Search NASA⌕ Search

SEARCH · Search NASA

Results for “State”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Experimental Definition of the S = 1 π vs S = 2 σ Reactivity and S = 2 Character in the Ground State of an S = 1 Fe IV O Complex

Iron(IV)-oxo intermediates found in iron enzymes and artificial catalysts are competent for H atom abstraction in catalytic cycles. For S = 2 intermediates, both axial and equatorial approaches are well-established. The mechanism for S = 1 sites is not as well understood: an equatorial approach is more energetically favorable, and an axial approach requires crossing from the S = 1 to the S = 2 surface. Here, in this study, we use 1s2p resonant inelastic X-ray scattering (RIXS) and Fe L-edge X-ray absorption spectroscopy on the S = 1 [Fe IV O(TMC)(CH3CN)] 2+ and observe both S = 2 and S = 1 final states, which enables the experimental evaluation of the energetics of the axial and equatorial reactivity of an S = 1 Fe IV O center on its S = 2 vs S = 1 surface. The observation of S = 2 final states in the RIXS spectrum demonstrates significant S = 2 character spin–orbit mixed into the S = 1 ground state.

energy↗
DOE OSTI2025

Sharp spectroscopic fingerprints of disorder in an incompressible magnetic state

Disorder significantly impacts the electronic properties of conducting quantum materials by inducing electron localization and thus altering the local density of states and electric transport. In insulating quantum magnetic materials, the effects of disorder are less understood and can drastically impact fluctuating spin states like quantum spin liquids. In the absence of transport tools, disorder is typically characterized using chemical methods or by semi-classical modeling of spin dynamics. This requires high magnetic fields that may not always be accessible. Here, we show that magnetization plateaus—incompressible states found in many quantum magnets—provide an exquisite platform to uncover small amounts of disorder, regardless of the origin of the plateau. Using optical magneto-spectroscopy on the Ising-Heisenberg triangular-lattice antiferromagnet K 2 Co(SeO 3 ) 2 exhibiting a 1/3 magnetization plateau, we identify sharp spectroscopic lines, the fine structure of which serves as a hallmark signature of disorder. Through analytical and numerical modeling, we show that these fingerprints not only enable us to quantify minute amounts of disorder but also reveal its nature—as dilute vacancies. Remarkably, this model explains all details of the thermomagnetic response of our system, including the existence of multiple plateaus. Our findings provide a new approach to identifying disorder in quantum magnets.

Infrared spectroscopy↗
DOE OSTI2025

Valence 1⁢𝑠−0⁢𝑑 proton vacancy of the 32 Si ground state

The 32 Si( 3 He,d) 33 P reaction was studied in inverse kinematics at 6.3 MeV/u. States in 33 P corresponding to the proton 1s-0d single-particle orbitals were identified up to ≈ 4.5 MeV in excitation energy. The ( 3 He,d) spectroscopic factors were determined from distorted-wave Born approximation calculations. When combined with complementary neutron-adding data, the 1s-0d proton vacancies in the 32 Si ground state were extracted. In conjunction with a reanalysis of data from previous single-particle measurements, the trends in proton and neutron vacancy were explored across the 28,30,32,34 Si isotopes. Both proton and neutron vacancy data show gradual changes in their occupancies. The proton 1s 1/2 orbitals in 32 Si and 34 Si are both consistent with being empty. In conclusion, the ground-state nucleon distributions are described by shell-model calculations constrained to the 1s-0d model space.

Watwood, N. [Argonne National Laboratory (ANL), Ar↗
DOE OSTI2025

Unsteady- and Steady-State Relative Permeability Study with X-ray and Acoustic Monitoring for CO 2 Storage in Deep Saline Aquifers

