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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

State Machine Operation of Complex Systems

Operation of complex systems which depend on one or more other systems with many process variables often operate in more than one state. For each state there may be a variety of parameters of interest, and for each of these, one may require different alarm limits, different archiving needs, and have different critical parameters. Relying on operators to reliably change 10s-1000s of parameters for each system for each state is unreasonable. Not changing these parameters results in alarms being ignored or disabled, critical changes missed, and/or possible data archiving problems. To reliably manage the operation of complex systems, such as cryomodules (CMs), Fermilab is implementing state machines for each CM and an over-arching state machine for the PIP-II superconducting linac (SCL). The state machine transitions and operating parameters are stored/restored to/from a configuration database. Proper implementation of the state machines will not only ensure safe and reliable operation of the CMs, but will help ensure reliable data quality. A description of PIP-II SCL, details of the state machines, and lessons learned from limited use of the state machines in recent CM testing will be discussed.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

State Machine Operation of Complex Systems

Operation of complex systems which depend on one or more other systems with many process variables often operate in more than one state. For each state there may be a variety of parameters of interest, and for each of these, one may require different alarm limits, different archiving needs, and have different critical parameters. Relying on operators to reliably change 10s-1000s of parameters for each system for each state is unreasonable.Not changing these parameters results in alarms being ignored or disabled, critical changes missed, and/or possible data archiving problems.To reliably manage the operation of complex systems, such as cryomodules (CMs), Fermilab is implementing state machines for each CM and an over-arching state machine for the PIP-II superconducting linac (SCL). The state machine transitions and operating parameters are stored/restored to/from a configuration database. Proper implementation of the state machines will not only ensure safe and reliable operation of the CMs, but will help ensure reliable data quality. A description of PIP-II SCL, details of the state machines, and lessons learned from limited use of the state machines in recent CM testing will be discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

State Machine Operation of Complex Systems

Operation of complex systems which depend on one, or more, sub-systems with many process variables often operate in more than one state. For each state there may be a variety of parameters of interest, and for each of these, one may require different alarm limits, different archiving needs, and have different critical parameters. Relying on operators to reliably change 102-105 parameters for each system for each state is unreasonable. Not changing these parameters results in alarms being ignored or disabled, critical changes missed, and/or data archiving inefficiencies. To reliably manage the operation of complex systems, such as cryomodules (CMs), Fermilab is implementing state machines for each CM and an over-arching state machine for the PIP-II superconducting LINAC (SCL). The state machine transitions and operating parameters are stored/restored to/from a configuration database. Proper implementation of the state machines will not only ensure safe and reliable operation of the CMs, but will help ensure reliable data quality. A description of PIP-II SCL, details of the state machines, and plans for imminent use the state machines for CM testing will be discussed.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Carbon and energy cost impacts of electrification of space heating with heat pumps in the US

In order to meet climate goals, it will be necessary to significantly reduce the greenhouse gases emitted by homes. A key factor in the US is to reduce the on-site combustion of fossil fuels for heating end-uses and to replace this with use of electric heat pump technologies connected to a low-carbon grid. The replacement of natural gas furnaces with electric heat pumps is a key home decarbonization strategy. However, the potential for space heating electrification to reduce greenhouse gas emissions depends on the carbon dioxide equivalent (CO 2 e) content of the electricity used by the heat pump. This varies considerably depending on the source of electricity, with large state to state variability. Furthermore, household energy costs are likely to be impacted by the electrification of space heating, because retail energy prices for both natural gas and electricity in each state vary by factors of seven and four, respectively. Contractors, energy programs, government and building code officials, as well as consumers need clear indications of the likely CO 2 e and energy cost impacts of proposed electrification projects, because these will affect decarbonization choices and rationales around scaled heating electrification. Government and utility programs also need to be aware of the likely outcomes of any supported/incentivized measures. Here, in this paper, we investigate these effects by looking at new metrics to analyze the change in CO 2 e emitted and the cost to meet home heating loads when switching from a natural gas furnace to a heat pump for the contiguous 48 states of the mainland US.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Editorial: Applications of spectroscopy and chemometrics in nuclear materials analysis

