arXiv subjects

Ryosuke Shimizu

Publications and source records attributed to Ryosuke Shimizu.

At least 19 recordsLinked to original sources

arXiv2026

Sample-half-inserted quantum interferometer

Quantum technologies have been widely recognized as unprecedented opportunities for ultra-high precision metrology. As a celebrated example in modern quantum optics, the Hong-Ou-Mandel (HOM) interferometer is well-known for enabling temporal resolutions on the attosecond scale. However, the relatively low Fisher information per trial in ordinary HOM measurements typically necessitates tens of thousands of repetitions to achieve such precision. Here, we propose and demonstrate a sample-half-inserted HOM (SHOM) interferometer, which enhances the Fisher information by five orders of magnitude in a single interference event. By introducing an asymmetric photon-sample interaction, the SHOM configuration produces a distinctive dip-bump-dip interference structure, converting what was previously viewed as an artifact into a helpful metrological resource. Experimentally, we measured the optical path difference with an average precision of 4.09 nm (13.63 as) and an average accuracy of 1.22 nm (4.07 as) using $O(10^7)$ photons. Our results establish SHOM interferometry as an efficient phase-insensitive approach, not only paving the way toward practical quantum-enhanced thickness measurement for transparent materials, but also serving as an elegant strategy to improve the performance of various quantum devices.

quant-ph↗

arXiv2026

Quantum optical synthesis of high-dimensional ultrafast frequency-bin qudits

Frequency modes of light are one of the most promising platforms that provide access to high-dimensional quantum states amongst different photonic degrees of freedom capable of high-dimensionality, enabling robust, error-tolerant, and scalable quantum optical information systems. We demonstrate engineering of precisely controlled two-photon high-dimensional states entangled in frequency through time-domain Fourier optical synthesis. We generate and convert a continuous broadband frequency-entangled state into a large range of discrete frequency bins suitable for ITU standards, with spacings ranging from 12.5 GHz to 750 GHz, and observe spectral anticorrelations over 38 frequency bins, including intra-bin pure states at a 100 GHz bin spacing. We characterize the full quantum state dimensionality via Schmidt decomposition and observe lower bounds on the frequency-binned Hilbert-space dimensionalities of at least 289, formed by two entangled qudits with dimension 17. Furthermore, we demonstrate quantum nonlocality via frequency correlations in a transmission experiment over a campus-scale two-node fiber network. This work represents a crucial step towards building a versatile and relatively simple way of generating precisely controlled high-dimensional spectral qudits, with the potential of harnessing in wavelength-multiplexed quantum networks, high-dimensional information processing, and communication of quantum states specifically, and fiber-optic quantum remote sensing.

quant-ph↗

arXiv2025

Hybrid biphoton spectrometer for time-resolved quantum spectroscopy across visible and near-infrared regions

Joint spectral measurements are a powerful tool for characterising biphoton spectral correlation, which is crucial for quantum information and communication technologies. In these applications, highly pure biphoton states are essential in any time- and frequency-mode, often obviating the need for time-resolved measurements. Conversely, spectroscopy utilising entangled photon pairs is gaining significant attention for its ability to unveil molecular dynamics, a field that critically demands time-resolved capabilities. Here, we introduce a methodology for capturing a biphoton spectrum that comprises visible and near-infrared photons, resulting in a highly non-degenerate joint spectrum. Our system employs two non-scanning spectrographs: a fibre spectrometer for near-infrared photons and a delay-line-anode single-photon imager for visible photons. We successfully measure the joint spectral intensity by leveraging a time-tagging acquisition strategy. Furthermore, our approach uniquely enables time-resolved joint spectral measurements with respect to the laser synchronisation against the hundreds-of-picosecond instrument response function. Our methodology could advance heralded fluorescence spectroscopy using biphoton sources to investigate temporal dynamics of complex biological, chemical, and physical systems.

quant-ph↗

arXiv2025

Construction of self-similar energy forms and singularity of Sobolev spaces on Laakso-type fractal spaces