In this study, we link the multiphase flow measurements with controls of sedimentary structures (e.g., heterogeneity and anisotropy) on relative permeability to variations in ultrasonic velocities for two deep saline aquifer formations (Entrada and Bluff Sandstones) in the San Juan Basin of the Southwestern USA. The rock specimens were extracted from outcrop sites near Durango, CO, USA. They have distinct differences in grain size, cementation composition, and individual chemical amounts, despite both formations being eolian sandstones. We performed a series of unsteady- and steady-state CO 2 -brine relative permeability experiments under capillary-controlled displacement rates. Unsteady-state experiments were conducted at 71 °C and 9.65 MPa; steady-state experiments were conducted at 85 °C and 22.8 MPa and 89 °C and 24.1 MPa for the Bluff and Entrada Sandstones, respectively. During the unsteady experiments, X-ray computed tomography was used to visualize multiphase flow in porous media and quantify saturations during brine drainage under various flow rates. Scan images and saturation profiles indicate that the CO 2 distribution in the pore volume was strongly impacted by the presence of high-angle cross-laminations, heterogeneous rock structure, and direction of bedding orientation. Those factors contribute to dramatic and quick initial breakthroughs and affect the overall saturation dynamics. Steady-state relative permeability tests were conducted at net flow rates of 1 mL/min for both brine drainage and imbibition. During the experimental steps, the CO 2 fractional flow was increased and decreased for both drainage and imbibition scenarios to mimic the front when CO 2 contacts brine and behind the front when brine enters space previously occupied by CO 2 . It was found that compressional velocity decreased, while shear waves slightly increased as brine saturation decreased. The hysteresis effects for the relative permeability and acoustic velocities were distinct. Furthermore, the CO 2 /brine front stability is quantified by applying a mobility ratio approach to spot saturations at which the boundary line between fluids becomes uneven. The results presented in this work can potentially boost the quality and precision of forecasts for the CO 2 storage projects in which the vertical and horizontal core-scale heterogeneity and anisotropy impact the plume migration within host reservoirs.

carbon dioxide (CO2)↗
DOE OSTI2026

Electronic Trap-State Modulation in Sm-Doped SnO 2 Nanofibers Enables Ultrasensitive Hydrogen Sensing

The demand for sub-ppm hydrogen (H 2 ) sensing is growing across emerging applications such as environmental monitoring, breath-based disease diagnostics, and early-stage battery failure detection. However, achieving reliable ppb-level detection with chemiresistive metal oxide sensors remains challenging. At trace gas concentrations, resistance modulation is often insufficient, particularly in the absence of noble metal catalysts. Here, we report samarium-doped tin dioxide (Sm-SnO 2 ) nanofibers in which electronic trap-state modulation is exploited to enable ultrasensitive hydrogen sensing. The 2 at% Sm-doped SnO 2 nanofibers exhibited markedly enhanced H 2 sensitivity, achieving clear detection down to 25 ppb H 2 at 200 °C, with a theoretical limit of detection of 4.5 ppb, placing this material among the most sensitive noble-metal-free SnO 2 -based H 2 sensors reported to date. Mechanistic investigations through X-ray photoelectron spectroscopy and electron energy loss spectroscopy revealed that Sm 3+ doping introduces deep trap states associated with charge-compensating defect complexes. These states reduce free carrier density, increase baseline resistance, and enable trap-assisted charge release during H 2 exposure, thereby amplifying the sensing response. Trap-state engineering via rare-earth doping, exemplified by Sm-SnO 2 , provides an effective pathway for achieving ppb-level hydrogen detection in noble-metal-free chemiresistive sensors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Synthesis, Structure, and Redox Reactivity of Ni Complexes Bearing a Redox and Acid–Base Non-innocent Ligand with Ni II , Ni III , and Ni IV Formal Oxidation States

Here, a series of Ni complexes bearing a redox and acid–base noninnocent tetraamido macrocyclic ligand, H 4 -(TAML-4) {H 4 -(TAML-4) = 15,15-dimethyl-5,8,13,17-tetrahydro-5,8,13,17-tetraaza-dibenzo[a,g]cyclotridecene-6,7,14,16-tetraone}, with formal oxidation states of Ni II , Ni III , and Ni IV were synthesized and characterized structurally and spectroscopically. The X-ray crystallographic analysis of the Ni complexes revealed a square planar geometry, and the [Ni(TAML-4)] complex with the formal oxidation state of Ni IV was characterized to be [Ni III (TAML-4 •+ )] with the oxidation state of the Ni III ion and the one-electron oxidized TAML-4 ligand, TAML-4 •+ . The Ni III oxidation state and the TAML-4 radical cation ligand, TAML-4 •+ , were supported by X-ray absorption spectroscopy and density functional theory calculations. The reversible interconversions between [Ni II (TAML-4)] 2– and [Ni III (TAML-4)] − and between [Ni III (TAML-4)] − and [Ni III (TAML-4 •+ )] were demonstrated in spectroelectrochemical measurements as well as in chemical oxidation and reduction reactions. The reactivities of [Ni III (TAML-4)] − and [Ni III (TAML-4 •+ )] were then investigated in hydride transfer reactions using NADH analogs. Hydride transfer from 9,10-dihydro-10-methylacridine (AcrH 2 ) to [Ni III (TAML-4 •+ )] was found to proceed via electron transfer (ET) from AcrH 2 to [Ni III (TAML-4 •+ )] with no deuterium kinetic isotope effect (k H /k D = 1.0(2)). In contrast, hydride transfer from AcrH 2 to [NiIII(TAML-4)] − proceeded much more slowly via a concerted proton-coupled electron transfer (PCET) process with k H /k D = 7.0(5). In the latter reaction, an electron and a proton were transferred to the Ni III center and the TAML-4 ligand, respectively. The mechanisms of the ET by [Ni III (TAML-4 •+ )] and the concerted PCET by [Ni III (TAML-4)] − were ascribed to the different redox potentials of the Ni complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Statistical White-Line Analysis in High-Throughput TXM-XANES for Chemical State Quantification

