arXiv subjects

Hideo Mabuchi

Publications and source records attributed to Hideo Mabuchi.

At least 19 recordsLinked to original sources

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↗

arXiv2025

The geometry and dynamics of annealed optimization in the coherent Ising machine with hidden and planted solutions

The coherent Ising machine (CIM) is a nonconventional hardware architecture for finding approximate solutions to large-scale combinatorial optimization problems. It operates by annealing a laser gain parameter to adiabatically deform a high-dimensional energy landscape over a set of soft spins, going from a simple convex landscape to the more complex optimization landscape of interest. We address how the evolving energy landscapes guides the optimization dynamics against problems with hidden planted solutions. We study the Sherrington-Kirkpatrick spin-glass with ferromagnetic couplings that favor a hidden configuration by combining the replica method, random matrix theory, the Kac-Rice method and dynamical mean field theory. We characterize energy, number, location, and Hessian eigenspectra of global minima, local minima, and critical points as the landscape evolves. We find that low energy global minima develop soft-modes which the optimization dynamics can exploit to descend the energy landscape. Even when these global minima are aligned to the hidden configuration, there can be exponentially many higher energy local minima that are all unaligned with the hidden solution. Nevertheless, the annealed optimization dynamics can evade this cloud of unaligned high energy local minima and descend near to aligned lower energy global minima. Eventually, as the landscape is further annealed, these global minima become rigid, terminating any further optimization gains from annealing. We further consider a second optimization problem, the Wishart planted ensemble, which contains a hidden planted solution in a landscape with tunable ruggedness. We describe CIM phase transitions between recoverability and non-recoverability of the hidden solution. Overall, we find intriguing relations between high-dimensional geometry and dynamics in analog machines for combinatorial optimization.

cond-mat.dis-nn↗

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

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

Photonic integrated circuits with second-order ($χ^{(2)}$) 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 $χ^{(2)}$ nonlinearities, the frameworks developed here are general and are readily extended to the description of dynamical processes based on third-order ($χ^{(3)}$) 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 $χ^{(2)}$ (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

Geometric landscape annealing as an optimization principle underlying the coherent Ising machine

Given the fundamental importance of combinatorial optimization across many diverse application domains, there has been widespread interest in the development of unconventional physical computing architectures that can deliver better solutions with lower resource costs. These architectures embed discrete optimization problems into the annealed, analog evolution of nonlinear dynamical systems. However, a theoretical understanding of their performance remains elusive, unlike the cases of simulated or quantum annealing. We develop such understanding for the coherent Ising machine (CIM), a network of optical parametric oscillators that can be applied to any quadratic unconstrained binary optimization problem. Here we focus on how the CIM finds low-energy solutions of the Sherrington-Kirkpatrick spin glass. As the laser gain is annealed, the CIM interpolates between gradient descent on the soft-spin energy landscape, to optimization on coupled binary spins. By exploiting spin-glass theory, we develop a detailed understanding of the evolving geometry of the high-dimensional CIM energy landscape as the laser gain increases, finding several phase transitions, from flat, to rough, to rigid. Additionally, we develop a cavity method that provides a precise geometric interpretation of supersymmetry breaking in terms of the response of a rough landscape to specific perturbations. We confirm our theory with numerical experiments, and find detailed information about critical points of the landscape. Our extensive analysis of phase transitions provides theoretically motivated optimal annealing schedules that can reliably find near-ground states. This analysis reveals geometric landscape annealing as a powerful optimization principle and suggests many further avenues for exploring other optimization problems, as well as other types of annealed dynamics, including chaotic, oscillatory or quantum dynamics.

cond-mat.dis-nn↗

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 ($χ^{(3)}$) waveguides to saturated $χ^{(2)}$ 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 $χ^{(2)}$ 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 Schrödinger 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 natïve 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

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↗

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., $χ^{(2)}$) 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 $χ^{(2)}$ 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 $χ^{(2)}$ 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 $χ^{(2)}$ 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

