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Two-dimensional terahertz spectroscopy (2DTS) is a low-frequency analogue of two-dimensional optical spectroscopy that is rapidly maturing as a probe of a wide variety of condensed matter systems. However, a persistent problem of 2DTS is the long experimental acquisition times, preventing its broader adoption. A potential solution, requiring no increase in experimental complexity, is signal reconstruction via compressive sensing. In this work, we apply the sparse exponential mode analysis (SEMA) technique to 2DTS of a cuprate superconductor. We benchmark the performance of the algorithm in reconstructing the terahertz nonlinearities and find that SEMA reproduces the asymmetric photon echo lineshapes with as low as a 10% sampling rate and reaches the reconstruction noise floor with beyond 20-30% sampling rate. The success of SEMA in reproducing such subtle, asymmetric lineshapes confirms compressive sensing as a general method to accelerate 2DTS and multidimensional spectroscopies more broadly.

Multidimensional spectroscopy has a long history originating from nuclear magnetic resonance, and has now found widespread application at infrared and optical frequencies as well. However, the energy scales of traditional multidimensional probes have been ill-suited for studying quantum materials. Recent technological advancements have now enabled extension of these multidimensional techniques to the terahertz frequency range, in which collective excitations of quantum materials are typically found. This Perspective introduces the technique of two-dimensional terahertz spectroscopy (2DTS) and the unique physics of quantum materials revealed by 2DTS spectra, accompanied by a selection of the rapidly expanding experimental and theoretical literature. While 2DTS has so far been primarily applied to quantum materials at equilibrium, we provide an outlook for its application towards understanding their dynamical non-equilibrium states and beyond.

Recently, two-dimensional terahertz spectroscopy (2DTS) has attracted increasing attention for studying complex solids. A number of recent studies have applied 2DTS either with long pulses or away from any material resonances, situations that yield unconventional 2DTS spectra that are often difficult to interpret. Here, we clarify the generic origins of observed spectral features by examining 2DTS spectra of ZnTe, a model system with a featureless optical susceptibility at low terahertz frequencies. These results also reveal possible artifacts that may arise from electro-optic sampling in collinear 2DTS experiments, including the observation of spurious rectified or second harmonic signals.

Two-dimensional terahertz spectroscopy (2DTS), a terahertz analogue of nuclear magnetic resonance, is a new technique poised to address many open questions in complex condensed matter systems. The conventional theoretical framework used ubiquitously for interpreting multidimensional spectra of discrete quantum level systems is, however, insufficient for the continua of collective excitations in strongly correlated materials. Here, we develop a theory for 2DTS of a model collective excitation, the Josephson plasma resonance in layered superconductors. Starting from a mean-field approach at temperatures well below the superconducting phase transition, we obtain expressions for the multidimensional nonlinear responses that are amenable to intuition derived from the conventional single-mode scenario. We then consider temperatures near the superconducting critical temperature $T_c$, where dynamics beyond mean-field become important and conventional intuition fails. As fluctuations proliferate near $T_c$, the dominant contribution to nonlinear response comes from an optical parametric drive of counter-propagating Josephson plasmons, which gives rise to 2D spectra that are qualitatively different from the mean-field predictions. As such, and in contrast to one-dimensional spectroscopy techniques, such as third harmonic generation, 2DTS can be used to directly probe thermally excited finite-momentum plasmons and their interactions. Our theory provides a clear interpretation of recent 2DTS measurements on cuprates, and we discuss implications beyond the present context of Josephson plasmons.

Multidimensional coherent spectroscopy is a powerful tool to characterize nonlinear optical response functions. Typically, multidimensional spectra are interpreted via a perturbative framework that straightforwardly provides intuition into the density matrix dynamics that give rise to specific spectral features. When the goal is to characterize system coupling to a thermal bath however, the perturbative formalism becomes unwieldy and yields less intuition. Here, we extend an approach developed by Vagov et al. to provide an exact expression for multidimensional spectra of a spin-boson Hamiltonian up to arbitrary order of electric field interaction. We demonstrate the utility of this expression by modeling polaron formation and coherent exciton-phonon coupling in quantum dots, which strongly agree with experiment.