Optical analysis techniques, including spectroscopy and image analysis, have many advantages when applied to the study of nuclear materials. They require small sample sizes, can be performed remotely, and can be proceduralized through consistent practice. Most importantly, they provide a wealth of information by generating multivariate data. For example, ultraviolet–visible–near-infrared absorbance spectroscopy of actinides in aqueous and organic solutions is dependent on the oxidation state, anionic complexation, and temperature. These variables are important for solution-based separation processes, and sensitivity to these factors, combined with online monitoring, can drive the efficiency and control of these processes. The morphology and chemical composition of actinide particles can also provide a vital clue to the mechanisms by which the particles were formed, providing forensic information on the origins of the particles.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Mobility, Energy, and Electric Vehicle Typology for New York State

Mobility patterns, technology adoption and associated energy outcomes vary tremendously across settlement types. This paper explores how a highly geographically resolved exploration of the social, economic, techno-infrastructural and environmental domains of New York State is key to understanding observed variations in transportation technology adoption and associated mobility and energy outcomes. Current socioeconomic and mobility data sets at the census block group level are integrated in a hierarchical clustering approach to show how variations in mobility and energy outcomes are shaped by these domains - which may enhance progress on investments, or effectively inform planning and other decisions for state-wide goals. The clustering produces four settlement types to predict dependent variables of electric vehicle (EV) adoption rates, commute mode, vehicle fuel economy, and vehicles per household. This typology shows EV adoption rates among the core urban population, which is wealthy and highly-educated, are high - 3 EVs/1000 vehicles versus 1 EV/1000 vehicles among the urban working class. Commuting mode is closely linked with population and employment density - more than 90% of core urbanites use transit or active modes, compared with only 22% of suburbanites and 17% of rural residents. Household vehicle ownership also varies, with 2 vehicles per household in rural areas and only 0.5 in core urban settings. Important findings on differences among the rural, suburban, urban, and urban core settlement types suggest a need to explore how best to manage and anticipate very different types of services that may be supportive in achieving energy-efficient and affordable mobility systems state-wide.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Data-driven models of nonautonomous systems

Nonautonomous dynamical systems are characterized by time-dependent inputs, which complicates the discovery of predictive models describing the spatiotemporal evolution of the state variables of quantities of interest from their temporal snapshots. When dynamic mode decomposition (DMD) is used to infer a linear model, this difficulty manifests itself in the need to approximate the time-dependent Koopman operators. Our approach is to approximate the original nonautonomous system with a modified system derived via a local parameterization of the time-dependent inputs. The modified system comprises a sequence of local parametric systems, which are subsequently approximated by a parametric surrogate model using the DRIPS (dimension reduction and interpolation in parameter space) framework. The offline step of DRIPS relies on DMD to build a linear surrogate model, endowed with reduced-order bases for the observables mapped from training data. The online step interpolates on suitable manifolds to construct a sequence of iterative parametric surrogate models; the target/test parameter points on these manifolds are specified by a local parameterization of the test time-dependent inputs. Here, we use numerical experimentation to demonstrate the robustness of our method and compare its performance with that of deep neural networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Theoretical Kinetics Predictions for Reactions on the NH 2 O Potential Energy Surface

Recent modeling studies of ammonia oxidation, which are motivated by the prospective role of ammonia as a zero-carbon fuel, have indicated significant discrepancies among the existing literature mechanisms. In this study, high-level theoretical kinetics predictions have been obtained for reactions on the NH 2 O potential energy surface, including the NH 2 + O, HNO + H, and NH + OH reactions. These reactions have previously been highlighted as important reactions in NH 3 oxidation with high sensitivity and high uncertainty. The potential energy surface is explored with coupled cluster calculations, including large basis sets and high-level corrections to yield high-accuracy (~0.2 kcal/mol 2σ uncertainty) estimates of the stationary point energies. Variational transition state theory is used to predict the microcanonical rate constants, which are then incorporated in master equation treatments of the temperature- and pressure-dependent kinetics. For radical–radical channels, the microcanonical rates are obtained from variable reaction coordinate transition state theory implementing directly evaluated multireference electronic energies. The analysis yields predictions for the total rate constants as well as the branching ratios. We find that the NO + H 2 channel contributes 10% of the total NH 2 + O flux at combustion temperatures, although this channel is not included in modern NH 3 oxidation mechanisms. Modeling is used to illustrate the ramifications of these rate predictions on the kinetics of NH 3 oxidation and NO x formation. Finally, the present results for NH 2 + O are important for predicting the chain branching and formation of NO in the oxidation of NH 3 and thermal DeNO x .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