The transmission X-ray microscopy (TXM) based X-ray absorption near-edge structure (XANES) technique provides three-dimensional mapping of element-specific chemical states at nanometer-scale spatial resolution and micrometer-scale fields of view. However, compared to conventional volume-averaged XANES (VA-XANES) measurements, the inherently small voxel size in TXM-XANES leads to a lower signal-to-noise ratio, making full-spectrum analysis computationally demanding and less robust. Here, we present the structural and compositional conditions for a statistical white-line analysis framework under which chemical state information can be directly extracted from the white-line peak position in voxel spectra without the need for voxel-wise background subtraction or normalization, under well-defined structural and compositional conditions. The method is validated on layered oxide cathode materials, where low-order polynomial fitting accurately reproduces white-line features, and the extracted energy distributions correlate strongly with VA-XANES results. This statistical approach enables high-throughput, dose-efficient, and noise-robust chemical state quantification in TXM-XANES, offering broad applicability to functional materials requiring nanoscale oxidation-state mapping.

TXM↗
DOE OSTI2026

Kramers nodal line in the charge density wave state of YTe 3 and the influence of twin domains

Recent studies have focused on the relationship between charge density wave (CDW) collective electronic ground states and nontrivial topological states. YTe 3 , a nonmagnetic quasi-two-dimensional chalcogenide, has been reported to exhibit a CDW state below 334 K. Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), we establish that YTe 3 is a CDW-induced Kramers nodal line (KNL) metal, a recently proposed topological state of matter. Scanning tunneling microscopy and low energy electron diffraction reveal two orthogonal domains, each with a unidirectional CDW and a similar wave vector (𝐪 CDW ). When the influence of twin domains is considered, the effective band structure (EBS) computations that utilize DFT-calculated bands using a noncentrosymmetric structure determined by x-ray crystallography, show excellent agreement with ARPES. The noncentrosymmetry of YTe 3 is established by Raman spectroscopy. The Fermi surface and ARPES intensity plots show weak shadow bands displaced by 𝐪 CDW from the main bands. Furthermore, these are linked to CDW modulation, as the EBS calculation confirms. Bilayer split main and shadow bands suggest the existence of crossings, according to theory and experiment. DFT bands, including spin-orbit coupling, indicate existence of a KNL along the Σ direction from multiple crossings of bands dispersing perpendicular to it. Additionally, doubly degenerate bands are only found along the KNL at all energies, with some bands dispersing through the Fermi level.

Angle-resolved photoemission spectroscopy↗
DOE OSTI2026

Quantum-State-Controlled Collisions of Ultracold Polyatomic Molecules

Collisions between ultracold calcium monohydroxide (CaOH) molecules are realized and studied. Inelastic collision rate constants are measured for CaOH prepared in ground and excited vibrational states, and the electric field dependence of these rates is measured for molecules in single quantum states of the parity-doubled bending mode. Theoretical calculations of collision rate coefficients are performed and found to agree with measured values. The lowest collisional loss rates are for states with repulsive long-range potentials that shield ultracold molecules from loss channels at short distance. These results unveil the collisional behavior of parity-doublet molecules in the ultracold regime and lay the foundation for future experiments to evaporatively cool polyatomic molecules to quantum degeneracy.

