guidepost as we begin to navigate this new frontier in ultrafast quantum nonlinear optics.

quant-ph↗

arXiv2023

Using system-reservoir methods to derive effective field theories for broadband nonlinear quantum optics: a case study on cascaded quadratic nonlinearities

In broadband quantum optical systems, nonlinear interactions among a large number of frequency components induce complex dynamics that may defy heuristic analysis. In this work we introduce a perturbative framework for factoring out reservoir degrees of freedom and establishing a concise effective model (effective field theory) for the remaining system. Our approach combines approximate diagonalization of judiciously partitioned subsystems with master equation techniques. We consider cascaded optical $\chi^{(2)}$ (quadratic) nonlinearities as an example and show that the dynamics can be construed (to leading order) as self-phase modulations of dressed fundamental modes plus cross-phase modulations of dressed fundamental and second-harmonic modes. We then formally eliminate the second-harmonic degrees of freedom and identify emergent features of the fundamental wave dynamics, such as two-photon loss channels, and examine conditions for accuracy of the reduced model in dispersive and dissipative parameter regimes. Our results highlight the utility of system-reservoir methods for deriving accurate, intuitive reduced models for complex dynamics in broadband nonlinear quantum photonics.

quant-ph↗

arXiv2023

Quantum noise dynamics in nonlinear pulse propagation

The propagation of ultrafast pulses in dispersion-engineered waveguides, exhibiting strong field confinement in both space and time, is a promising avenue towards single-photon nonlinearities in an all-optical platform. However, quantum engineering in such systems requires new numerical tools and physical insights to harness their complicated multimode and nonlinear quantum dynamics. In this work, we use a self-consistent, multimode Gaussian-state model to capture the nonlinear dynamics of broadband quantum fluctuations and correlations, including entanglement. Notably, despite its parametrization by Gaussian states, our model exhibits nonlinear dynamics in both the mean field and the quantum correlations, giving it a marked advantage over conventional linearized treatments of quantum noise, especially for systems exhibiting gain saturation and strong nonlinearities. Numerically, our approach takes the form of a Gaussian split-step Fourier (GSSF) method, naturally generalizing highly efficient SSF methods used in classical ultrafast nonlinear optics; the equations for GSSF evaluate in $O(M^2\log M)$ time for an $M$-mode system with $O(M^2)$ quantum correlations. To demonstrate the broad applicability of GSSF, we numerically study quantum noise dynamics and multimode entanglement in several ultrafast systems, from canonical soliton propagation in third-order ($\chi^{(3)}$) waveguides to saturated $\chi^{(2)}$ broadband parametric generation and supercontinuum generation, e.g., as recently demonstrated in thin-film lithium niobate nanophotonics.

quant-ph↗

arXiv2023

Engineering cubic quantum nondemolition Hamiltonian with mesoscopic optical parametric interactions

We propose a scheme to realize cubic quantum nondemolition (QND) Hamiltonian with optical parametric interactions. We show that strongly squeezed fundamental and second harmonic fields propagating in a $\chi^{(2)}$ nonlinear medium effectively evolve under a cubic QND Hamiltonian. We highlight the versatility offered by such Hamiltonian for engineering non-Gaussian quantum states, such as Schr\"odinger cat states and cubic phase states. We show that our scheme can be highly tolerant against overall detection inefficiency with an auxiliary high-gain phase-sensitive optical amplifier. Our proposal involves parametric interactions in a mesoscopic photon-number regime, significantly enhancing the effective nonlinear coupling from the nat\"ive single-photon coupling rate while providing powerful means to fight photon propagation loss. Experimental numbers suggest that our scheme might be feasible in the near future, particularly with pulsed nonlinear nanophotonics.

quant-ph↗

arXiv2022

Quantum nondemolition measurements with optical parametric amplifiers for ultrafast universal quantum information processing

Realization of a room-temperature ultra-fast photon-number-resolving (PNR) quantum nondemolition (QND) measurement would have significant implications for photonic quantum information processing (QIP), enabling, e.g., deterministic quantum computation in discrete-variable architectures, but the requirement for strong coupling has hampered the development of scalable implementations. In this work, we propose and analyze a nonlinear-optical route to PNR QND using quadratic (i.e., $\chi^{(2)}$) nonlinear interactions. We show that the coherent pump field driving a phase-mismatched optical parametric amplifier (OPA) experiences displacements conditioned on the number of signal Bogoliubov excitations. A measurement of the pump displacement thus provides a QND measurement of the signal Bogoliubov excitations, projecting the signal mode to a squeezed photon-number state. We then show how our nonlinear OPA dynamics can be utilized for deterministically generating Gottesman-Kitaev-Preskill states only with additional Gaussian resources, offering an all-optical route for fault-tolerant QIP in continuous-variable systems. Finally, we place these QND schemes into a more traditional context by highlighting analogies between the phase-mismatched optical parametric oscillator and multilevel atom-cavity QED systems, by showing how continuous monitoring of the outcoupled pump quadrature induces conditional localization of the intracavity signal mode onto squeezed photon-number states. Our analysis suggests that our proposal may be viable in near-term $\chi^{(2)}$ nonlinear nanophotonics, highlighting the rich potential of OPA as a universal tool for ultrafast non-Gaussian quantum state engineering and quantum computation.