Nonlinear Quantum Behavior of Ultrashort-Pulse Optical Parametric Oscillators

The quantum features of ultrashort-pulse optical parametric oscillators (OPOs) are investigated theoretically in the nonlinear regime near and above threshold. Viewing the pulsed OPO as a multimode open quantum system, we rigorously derive a general input-output model that features nonlinear coupling among many cavity (i.e., system) signal modes and a broadband single-pass (i.e., reservoir) pump field. Under appropriate assumptions, our model produces a Lindblad master equation with multimode nonlinear Lindblad operators describing two-photon dissipation and a multimode four-wave-mixing Hamiltonian describing a broadband, dispersive optical cascade, which we show is required to preserve causality. To simplify the multimode complexity of the model, we employ a supermode decomposition to perform numerical simulations in the regime where the pulsed supermodes experience strong single-photon nonlinearity. We find that the quantum nonlinear dynamics induces pump depletion as well as corrections to the below-threshold squeezing spectrum predicted by linearized models. We also observe the formation of non-Gaussian states with Wigner-function negativity and show that the multimode interactions with the pump, both dissipative and dispersive, can act as effective decoherence channels. Finally, we briefly discuss some experimental considerations for potentially observing such quantum nonlinear phenomena with ultrashort-pulse OPOs on nonlinear nanophotonic platforms.

quant-ph↗

arXiv2022

Efficient sampling of ground and low-energy Ising spin configurations with a coherent Ising machine

We show that the nonlinear stochastic dynamics of a measurement-feedback-based coherent Ising machine (MFB-CIM) in the presence of quantum noise can be exploited to sample degenerate ground and low-energy spin configurations of the Ising model. We formulate a general discrete-time Gaussian-state model of the MFB-CIM which faithfully captures the nonlinear dynamics present at and above system threshold. This model overcomes the limitations of both mean-field models, which neglect quantum noise, and continuous-time models, which assume long photon lifetimes. Numerical simulations of our model show that when the MFB-CIM is operated in a quantum-noise-dominated regime with short photon lifetimes (i.e., low cavity finesse), homodyne monitoring of the system can efficiently produce samples of low-energy Ising spin configurations, requiring many fewer roundtrips to sample than suggested by established high-finesse, continuous-time models. We find that sampling performance is robust to, or even improved by, turning off or altogether reversing the sign of the parametric drive, but performance is critically reduced in the absence of optical nonlinearity. For the class of MAX-CUT problems with binary-signed edge weights, the number of roundtrips sufficient to fully sample all spin configurations up to the first-excited Ising energy, including all degeneracies, scales as $1.08^N$. At a problem size of $N = 100$ with a few dozen (median of 20) such desired configurations per instance, we have found median sufficient sampling times of $6\times10^6$ roundtrips; in an experimental implementation of an MFB-CIM with a 10 GHz repetition rate, this corresponds to a wall-clock sampling time of 60 ms.

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 naïve 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

Mid-infrared nonlinear optics in thin-film lithium niobate on sapphire

Periodically poled thin-film lithium niobate (TFLN) waveguides have emerged as a leading platform for highly efficient frequency conversion in the near-infrared. However, the commonly used silica bottom-cladding results in high absorption loss at wavelengths beyond 2.5 $μ$m. In this work, we demonstrate efficient frequency conversion in a TFLN-on-sapphire platform, which features high transparency up to 4.5 $μ$m. In particular, we report generating mid-infrared light up to 3.66 $μ$m via difference-frequency generation of a fixed 1-$μ$m source and a tunable telecom source, with normalized efficiencies up to 200%/W-cm$^2$. These results show TFLN-on-sapphire to be a promising platform for integrated nonlinear nanophotonics in the mid-infrared.

physics.optics↗

arXiv2021

Towards an Engineering Framework for Ultrafast Quantum Nonlinear Optics

The advent of dispersion-engineered and highly nonlinear nanophotonics is expected to open up an all-optical path towards the strong-interaction regime of quantum optics by combining high transverse field confinement with ultra-short-pulse operation. Obtaining a full understanding of photon dynamics in such broadband devices, however, poses major challenges in the modeling and simulation of multimode non-Gaussian quantum physics, highlighting the need for sophisticated reduced models that facilitate efficient numerical study while providing useful physical insight. In this manuscript, we review our recent efforts in modeling broadband optical systems at varying levels of abstraction and generality, ranging from multimode extensions of quantum input-output theory for sync-pumped oscillators to the development of numerical methods based on a field-theoretic description of nonlinear waveguides. We expect our work not only to guide ongoing theoretical and experimental efforts towards next-generation quantum devices but also to uncover essential physics of broadband quantum photonics.

quant-ph↗