We construct self-similar $p$-energy forms $\mathscr{E}_p$ on a rich class of \emph{Laakso-type fractal spaces} and study the properties of the associated Sobolev spaces $\mathscr{F}_p$. The main result of the paper is the discovery of a new analytic phenomenon, which we refer to as \emph{singularity of Sobolev spaces}. This means that the associated Sobolev spaces $\mathscr{F}_{p_1}$ and $\mathscr{F}_{p_2}$ for distinct $p_1,p_2 \in (1,\infty)$ intersect only at constant functions. We show that the Laakso diamond space of Lang--Plaut is one such example, and explain why this does not contradict the inverse limit construction of Cheeger--Kleiner which proves Laakso Diamond to support Poincar\'e inequality of Heinonen--Koskela.

math.MG↗

arXiv2025

Two-dimensional fluorescence spectroscopy with quantum entangled photons and time- and frequency-resolved two-photon coincidence detection

Recent theoretical studies in quantum spectroscopy have emphasized the potential of non-classical correlations in entangled photon pairs for selectively targeting specific nonlinear optical processes in nonlinear optical responses. However, because of the extremely low intensity of the nonlinear optical signal generated by irradiating molecules with entangled photon pairs, time-resolved spectroscopic measurements using entangled photons have yet to be experimentally implemented. In this paper, we theoretically propose a quantum spectroscopy measurement employing a time-resolved fluorescence approach that aligns with the capabilities of current photon detection technologies. The proposed quantum spectroscopy affords two remarkable advantages over conventional two-dimensional electronic spectroscopy. First, it enables the acquisition of two-dimensional spectra without requiring control over multiple pulsed lasers. Second, it reduces the complexity of the spectra because the spectroscopic signal is contingent upon the nonlinear optical process of spontaneous emission. These advantages are similar to those achieved in a previous study [Fujihashi et al., J. Chem. Phys. 160, 104201 (2024)]. However, our approach achieves sufficient signal intensities that can be readily detected using existing photon detection technologies, thereby rendering it a practicable. Our findings will potentially facilitate the first experimental real-time observation of dynamic processes in molecular systems using quantum entangled photon pairs.

physics.chem-ph↗

arXiv2025

$p$-Energy forms on fractals: recent progress

In this article, we survey recent progress on self-similar $p$-energy forms on self-similar fractals, where $p\in(1,\infty)$. While for $p=2$ the notion of such forms coincides with that of self-similar Dirichlet forms and there have been plenty of studies on them since the late 1980s, studies on the case of $p\in(1,\infty)\setminus\{2\}$ was initiated much later in 2004 by Herman, Peirone and Strichartz [Potential Anal. 20 (2004), 125--148] and Strichartz and Wong [Nonlinearity 17 (2004), 595--616] and no essential progress on this case had been made since then until a few years ago. The recent progress by Kigami, Shimizu, Cao--Gu--Qiu and Murugan--Shimizu has established the existence of such $p$-energy forms on general post-critically finite (p.-c.f.) self-similar sets and on large classes of low-dimensional infinitely ramified self-similar sets, and the authors have proved further detailed properties of these forms and associated $p$-harmonic functions, mainly for p.-c.f. self-similar sets. This article is devoted to a review of these results, focusing on the most recent developments by the authors and illustrating them in the simplest non-trivial setting of the two-dimensional standard Sierpi\'{n}ski gasket.

math.FA↗

arXiv2024

Grain Selection Growth of Soft Metal in Electrochemical Processes

Soft metals like lithium and sodium play a critical role in battery technology owing to their high energy density. Texture formation by grain selection growth of soft metals during electrochemical processes is a crucial factor affecting power and safety. Developing a framework to understand and control grain growth is a multifaceted challenge. Here, a general thermodynamic theory and phase-field model are formulated to study grain selection growth of soft metals. Our study focuses on the interplay between surface energy and atomic mobility-related intrinsic strain energy in grain selection growth. Differences in grain selection growth arise from the anisotropy in surface energy and diffusion barrier of soft metal atoms. Our findings highlight the kinetic limitations of solid-state Li metal batteries, which originate from load stress-induced surface energy anisotropy. These insights lead to the development of an amorphous LixSi1-x (0.50<x<0.79) seed layer, improving the critical current density at room temperature for anode-free Li solid-state batteries through the control of grain selection growth.