The influence of variability in meridional over turning on global ocean circulation

The Atlantic Meridional Overturning circulation (AMOC) is an important global scale circulation and changes in AMOC can induce significant regional and global climate impacts. In this work, we study the stability of AMOC and its influence on global ocean circulation and the surface climate though analyzing a set of sensitivity experiments using the Community Climate System Model version 1 (CESM1). Results show that a collapsed AMOC can induce changes in global ocean circulation, such as reduced (or reversed) Bering Strait transport, weakened Indonesia throughflow and Agulhas current, but strengthened Drake Passage transport. It also changes the global wind pattern and surface temperature, such as a seesaw-like surface temperature change between Northern and Southern Hemispheres, a weakening of Indian-Australia summer monsoon, a southward shift of the Southern ocean westerlies, etc. We also found that AMOC and the Pacific deep meridional overturning circulation (or PMOC) do not form a natural seesaw under modern day climate and geography. A collapsed AMOC (active PMOC) is not stable under modern conditions if there is no additional freshwater (salt) input in the subpolar North Atlantic (Pacific), suggesting that the modern mean state of AMOC (PMOC) does not depend on local haline forcing although its variability and changes do.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Comparing computational times for simulations when using PBPK model template and stand-alone implementations of PBPK models

Introduction We previously developed a PBPK model template that consists of a single model “superstructure” with equations and logic found in many physiologically based pharmacokinetic (PBPK) models. Using the template, one can implement PBPK models with different combinations of structures and features. Methods To identify factors that influence computational time required for PBPK model simulations, we conducted timing experiments using various implementations of PBPK models for dichloromethane and chloroform, including template and stand-alone implementations, and simulating four different exposure scenarios. For each experiment, we measured the required computational time and evaluated the impacts of including various model features (e.g., number of output variables calculated) and incorporating various design choices (e.g., different methods for estimating blood concentrations). Results We observed that model implementations that treat body weight and dependent quantities as constant (fixed) parameters can result in a 30% time savings compared with options that treat body weight and dependent quantities as time-varying. We also observed that decreasing the number of state variables by 36% in our PBPK model template led to a decrease of 20–35% in computational time. Other factors, such as the number of output variables, the method for implementing conditional statements, and the method for estimating blood concentrations, did not have large impacts on simulation time. In general, simulations with PBPK model template implementations of models required more time than simulations with stand-alone implementations, but the flexibility and (human) time savings in preparing and reviewing a model implemented using the PBPK model template may justify the increases in computational time requirements. Conclusion Our findings concerning how PBPK model design and implementation decisions impact computational speed can benefit anyone seeking to develop, improve, or apply a PBPK model, with or without the PBPK model template.

Bernstein, Amanda S.↗
DOE OSTI2021

Theoretical kinetics predictions for NH 2 + HO 2

Recent modeling studies of NH 3 oxidation, which are motivated by the prospective role of ammonia as a zero-carbon fuel, have indicated significant discrepancies between existing literature mechanisms. In this study high level theoretical kinetics predictions have been obtained for the reaction of NH 2 with HO 2 , which has previously been highlighted as an important reaction with high sensitivity and high uncertainty. The potential energy surface is explored with coupled cluster calculations including large basis sets and high-level corrections to yield high accuracy (~0.2 kcal/mol) estimates of the stationary point energies. Variational transition state theory is used to predict the microcanonical rate constants, which are then incorporated in master equation treatments of the temperature and pressure dependent kinetics. For the radical-radical channels, the microcanonical rates are obtained from variable reaction coordinate transition state theory implementing directly evaluated multireference electronic energies. The analysis yields predictions for the total rate constant as well as the branching to the NH 3 + O 2 , H 2 NO + OH, and HNO + H 2 O channels. Rate constants are also reported for the H 2 NO + OH reaction as they arise naturally from the analysis. The rate constant and branching fraction determined in this work for the NH 2 + HO 2 reaction deviate significantly from values used in most previous modeling studies. The fact that the main product channel is chain terminating, rather than propagating, has strong implications for modeling NH 3 ignition and oxidation, in particular at intermediate temperatures and elevated pressure.