quant-ph↗

arXiv2022

Degenerate optical parametric amplification in CMOS silicon

Silicon is a common material for photonics due to its favorable optical properties in the telecom and mid-wave IR bands, as well as compatibility with a wide range of complementary metal-oxide semiconductor (CMOS) foundry processes. Crystalline inversion symmetry precludes silicon from natively exhibiting second-order nonlinear optical processes. In this work, we build on recent work in silicon photonics that break this material symmetry using large bias fields, thereby enabling $\chi^{(2)}$ interactions. Using this approach, we demonstrate both second-harmonic generation (with a normalized efficiency of $0.2\,\%\,\mathrm{W^{-1} cm^{-2}}$) and, to our knowledge, the first degenerate $\chi^{(2)}$ optical parametric amplifier (with relative gain of $0.02\,\mathrm{dB}$ using $3\,\mathrm{mW}$ of pump power on-chip at a pump wavelength of $1196\,\mathrm{nm}$) using silicon-on-insulator waveguides fabricated in a CMOS-compatible commercial foundry. We expect this technology to enable the integration of novel nonlinear optical devices such as optical parametric amplifiers, oscillators, and frequency converters into large-scale, hybrid photonic-electronic systems by leveraging the extensive ecosystem of CMOS fabrication.

physics.optics↗

arXiv2022

Ultra-broadband mid-infrared generation in dispersion-engineered thin-film lithium niobate

Thin-film lithium niobate (TFLN) is an emerging platform for compact, low-power nonlinear-optical devices, and has been used extensively for near-infrared frequency conversion. Recent work has extended these devices to mid-infrared wavelengths, where broadly tunable sources may be used for chemical sensing. To this end, we demonstrate efficient and broadband difference frequency generation between a fixed 1-micron pump and a tunable telecom source in uniformly-poled TFLN-on-sapphire by harnessing the dispersion-engineering available in tightly-confining waveguides. We show a simultaneous 1-2 order-of-magnitude improvement in conversion efficiency and ~5-fold enhancement of operating bandwidth for mid-infrared generation when compared to conventional lithium niobate waveguides. We also examine the effects of mid-infrared loss from surface-adsorbed water on the performance of these devices.

physics.optics↗

arXiv2022

Temporal trapping: a route to strong coupling and deterministic optical quantum computation

The realization of deterministic photon-photon gates is a central goal in optical quantum computation and engineering. A longstanding challenge is that optical nonlinearities in scalable, room-temperature material platforms are too weak to achieve the required strong coupling, due to the critical loss-confinement tradeoff in existing photonic structures. In this work, we introduce a novel confinement method, dispersion-engineered temporal trapping, to circumvent the tradeoff, paving a route to all-optical strong coupling. Temporal confinement is imposed by an auxiliary trap pulse via cross-phase modulation, which, combined with the spatial confinement of a waveguide, creates a "flying cavity" that enhances the nonlinear interaction strength by at least an order of magnitude. Numerical simulations confirm that temporal trapping confines the multimode nonlinear dynamics to a single-mode subspace, enabling high-fidelity deterministic quantum gate operations. With realistic dispersion engineering and loss figures, we show that temporally trapped ultrashort pulses could achieve strong coupling on near-term nonlinear nanophotonic platforms. Our results highlight the potential of ultrafast nonlinear optics to become the first scalable, high-bandwidth, and room-temperature platform that achieves a strong coupling, opening a new path to quantum computing, simulation, and light sources.

quant-ph↗

arXiv2021

Onset of non-Gaussian quantum physics in pulsed squeezing with mesoscopic fields

We study the emergence of non-Gaussian quantum features in pulsed squeezed light generation with a mesoscopic number (i.e., dozens to hundreds) of pump photons. Due to the strong optical nonlinearities necessarily involved in this regime, squeezing occurs alongside significant pump depletion, compromising the predictions made by conventional semiclassical models for squeezing. Furthermore, nonlinear interactions among multiple frequency modes render the system dynamics exponentially intractable in na\"ive quantum models, requiring a more sophisticated modeling framework. To this end, we construct a nonlinear Gaussian approximation to the squeezing dynamics, defining a "Gaussian interaction frame" (GIF) in which non-Gaussian quantum dynamics can be isolated and concisely described using a few dominant (i.e., principal) supermodes. Numerical simulations of our model reveal non-Gaussian distortions of squeezing in the mesoscopic regime, largely associated with signal-pump entanglement. We argue that the state of the art in nonlinear nanophotonics is quickly approaching this regime, providing an all-optical platform for experimental studies of the semiclassical-to-quantum transition in a rich paradigm of coherent, multimode nonlinear dynamics. Mesoscopic pulsed squeezing thus provides an intriguing case study of the rapid rise in dynamic complexity associated with semiclassical-to-quantum crossover, which we view as a correlate of the emergence of new information-processing capacities in the quantum regime.

quant-ph↗

arXiv2021

Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling

Both Bayesian and varying coefficient models are very useful tools in practice as they can be used to model parameter heterogeneity in a generalizable way. Motivated by the need of enhancing Marketing Mix Modeling at Uber, we propose a Bayesian Time Varying Coefficient model, equipped with a hierarchical Bayesian structure. This model is different from other time varying coefficient models in the sense that the coefficients are weighted over a set of local latent variables following certain probabilistic distributions. Stochastic Variational Inference is used to approximate the posteriors of latent variables and dynamic coefficients. The proposed model also helps address many challenges faced by traditional MMM approaches. We used simulations as well as real world marketing datasets to demonstrate our model superior performance in terms of both accuracy and interpretability.

stat.AP↗