Inhomogeneities play a crucial role in determining the properties of quantum materials. Yet methods that can measure these inhomogeneities are few, and apply to only a fraction of the relevant microscopic phenomena. For example, the electronic properties of cuprate materials are known to be inhomogeneous over nanometer length scales, although questions remain about how such disorder influences supercurrents and their dynamics. Here, two-dimensional terahertz spectroscopy is used to study interlayer superconducting tunneling in near-optimally-doped La1.83Sr0.17CuO4. We isolate a 2 THz Josephson echo signal with which we disentangle intrinsic lifetime broadening from extrinsic inhomogeneous broadening. We find that the Josephson plasmons are only weakly inhomogeneously broadened, with an inhomogeneous linewidth that is three times smaller than their intrinsic lifetime broadening. This extrinsic broadening remains constant up to 0.7Tc, above which it is overcome by the thermally-increased lifetime broadening. Crucially, the effects of disorder on the Josephson plasma resonance are nearly two orders of magnitude smaller than the in-plane variations in the superconducting gap in this compound, which have been previously documented using Scanning Tunnelling Microscopy (STM) measurements. Hence, even in the presence of significant disorder in the superfluid density, the finite frequency interlayer charge fluctuations exhibit dramatically reduced inhomogeneous broadening. We present a model that relates disorder in the superfluid density to the observed lifetimes.

We revisit the problem of designing scalable protocols for private statistics and private federated learning when each device holds its private data. Locally differentially private algorithms require little trust but are (provably) limited in their utility. Centrally differentially private algorithms can allow significantly better utility but require a trusted curator. This gap has led to significant interest in the design and implementation of simple cryptographic primitives, that can allow central-like utility guarantees without having to trust a central server. Our first contribution is to propose a new primitive that allows for efficient implementation of several commonly used algorithms, and allows for privacy accounting that is close to that in the central setting without requiring the strong trust assumptions it entails. {\em Shuffling} and {\em aggregation} primitives that have been proposed in earlier works enable this for some algorithms, but have significant limitations as primitives. We propose a {\em Samplable Anonymous Aggregation} primitive, which computes an aggregate over a random subset of the inputs and show that it leads to better privacy-utility trade-offs for various fundamental tasks. Secondly, we propose a system architecture that implements this primitive and perform a security analysis of the proposed system. Our design combines additive secret-sharing with anonymization and authentication infrastructures., Comment: 34 pages

Privately learning statistics of events on devices can enable improved user experience. Differentially private algorithms for such problems can benefit significantly from interactivity. We argue that an aggregation protocol can enable an interactive private federated statistics system where user's devices maintain control of the privacy assurance. We describe the architecture of such a system, and analyze its security properties.

Spontaneous low-frequency oscillations on the order of several hertz are the drivers of many crucial processes in nature. From bacterial swimming to mammal gaits, the conversion of static energy inputs into slowly oscillating electrical and mechanical power is key to the autonomy of organisms across scales. However, the fabrication of slow artificial oscillators at micrometre scales remains a major roadblock towards the development of fully-autonomous microrobots. Here, we report the emergence of a low-frequency relaxation oscillator from a simple collective of active microparticles interacting at the air-liquid interface of a peroxide drop. Their collective oscillations form chemomechanical and electrochemical limit cycles that enable the transduction of ambient chemical energy into periodic mechanical motion and on-board electrical currents. Surprisingly, the collective can oscillate robustly even as more particles are introduced, but only when we add a single particle with modified reactivity to intentionally break the system's permutation symmetry. We explain such emergent order through a novel thermodynamic mechanism for asymmetry-induced order. The energy harvested from the stabilized system oscillations enables the use of on-board electronic components, which we demonstrate by cyclically and synchronously driving microrobotic arms. This work highlights a new strategy for achieving low-frequency oscillations at the microscale that are otherwise difficult to observe outside of natural systems, paving the way for future microrobotic autonomy., Comment: Main text contains 13 pages and 4 figures. Supplementary information contains 21 pages and 16 supplementary figures. For associated supplementary videos, see https://www.dropbox.com/sh/2bwenfiifqnkx3i/AABcLH2mVQ_8uPxnnbzu4rGWa?dl=0

This report describes four measures of the price of undergraduate education in the 2015-16 academic year: total price of attendance (tuition and living expenses), net price of attendance after all grants, out-of-pocket net price after all financial aid, and out-of-pocket net price after all aid excluding student loans. Estimates are based on the 2015-16 National Postsecondary Student Aid Study (NPSAS:16), a nationally representative study of students enrolled in postsecondary institutions in the 50 states, the District of Columbia, and Puerto Rico. Estimates are compared across four institution types: public 2-year institutions, public 4-year institutions, for-profit institutions at all levels (less-than-2-year, 2-year, and 4-year), and private nonprofit 4-year institutions. Prices are also presented separately for dependent and independent students, with these estimates being further separated by income level and institution control and level.