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

Synthesis of ARM User Facility Surface Rainfall Datasets to Construct a Best Estimate Value Added Product (PrecipBE)

Surface precipitation measurements are essential for Earth system model (ESM) evaluation and understanding cloud processes. An ever-growing need for robust, temporally evolving, and easy-to-use statistical datasets provides motivation for a baseline ground-based precipitation properties data product. The U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility operates an extensive suite of precipitation instruments with various sensitivities and operating mechanisms, which render the decision of which instrument to use based on one or more fixed thresholds challenging and prone to errors and bias. Using a long-term instrument inter-comparison from a unique per-precipitation event perspective, rather than instantaneous sample comparison, we demonstrate that ARM rainfall-measuring instruments are generally consistent with each other at the statistical level. Inter-instrument deviations at the single event level can be large, especially for specific rainfall event properties such as maximum precipitation rates. A machine-learning (ML) analysis using a random forest regressor indicates that in some cases, depending on instrument, local site climatology, and/or specific deployment configuration, certain atmospheric state variables influence the measured quantities in an unpredictable manner. Thus, a-priori weighting of different instruments does not necessarily lead to more accurate and less biased synthesis of instrument data. These results motivate the design of the ARM precipitation best-estimate (PrecipBE) value-added product, which incorporates all valid precipitation data while considering data quality and other instrument limitations. PrecipBE consists of time series and tabular statistics datasets in an easy-to-use and insightful per-precipitation event format. It provides a large set of precipitation event properties supplemented with ancillary data from ARM datasets that correspond to the detected precipitation events. We describe the PrecipBE algorithm and demonstrate its use via the examination of a single-day output as well as a long-term trend analysis of precipitation events at the ARM Southern Great Plains (SGP) site, covering more than 30 years of data. The trend analysis tentatively suggests a long-term temporal tendency for mainly shorter and less intense precipitation events at the SGP site, but a long-term increase in annual rainfall by more than 36 mm (5 %) per decade. This rainfall trend is catalyzed primarily by more extreme event properties of relatively rare, intense precipitation events, with event total and 1 min maximum precipitation rate at a 1 year timeframe increasing up to 5 mm and 9 mm h −1 (several percent) per decade, respectively. While the currently available PrecipBE datasets (at https://adc.arm.gov/discovery/, last access: 8 December 2025) cover rainfall from multiple ARM deployments up to March 2025, PrecipBE is planned to be expanded to include solid-phase precipitation and will soon become an operational product with a several-day lag from real-time. We invite the ARM user community to leverage this new product and welcome user feedback to further enhance the dataset.

Silber, Israel [Pacific Northwest National Laborat↗
DOE OSTI2023

Seasonal forecasting skill for the High Mountain Asia region in the Goddard Earth Observing System

Seasonal variability of the global hydrologic cycle directly impacts human activities, including hazard assessment and mitigation, agricultural decisions, and water resources management. This is particularly true across the High Mountain Asia (HMA) region, where availability of water resources can change depending on local seasonality of the hydrologic cycle. Forecasting the atmospheric states and surface conditions, including hydrometeorologically relevant variables, at subseasonal-to-seasonal (S2S) lead times of weeks to months is an area of active research and development. NASA's Goddard Earth Observing System (GEOS) S2S prediction system has been developed with this research goal in mind. Here, we benchmark the forecast skill of GEOS-S2S (version 2) hydrometeorological forecasts at 1–3-month lead times in the HMA region, including a portion of the Indian subcontinent, during the retrospective forecast period, 1981–2016. To assess forecast skill, we evaluate 2 m air temperature, total precipitation, fractional snow cover, snow water equivalent, surface soil moisture, and terrestrial water storage forecasts against the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) and independent reanalysis data, satellite observations, and data fusion products. Anomaly correlation is highest when the forecasts are evaluated against MERRA-2 and particularly in variables with long memory in the climate system, likely due to the similar initial conditions and model architecture used in GEOS-S2S and MERRA-2. When compared to MERRA-2, results for the 1-month forecast skill range from an anomaly correlation of R anom =0.18 for precipitation to R anom =0.62 for soil moisture. Anomaly correlations are consistently lower when forecasts are evaluated against independent observations; results for the 1-month forecast skill range from R anom =0.13 for snow water equivalent to R anom =0.24 for fractional snow cover. We find that, generally, hydrometeorological forecast skill is dependent on the forecast lead time, the memory of the variable within the physical system, and the validation dataset used. Overall, these results benchmark the GEOS-S2S system's ability to forecast HMA hydrometeorology.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