Vilas, Nathaniel B. [Harvard University, Cambridge↗
DOE OSTI2024

Heavy states in 3d gravity and 2d CFT

We discuss correlators of light fields in heavy states in AdS 3 gravity and holographic 2d CFTs. In the bulk, the propagator of free fields in AdS backgrounds containing a conical defect or a BTZ black hole can be obtained by solving a wave equation, as well as by the method of images. On the boundary, these geometries are sourced by heavy operator insertions, and the propagator is dual to a heavy-light (HHLL) correlator. By matching its expansion in Virasoro blocks to our bulk results, we determine the OPE coefficients of all contributing states in both the s and t channels. In the s channel, these states are excitations of the light field on top of the heavy state, and their OPE coefficients are the amplitudes to create them. The t-channel OPE is dominated by the Virasoro vacuum block, but there is also an infinite family of light two-particle states that contribute to the correlator. The OPE coefficients that couple these states to heavy operators represent their expectation values in heavy backgrounds. We determine them exactly, derive their asymptotic form at large twist, and discuss their behavior near and above the BTZ threshold, where they become thermal one-point functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Chiral spin-liquid-like state in pyrochlore iridate thin films

The pyrochlore iridates have become ideal platforms to unravel fascinating correlated and topological phenomena that stem from the intricate interplay among strong spin-orbit coupling, electronic correlations, lattice with geometric frustration, and itinerancy of the 5d electrons. The all-in-all-out antiferromagnetic state, commonly considered as the magnetic ground state, can be dramatically altered in reduced dimensionality, leading to exotic or hidden quantum states inaccessible in bulk. Here, by means of magnetotransport, resonant elastic and inelastic x-ray scattering experiments, we discover an emergent quantum disordered state in (111) Y 2 Ir 2 O 7 thin films (thickness ≤30 nm) persisting down to 5 K, characterized by dispersionless magnetic excitations. The anomalous Hall effect observed below an onset temperature near 125 K corroborates the presence of chiral short-range spin configurations expressed in non-zero scalar spin chirality, breaking the macroscopic time-reversal symmetry. The origin of this chiral state is ascribed to the restoration of magnetic frustration on the pyrochlore lattice in lower dimensionality, where the competing exchange interactions together with enhanced quantum fluctuations suppress any long-range order and trigger spin-liquid-like behavior with degenerate ground-state manifold.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Superionic conducting vacancy-rich β-Li 3 N electrolyte for stable cycling of all-solid-state lithium metal batteries

The advancement of all-solid-state lithium metal batteries requires breakthroughs in solid-state electrolytes (SSEs) for the suppression of lithium dendrite growth at high current densities and high capacities (>3 mAh cm -2 ) and innovation of SSEs in terms of crystal structure, ionic conductivity and rigidness. Here we report a superionic conducting, highly lithium-compatible and air-stable vacancy-rich β-Li 3 N SSE. This vacancy-rich β-Li 3 N SSE shows a high ionic conductivity of 2.14 × 10 -3 S cm -1 at 25 °C and surpasses almost all the reported nitride-based SSEs. A Li- and N-vacancy-mediated fast lithium-ion migration mechanism is unravelled regarding vacancy-triggered reduced activation energy and increased mobile lithium-ion population. All-solid-state lithium symmetric cells using vacancy-rich β-Li 3 N achieve breakthroughs in high critical current densities up to 45 mA cm -2 and high capacities up to 7.5 mAh cm -2 , and ultra-stable lithium stripping and plating processes over 2,000 cycles. The high lithium compatibility mechanism of vacancy-rich β-Li 3 N is unveiled as intrinsic stability to lithium metal. In addition, β-Li 3 N possesses excellent air stability through the formation of protection surfaces. All-solid-state lithium metal batteries using the vacancy-rich β-Li 3 N as SSE interlayers and lithium cobalt oxide (LCO) and Ni-rich LiNi 0.83 Co 0.11 Mn 0.06 O 2 (NCM83) cathodes exhibit excellent battery performance. Extremely stable cycling performance is demonstrated with high capacity retentions of 82.05% with 95.2 mAh g -1 over 5,000 cycles at 1.0 C for LCO and 92.5% with 153.6 mAh g -1 over 3,500 cycles at 1.0 C for NCM83. Utilizing the vacancy-rich β-Li 3 N SSE and NCM83 cathodes, the all-solid-state lithium metal batteries successfully accomplished mild rapid charge and discharge rates up to 5.0 C, retaining 60.47% of the capacity. Notably, these batteries exhibited a high areal capacity, registering approximately 5.0 mAh cm -2 for the compact pellet-type cells and around 2.2 mAh cm -2 for the all-solid-state lithium metal pouch cells.