cond-mat.mtrl-sci↗

arXiv2024

Characterizations of Sobolev functions via Besov-type energy functionals in fractals

In the spirit of the ground-breaking result of Bourgain--Brezis--Mironescu, we establish some characterizations of Sobolev functions in metric measure spaces including fractals like the Vicsek set, the Sierpi\'{n}ski gasket and the Sierpi\'{n}ski carpet. As corollaries of our characterizations, we present equivalent norms on the Korevaar--Schoen--Sobolev space, and show that the domain of a $p$-energy form is identified with a Besov-type function space under a suitable $(p,p)$-Poincar\'e inequality, capacity upper bound and the volume doubling property.

math.FA↗

arXiv2024

Finite dimensionality of Besov spaces and potential-theoretic decomposition of metric spaces

In the context of a metric measure space $(X,d,\mu)$, we explore the potential-theoretic implications of having a finite-dimensional Besov space. We prove that if the dimension of the Besov space $B^\theta_{p,p}(X)$ is $k>1$, then $X$ can be decomposed into $k$ number of irreducible components (Theorem 1.1). Note that $\theta$ may be bigger than $1$, as our framework includes fractals. We also provide sufficient conditions under which the dimension of the Besov space is $1$. We introduce critical exponents $\theta_p(X)$ and $\theta_p^{\ast}(X)$ for the Besov spaces. As examples illustrating Theorem 1.1, we compute these critical exponents for spaces $X$ formed by glueing copies of $n$-dimensional cubes, the Sierpi\'{n}ski gaskets, and of the Sierpi\'{n}ski carpet.

math.FA↗

arXiv2024

Capturing the spectrotemporal structure of a biphoton wave packet with delay-line-anode single-photon imagers

Distinguishing photon-arrival time and position is crucial for advancing quantum technology. However, capturing spatial and temporal information efficiently remains challenging. Here, we present a novel photon-detection technique to achieve a significantly more efficient measurement of frequency-entangled biphoton than conventional photon detectors. We utilize a delay-line-anode single-photon detector (DLD), which consists of a position-sensitive delay line anode sensor behind a microchannel plate. Biphotons are obtained from the decay of biexcitons in the copper chloride semiconductor crystal. Two DLDs are coupled with a grating spectrometer exit to measure the joint spectral distributions of the biphoton. The resulting non-scanning process requires only a few minutes to obtain a temporally and spectrally resolved image, which is much quicker than the conventional biphoton frequency measurement. Our technique paves the way for all experiments in multi-mode quantum science requiring coincidence measurement.

quant-ph↗

arXiv2024

Contraction properties and differentiability of $p$-energy forms with applications to nonlinear potential theory on self-similar sets

We introduce a new contraction property, which we call the generalized $p$-contraction property, for $p$-energy forms as generalizations of many well-known inequalities, such as $p$-Clarkson's inequality, the strong subadditivity and the Markov property in the theory of nonlinear Dirichlet forms, and show that any $p$-energy form satisfying $p$-Clarkson's inequality is Fr\'{e}chet differentiable. We also verify the generalized $p$-contraction property for $p$-energy forms on fractals constructed by Kigami [Mem. Eur. Math. Soc. 5 (2023)] and by Cao--Gu--Qiu [Adv. Math. 405 (2022), no. 108517]. As a general framework of $p$-energy forms taking the generalized $p$-contraction property into consideration, we introduce the notion of $p$-resistance form and investigate fundamental properties of $p$-harmonic functions with respect to $p$-resistance forms. In particular, some new estimates on scaling factors of self-similar $p$-energy forms on self-similar sets are obtained by establishing H\"{o}lder regularity estimates for $p$-harmonic functions, and the $p$-walk dimensions of any generalized Sierpi\'{n}ski carpet and the $D$-dimensional level-$l$ Sierpi\'{n}ski gasket are shown to be strictly greater than $p$.