A copula-based rank histogram ensemble filter

Serial ensemble filters implement triangular probability transport maps to reduce high-dimensional inference problems to sequences of state-by-state univariate inference problems. The univariate inference problems are solved by sampling posterior probability densities obtained by combining constructed prior densities with observational likelihoods according to Bayes' rule. Many serial filters in the literature focus on representing the marginal posterior densities of each state. However, rigorously capturing the conditional dependencies between the different univariate inferences is crucial to correctly sampling multidimensional posteriors. This work proposes a new serial ensemble filter, called the copula rank histogram filter (CoRHF), that seeks to capture the conditional dependency structure between variables via empirical copula estimates; these estimates are used to rigorously implement the triangular (state-by-state univariate) Bayesian inference. The success of the CoRHF is demonstrated on two-dimensional examples and the Lorenz'63 problem. A practical extension to the high-dimensional setting is developed by localizing the empirical copula estimation, and is demonstrated on the Lorenz'96 problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Cluster analysis of occupancy schedules in residential buildings in the United States

The energy performance of residential buildings significantly depends on the building occupants’ behavior, which can be highly variable. When the heating, ventilation and air conditioning (HVAC) system is controlled based on the presence or absence of occupants in a building, occupant behavior is of even further importance to its energy performance. In current practice, building energy simulation tools generally use a single occupancy profile to represent the building’s occupancy schedule, the schedule of which is considered to be the same, regardless of the type of household being modeled. Thus, there is significant potential for improvement to allow for more flexibility and accuracy in calculation of occupancy. The objective of this study is to assess the variations in the typical types of occupancy schedules followed by the U.S. population using cluster analysis. American Time Use Survey data, which statically represents the overall U.S. population’s activities, across 12 years (2006–2017), is used. The ATUS data is segregated into smaller groups based on age and weekday/weekend, then divided into activities that are considered “at home” and “away from home”, which are mapped to the presence or non-presence of occupants in the home. Cluster analysis is then used to identify common types of occupancy schedule patterns for each age group. Three main types of patterns are obtained from cluster analysis for each age group, which together represent approximately 88% of people in the United States. The output of the cluster analysis is further analyzed to evaluate the variation in characteristics, including the number of times leaving home, time of day when leaving the home, and the timespan of absence from the home. The results of this study provide detailed insights on how typical occupants in the United States spend their time in residential spaces which can be used to create occupancy profiles for residential buildings. Finally, these occupancy profiles could be utilized inform an assessment of the energy use impact of occupancy-based controls of energy consuming systems and technologies.

42 ENGINEERING↗
DOE OSTI2020

An Improved Fracture Mechanics-Informed Multiscale Thermomechanical Damage Model for Ceramic Matrix Composites

This paper extends recent work done by the authors in modeling length scale-dependent damage behavior of ceramic matrix composites (CMCs) to include effects of local anisotropy introduced by matrix cracking. This model captures scale-dependent damage initiation and propagation behavior of the brittle matrix by employing internal state variable (ISV) theory within a multiscale modeling framework to obtain damaged matrix stress/strain constitutive relationships at each length scale. The damage ISV captures the effects of matrix cracking and growth by using fracture mechanics and the self-consistent scheme to determine the reduced stiffness of the cracked matrix. Matrix cracks, which activate when stress intensity factors near manufacturing induced cavities exceed the fracture toughness of the material, are assumed to be transversely isotropic in the plane of the crack, and matrix anisotropy occurs when the damaged stiffness tensor is rotated from the crack plane to the global axes. The crack progression and temporal evolution of the damage ISV are governed by fracture mechanics and crack growth kinetics. The model effectively captures first matrix cracking, which is the first significant deviation from linear elasticity. The nonlinear predictive capabilities of the material model are demonstrated for monolithic silicon carbide (SiC) and a 2D woven five-harness satin (5HS) carbon fiber SiC matrix (C/SiC) CMC.