25 ENERGY STORAGE↗
DOE OSTI2024

Local probe of bulk and edge states in a fractional Chern insulator

The fractional quantum Hall effect is a key example of topological quantum many-body phenomena, arising from the interplay between strong electron correlation, topological order and time-reversal symmetry breaking. Recently, a lattice analogue of the fractional quantum Hall effect at zero magnetic field has been observed, confirming the existence of a zero-field fractional Chern insulator (FCI). Despite this, the bulk–edge correspondence—a hallmark of a FCI featuring an insulating bulk with conductive edges—has not been directly observed. In fact, this correspondence has not been visualized in any system for fractional states owing to experimental challenges. Here we report the imaging of FCI edge states in twisted MoTe 2 (t-MoTe 2 ) using microwave impedance microscopy. By tuning the carrier density, we observe the system evolving between metallic and FCI states, the latter of which exhibits insulating bulk and conductive edges, as expected from the bulk–boundary correspondence. Further analysis suggests the composite nature of the FCI edge states. We also observe the evolution of edge states across the topological phase transition as a function of interlayer electric field and reveal exciting prospects of neighbouring domains with different fractional orders. Furthermore, these findings pave the way for research into topologically protected one-dimensional interfaces between various anyonic states at zero magnetic field, such as gapped one-dimensional symmetry-protected phases with non-zero topological entanglement entropy, Halperin–Laughlin interfaces and the creation of non-abelian anyons.

Imaging techniques↗
DOE OSTI2026

A curated benchmark for cofolding models on kinase conformational states

Abstract Protein kinases are critical drug targets, requiring therapeutics that can modulate their active and inactive conformational states. While cofolding models can generate global folds directly from kinase sequences and ligand SMILES strings, these models have not yet been tested on their ability to recover ligand-induced-fit conformational states of the kinase proteins. Here, we introduce KinConfBench, a curated benchmark of 2225 high-quality human kinase chains to evaluate the ability of four state-of-the-art cofolding models—Boltz-2, Chai-1, Protenix, and RoseTTAFold-All-Atom—to recover both canonical and rare conformational states. We show that geometric success metrics of a ligand pose in the active site do not correlate strongly with the correct kinase conformational state, motivating a new set of dynamical benchmarks for assessing cofolding models. While all four cofolding models achieve ~60–80% prediction accuracy for kinase conformational classification, they exhibit severe mode collapse when performing multiple inferences, show negligible structural diversity in sampling induced-fit motions, and display a prevalent “apo-drift” in which most cofolding models predominantly predict the kinase to be in its ligand-free state. Our results highlight that capturing ligand-induced protein conformational diversity, not just geometric fit, is critical for next-generation structure-based drug discovery.

Sun, Kunyang↗
DOE OSTI2024

Observation of bound valence excited electronic states of deprotonated 2-hydroxytriphenylene using photoelectron, photodetachment, and resonant two-photon detachment spectroscopy of cryogenically cooled anions

Polycyclic aromatic hydrocarbons (PAHs) are common atmospheric pollutants, and they are also ubiquitous in the interstellar medium. Here, we report the study of a complex O-containing PAH anion, the deprotonated 2-hydroxytriphenylene (2-OtPh–), using high-resolution photoelectron imaging and photodetachment spectroscopy of cryogenically cooled anions. Vibrationally resolved photoelectron spectra yield the electron affinity of the 2-OtPh radical as 2.629(1) eV and several vibrational frequencies for its ground electronic state. Photodetachment spectroscopy reveals bound valence excited electronic states for the 2-OtPh– anion, with unprecedentedly rich vibronic features. Evidence is presented for a low-lying triplet state (T1) and two singlet states (S1 and S2) below the detachment threshold. Single-color resonant two-photon photoelectron spectroscopy uncovers rich photophysics for the 2-OtPh– anion, including vibrational relaxation in S1, internal conversion to the ground state of 2-OtPh–, intersystem crossing from S2 to T1, and a long-lived autodetaching shape resonance about 1.3 eV above the detachment threshold. The rich electronic structure and photophysics afforded by the current study suggest that 2-OtPh– would be an interesting system for pump–probe experiments to unravel the dynamics of the excited states of this complex PAH anion.