Lead-halide perovskite nanocrystals (PNCs) exhibit unique optoelectronic properties, many of which originate from a purported bright-triplet exciton fine-structure. A major impediment to measuring this fine-structure is inhomogeneous spectral broadening, which has limited most experimental studies to single-nanocrystal spectroscopies. It is shown here that the linearly-polarized single-particle selection rules in PNCs are preserved in nonlinear spectroscopies of randomly-oriented ensembles. Simulations incorporating rotational-averaging demonstrate that techniques such as transient absorption and two-dimensional coherent spectroscopy are capable of resolving exciton fine-structure in PNCs, even in the presence of inhomogeneous broadening and orientation disorder.

Polymers that extend covalently in two dimensions have attracted recent attention as a means of combining the mechanical strength and in-plane energy conduction of conventional two-dimensional (2D) materials with the low densities, synthetic processability, and organic composition of their one-dimensional counterparts. Efforts to date have proven successful in forms that do not allow full realization of these properties, such as polymerization at flat interfaces or fixation of monomers in immobilized lattices. A frequently employed synthetic approach is to introduce microscopic reversibility, at the cost of bond stability, to achieve 2D crystals after extensive error correction. Herein we demonstrate a synthetic route to 2D irreversible polycondensation directly in the solution phase, resulting in covalently bonded 2D polymer platelets that are chemically stable and highly processable. Further fabrication offers highly oriented, free-standing films which exhibit exceptional 2D elastic modulus and yield strength at 50.9 +- 15.0 GPa and 0.976 +- 0.113 GPa, respectively. Platelet alignment is evidenced by polarized photoluminescence centered at 580 and 680 nm from different dipole transitions. This new synthetic route provides opportunities for 2D polymers in applications ranging from composite structures to molecular sieving membranes., Comment: 13 pages, 4 figures

Perovskite nanoplatelets possess extremely narrow absorption and emission linewidths, which are crucial characteristics for many optical applications. However, their underlying intrinsic and extrinsic line-broadening mechanisms are poorly understood. Here, we apply multi-dimensional coherent spectroscopy to determine the homogeneous line-broadening of colloidal perovskite nanoplatelet ensembles. We demonstrate control of not only their intrinsic linewidths, but also control of various broadening mechanisms by tuning the platelet geometry. Remarkably, we find that decreasing nanoplatelet thickness by a single polyhedral layer results in a 2-fold reduction of the inhomogeneous linewidth and a 3-fold reduction of the intrinsic homogeneous linewidth to the sub-meV regime. In addition, our measurements suggest homogeneously broadened exciton resonances in 3-layer (but not necessarily 4-layer) nanoplatelets at room-temperature.

Many applications of nitrogen-vacancy (NV) centers in diamond crucially rely on a spectrally narrow and stable optical zero-phonon line transition. Though many impressive proof-of-principle experiments have been demonstrated, much work remains in engineering NV centers with spectral properties that are sufficiently robust for practical implementation. To elucidate the mechanisms underlying their interactions with the environment, we apply multi-dimensional coherent spectroscopy to an NV center ensemble in bulk diamond at cryogenic temperatures. Our spectra reveal thermal dephasing due to quasi-localized vibrational modes as well as ultrafast spectral diffusion on the picosecond timescale. The intrinsic, ensemble-averaged homogeneous linewidth is found to be in the tens of GHz range by extrapolating to zero temperature. We also observe a temperature-dependent Stark splitting of the excited state manifold, relevant to NV sensing protocols.

Incipient anomalies present milder symptoms compared to severe ones, and are more difficult to detect and diagnose due to their close resemblance to normal operating conditions. The lack of incipient anomaly examples in the training data can pose severe risks to anomaly detection methods that are built upon Machine Learning (ML) techniques, because these anomalies can be easily mistaken as normal operating conditions. To address this challenge, we propose to utilize the uncertainty information available from ensemble learning to identify potential misclassified incipient anomalies. We show in this paper that ensemble learning methods can give improved performance on incipient anomalies and identify common pitfalls in these models through extensive experiments on two real-world datasets. Then, we discuss how to design more effective ensemble models for detecting incipient anomalies., Comment: Submitted to Transactions on Cyber-Physical Systems for Special Issue on AI and Cyber-Physical Systems