math.FA↗

arXiv2024

Korevaar-Schoen $p$-energy forms and associated $p$-energy measures on fractals

We construct good $p$-energy forms on metric measure spaces as pointwise subsequential limits of Besov-type $p$-energy functionals under certain geometric/analytic conditions. Such forms are often called Korevaar-Schoen $p$-energy forms in the literature. As an advantage of our approach, the associated $p$-energy measures are obtained and investigated. We also prove that our construction is applicable to the settings of Kigami [Mem. Eur. Math. Soc. 5 (2023)] and Cao-Gu-Qiu [Adv. Math. 405 (2022), no. 108517], yields Korevaar-Schoen $p$-energy forms comparable to the $p$-energy forms constructed in these papers, and can be further modified in the case of self-similar sets to obtain self-similar $p$-energy forms keeping most of the good properties of Korevaar-Schoen ones.

math.FA↗

arXiv2023

Pathway selectivity in time-resolved spectroscopy using two-photon coincidence counting with quantum entangled photons

Ultrafast optical spectroscopy is a powerful technique for studying the dynamic processes of molecular systems in condensed phases. However, in molecular systems containing many dye molecules, the spectra can become crowded and difficult to interpret owing to the presence of multiple nonlinear optical contributions. In this work, we theoretically propose time-resolved spectroscopy based on the coincidence counting of two entangled photons generated via parametric down-conversion with a monochromatic laser. We demonstrate that the use of two-photon counting detection of entangled photon pairs enables the selective elimination of the excited-state absorption signal. This selective elimination cannot be realized with classical coherent light. We anticipate that the proposed spectroscopy will help to simplify the spectral interpretation in complex molecular and materials systems comprising multiple molecules.

physics.chem-ph↗

arXiv2023

Spectrally resolved Franson interference

Franson interference can be used to test the nonlocal features of energy-time entanglement and has become a standard in quantum physics. However, most of the previous Franson interference experiments were demonstrated in the time domain, and the spectral properties of Franson interference have not been fully explored. Here, we theoretically and experimentally demonstrate spectrally resolved Franson interference using biphotons with different correlations, including positive correlation, negative correlation, and non-correlation. It is found that the joint spectral intensities of the biphotons can be modulated along both the signal and idler directions, which has potential applications in generating high-dimensional frequency entanglement and time-frequency grid states. This work may provide a new perspective for understanding the spectral-temporal properties of the Franson interferometer.

quant-ph↗

arXiv2023

Comparison of multi-mode Hong-Ou-Mandel interference and multi-slit interference

Hong-Ou-Mandel (HOM) interference of multi-mode frequency entangled states plays a crucial role in quantum metrology. However, as the number of modes increases, the HOM interference pattern becomes increasingly complex, making it challenging to comprehend intuitively. To overcome this problem, we present the theory and simulation of multi-mode-HOM interference (MM-HOMI) and compare it to multi-slit interference (MSI). We find that these two interferences have a strong mapping relationship and are determined by two factors: the envelope factor and the details factor. The envelope factor is contributed by the single-mode HOM interference (single-slit diffraction) for MM-HOMI (MSI). The details factor is given by $\sin(Nx)/ \sin(x)$ ($[\sin(Nv)/\sin(v)]^2$) for MM-HOMI (MSI), where $N$ is the mode (slit) number and $x (v)$ is the phase spacing of two adjacent spectral modes (slits). As a potential application, we demonstrate that the square root of the maximal Fisher information in MM-HOMI increases linearly with the number of modes, indicating that MM-HOMI is a powerful tool for enhancing precision in time estimation. We also discuss multi-mode Mach-Zehnder interference, multi-mode NOON-state interference, and the extended Wiener-Khinchin theorem. This work may provide an intuitive understanding of MM-HOMI patterns and promote the application of MM-HOMI in quantum metrology.

quant-ph↗

arXiv2023

Elucidating Dynamic Conductive State Changes in Amorphous Lithium Lanthanum Titanate for Resistive Switching Devices