Chemistry↗
DOE OSTI2024

Distinct vibrational motions promote disparate excited-state decay pathways in cofacial perylenediimide dimers

A complex interplay of structural, electronic, and vibrational degrees of freedom underpins the fate of molecular excited states. Organic assemblies exhibit a myriad of excited-state decay processes, such as symmetry-breaking charge separation (SB-CS), excimer (EX) formation, singlet fission, and energy transfer. Recent studies of cofacial and slip-stacked perylene-3,4:9,10-bis(dicarboximide) (PDI) multimers demonstrate that slight variations in core substituents and H- or J-type aggregation can determine whether the system follows an SB-CS pathway or an EX one. However, questions regarding the relative importance of structural properties and molecular vibrations in driving the excited-state dynamics remain. Here, we use a combination of two-dimensional electronic spectroscopy, femtosecond stimulated Raman spectroscopy, and quantum chemistry computations to compare the photophysics of two PDI dimers. The dimer with 1,7-bis(pyrrolidin-1′-yl) substituents (5PDI2) undergoes ultrafast SB-CS from a photoexcited mixed state, while the dimer with bis-1,7-(3′,5′-di-t-butylphenoxy) substituents (PPDI2) rapidly forms an EX state. Examination of their quantum beating features reveals that SB-CS in 5PDI2 is driven by the collective vibronic coupling of two or more excited-state vibrations. In contrast, we observe signatures of low-frequency vibrational coherence transfer during EX formation by PPDI2, which aligns with several previous studies. We conclude that key electronic and structural differences between 5PDI2 and PPDI2 determine their markedly different photophysics.

Chemistry↗
DOE OSTI2024

Spectral broadening and vibronic dynamics of the S2 state of canthaxanthin in the orange carotenoid protein

We have performed a series of broadband multidimensional electronic spectroscopy experiments to probe the electronic and vibrational dynamics of the canthaxanthin chromophore of the Orange Carotenoid Protein (OCP) from Synechocystis sp. PCC 6803 in its photoactivated red state, OCPR. Cross-peaks observed below the diagonal of the two-dimensional electronic spectrum indicate that absorption transitions prepare the bright S2 state of the ketocarotenoid canthaxanthin near to a sequence of conical intersections, allowing passage to the dark S1 state via the Sx intermediate in <50 fs. Rapid damping of excited-state coherent wavepacket motions suggests that the branching coordinates of the conical intersections include out-of-plane deformation and C=C stretching coordinates of the π-conjugated isoprenoid backbone. The unusual proximity of the Franck–Condon S2 state structure to the conical intersections with Sx and S1 suggests that the protein surroundings of canthaxanthin prepare it to function as an excitation energy trap in the OCPR–phycobilisome complex. Numerical simulations using the multimode Brownian oscillator model demonstrate that the ground-state absorption spectrum of OCPR overlaps with the fluorescence emission spectrum of allophycocyanin due to spectral broadening derived especially from the intramolecular motions of the canthaxanthin chromophore in its binding site.

Yang, Kunwei↗
DOE OSTI2024

Learning linear optical circuits with coherent states

We analyze the energy and training data requirements for supervised learning of an M-mode linear optical circuit by minimizing an empirical risk defined solely from the action of the circuit on coherent states. When the linear optical circuit acts non-trivially only on k < M unknown modes (i.e. a linear optical k-junta), we provide an energy-efficient, adaptive algorithm that identifies the junta set and learns the circuit. We compare two schemes for allocating a total energy, E, to the learning algorithm. In the first scheme, each of the T random training coherent states has energy E/T. In the second scheme, a single random MT-mode coherent state with energy E is partitioned into T training coherent states. The latter scheme exhibits a polynomial advantage in training data size sufficient for convergence of the empirical risk to the full risk due to concentration of measure on the $(2MT-1)$-sphere. Specifically, generalization bounds for both schemes are proven, which indicate that for ε-approximation of the full risk by the empirical risk with high probability, $O(E^{2/3}M^{2/3}/\epsilon^{2/3})$ training states are sufficient for the first scheme and $O(E^{1/3}M^{1/3}/\epsilon^{2/3})$ training states are sufficient for the second scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