Skinner, Travis↗
DOE OSTI2023

Modeling dust mineralogical composition: sensitivity to soil mineralogy atlases and their expected climate impacts

Soil dust aerosols are a key component of the climate system, as they interact with short- and long-wave radiation, alter cloud formation processes, affect atmospheric chemistry and play a role in biogeochemical cycles by providing nutrient inputs such as iron and phosphorus. The influence of dust on these processes depends on its physicochemical properties, which, far from being homogeneous, are shaped by its regionally varying mineral composition. The relative amount of minerals in dust depends on the source region and shows a large geographical variability. However, many state-of-the-art Earth system models (ESMs), upon which climate analyses and projections rely, still consider dust mineralogy to be invariant. The explicit representation of minerals in ESMs is more hindered by our limited knowledge of the global soil composition along with the resulting size-resolved airborne mineralogy than by computational constraints. In this work we introduce an explicit mineralogy representation within the state-of-the-art Multiscale Online Nonhydrostatic AtmospheRe CHemistry (MONARCH) model. We review and compare two existing soil mineralogy datasets, which remain a source of uncertainty for dust mineralogy modeling and provide an evaluation of multiannual simulations against available mineralogy observations. Soil mineralogy datasets are based on measurements performed after wet sieving, which breaks the aggregates found in the parent soil. Our model predicts the emitted particle size distribution (PSD) in terms of its constituent minerals based on brittle fragmentation theory (BFT), which reconstructs the emitted mineral aggregates destroyed by wet sieving. Our simulations broadly reproduce the most abundant mineral fractions independently of the soil composition data used. Feldspars and calcite are highly sensitive to the soil mineralogy map, mainly due to the different assumptions made in each soil dataset to extrapolate a handful of soil measurements to arid and semi-arid regions worldwide. For the least abundant or more difficult-to-determine minerals, such as iron oxides, uncertainties in soil mineralogy yield differences in annual mean aerosol mass fractions of up to ~ 100 %. Although BFT restores coarse aggregates including phyllosilicates that usually break during soil analysis, we still identify an overestimation of coarse quartz mass fractions (above 2 µm in diameter). In a dedicated experiment, we estimate the fraction of dust with undetermined composition as given by a soil map, which makes up ~ 10 % of the emitted dust mass at the global scale and can be regionally larger. Changes in the underlying soil mineralogy impact our estimates of climate-relevant variables, particularly affecting the regional variability of the single-scattering albedo at solar wavelengths or the total iron deposited over oceans. All in all, this assessment represents a baseline for future model experiments including new mineralogical maps constrained by high-quality spaceborne hyperspectral measurements, such as those arising from the NASA Earth Surface Mineral Dust Source Investigation (EMIT) mission.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Studying phonon coherence with a quantum sensor

Nanomechanical oscillators offer numerous advantages for quantum technologies. Their integration with superconducting qubits shows promise for hardware-efficient quantum error-correction protocols involving superpositions of mechanical coherent states. Limitations of this approach include mechanical decoherence processes, particularly two-level system (TLS) defects, which have been widely studied using classical fields and detectors. In this manuscript, we use a superconducting qubit as a quantum sensor to perform phonon number-resolved measurements on a piezoelectrically coupled phononic crystal cavity. This enables a high-resolution study of mechanical dissipation and dephasing in coherent states of variable size ($\overline{n}$ ≃ 1 – 10 phonons). We observe nonexponential relaxation and state size-dependent reduction of the dephasing rate, which we attribute to TLS. Using a numerical model, we reproduce the dissipation signatures (and to a lesser extent, the dephasing signatures) via emission into a small ensemble (N = 5) of rapidly dephasing TLS. Our findings comprise a detailed examination of TLS-induced phonon decoherence in the quantum regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