Exploration of novel resistive switching materials attracts attention to replace conventional Si-based transistors and to achieve neuromorphic computing that can surpass the limit of the current Von-Neumann computing for the time of Internet of Things (IoT). Materials priorly used to serve in batteries have demonstrated metal-insulator transitions upon an electrical biasing due to resulting compositional change. This property is desirable for future resistive switching devices. Amorphous lithium lanthanum titanate (a-LLTO) was originally developed as a solid-state electrolyte with relatively high lithium ionic conductivity and low electronic conductivity among oxide-type solid electrolytes. However, it has been suggested that electric conductivity of a-LLTO changes depending on oxygen content. In this work, the investigation of switching behavior of a-LLTO was conducted by employing a range of voltage sweep techniques, ultimately establishing a stable and optimal operating condition within the voltage window of -3.5 V to 3.5 V. This voltage range effectively balances the desirable trait of a substantial resistance change by three orders of magnitude with the imperative avoidance of LLTO decomposition. This switching behavior is also confirmed at nanodevice of Ni/LLTO/Ni through in-situ biasing inside focused-ion beam/scanning electron microscope (FIB-SEM). Experiment and computation with different LLTO composition shows that LLTO has two distinct conductivity states due to Ti reduction. The distribution of these two states is discussed using simplified binary model, implying the conductive filament growth during low resistance state. Consequently, our study deepens understanding of LLTO electronic properties and encourages the interdisciplinary application of battery materials for resistive switching devices.

physics.app-ph↗

arXiv2023

First-order Sobolev spaces, self-similar energies and energy measures on the Sierpi\'{n}ski carpet

We construct and investigate $(1, p)$-Sobolev space, $p$-energy, and the corresponding $p$-energy measures on the planar Sierpi\'{n}ski carpet for all $p \in (1, \infty)$. Our method is based on the idea of Kusuoka and Zhou [Probab. Theory Related Fields $\textbf{93}$ (1992), no. 2, 169--196], where Brownian motion (the case $p = 2$) on self-similar sets including the planar Sierpi\'{n}ski carpet were constructed. Similar to this earlier work, we use a sequence of discrete graph approximations and the corresponding discrete $p$-energies to define the Sobolev space and $p$-energies. However, we need a new approach to ensure that our $(1, p)$-Sobolev space has a dense set of continuous functions when $p$ is less than the Ahlfors regular conformal dimension. The new ingredients are the use of Loewner type estimates on combinatorial modulus to obtain Poincar\'e inequality and elliptic Harnack inequality on a sequence of approximating graphs. An important feature of our Sobolev space is the self-similarity of our $p$-energy, which allows us to define corresponding $p$-energy measures on the planar Sierpi\'{n}ski carpet. We show that our Sobolev space can also be viewed as a Korevaar-Schoen type space. We apply our results to the attainment problem for Ahlfors regular conformal dimension of the Sierpi\'{n}ski carpet. In particular, we show that if the Ahlfors regular conformal dimension, say $\dim_{\mathrm{ARC}}$, is attained, then any optimal measure which attains $\dim_{\mathrm{ARC}}$ should be comparable with the $\dim_{\mathrm{ARC}}$-energy measure of some function in our $(1, \dim_{\mathrm{ARC}})$-Sobolev space up to a multiplicative constant. In this case, we also prove that the Newton-Sobolev space corresponding to any optimal measure and metric can be identified as our self-similar $(1, \dim_{\mathrm{ARC}})$-Sobolev space.

math.MG↗

arXiv2023

Spatial-spectral mapping to prepare the frequency entangled qudits

Entangled qudits, the high-dimensional entangled states, play an important role in the study of quantum information. How to prepare entangled qudits in an efficient and easy-to-operate manner is still a challenge in quantum technology. Here, we demonstrate a method to engineer frequency entangled qudits in a spontaneous parametric downconversion process. The proposal employs an angle-dependent phase-matching condition in a nonlinear crystal, which forms a classical-quantum mapping between the spatial (pump) and spectral (biphotons) degrees of freedom. In particular, the pump profile is separated into several bins in the spatial domain, and thus shapes the down-converted biphotons into discrete frequency modes in the joint spectral space. Our approach provides a feasible and efficient method to prepare a high-dimensional frequency entangled state. As an experimental demonstration, we generate a three-dimensional entangled state by using a homemade variable slit mask.

quant-ph↗