Vacancy centers in diamond have proven to be a viable solid-state platform for quantum coherent opto-electronic applications. Among the variety of vacancy centers, silicon-vacancy (SiV) centers have recently attracted much attention as an inversion-symmetric system that is less susceptible to electron-phonon interactions. Nevertheless, phonon-mediated processes still degrade the coherent properties of SiV centers, however characterizing their electron-phonon coupling is extremely challenging due to their weak spectroscopic signatures and remains an open experimental problem. In this paper we theoretically investigate signatures of electron-phonon coupling in simulated linear and nonlinear spectra of SiV centers. We demonstrate how even extremely weak electron-phonon interactions, such as in SiV centers, may be completely characterized via nonlinear spectroscopic techniques and even resolved between different fine-structure transitions.

Advances in opto-electronics require the development of materials with novel and engineered characteristics. A class of materials that has garnered tremendous interest is metal-halide perovskites, stimulated by meteoric increases in photovoltaic efficiencies of perovskite solar cells. In addition, recent advances have applied perovskite nanocrystals (NCs) in light-emitting devices. It was discovered recently that, for cesium lead-halide perovskite NCs, their unusually efficient light-emission may be due to a unique excitonic fine-structure composed of three bright triplet states that minimally interact with a proximal dark singlet state. To study this fine-structure without isolating single NCs, we use multi-dimensional coherent spectroscopy at cryogenic temperatures to reveal coherences involving triplet states of a CsPbI$_3$ NC ensemble. Picosecond timescale dephasing times are measured for both triplet and inter-triplet coherences, from which we infer a unique exciton fine-structure level-ordering comprised of a dark state energetically positioned within the bright triplet manifold.

Preparing youth with disabilities for successful futures is a longstanding priority for policymakers and educators. This priority is reflected in the federal Individuals with Disabilities Education Act (IDEA), last updated in 2004. This brief summarizes findings from surveys of secondary school youth with disabilities and their parents collected for the National Longitudinal Transition Study (NLTS) 2012, which is being conducted as part of an assessment of IDEA.

For more than 40 years, policymakers have committed to supporting the education of students with disabilities, who have grown as a share of all students in the United States. Beginning with landmark legislation in 1975, the U.S. Congress mandated that students with disabilities have access to a free and appropriate public education and provided funds to school districts nationwide to help serve them. Since then, the legislation has been updated six times, most recently in the 2004 Individuals with Disabilities Education Act (IDEA), which emphasized helping youth prepare for postsecondary education, careers, and independent living. These and other changes in the educational, social, and economic landscapes may have affected all youth, raising interest in how the characteristics, experiences, and challenges of youth with disabilities have changed over time. The National Longitudinal Transition Study (NLTS) 2012 provides updated information on youth with disabilities in light of these changes, to inform efforts to address their needs. Sponsored by the U.S. Department of Education under a congressional mandate to study IDEA 2004 and the students it serves, the NLTS 2012 is the third in a series of such studies. It describes the backgrounds of secondary school youth and their functional abilities, activities in school and with friends, academic supports received from schools and parents, and preparation for life after high school. Through surveys in 2012 and 2013, the study collected data on a nationally representative set of nearly 13,000 students--mostly those with an individualized education program (IEP) and expected to receive special education services. The study also includes students without an IEP, who either have no identified disability or who have an impairment that does not qualify them for special education but allows them to receive accommodations through a 504 plan under the Rehabilitation Act, another federal law pertaining to the rights and needs of youth with disabilities. This third volume of findings from the NLTS 2012 uses data from all three studies in the NLTS series to examine how the characteristics and experiences of youth in special education have changed over time, overall and for each of 12 disability groups defined by IDEA 2004. The trends from 2003 to 2012 for youth with an IEP ages 15 to 18 suggests several key points: (1) Youth with an IEP are more likely than a decade ago to live in households that face economic challenges; (2) Youth with an IEP are about as healthy and able to perform some typical tasks independently as in the past, but they are also more likely to use behavioral medicines and have trouble understanding others; (3) Engagement in school and extracurricular activities among youth with an IEP increased in the past decade, whereas the prevalence of negative events such as grade retention, suspensions, and expulsions was little changed; (4) Youth with an IEP are more likely than in the past to receive supports at school but less likely to get them at home; and (5) Participation in key transition activities by youth with an IEP and their parents has declined, although they are just as likely to have gone to an IEP meeting. [For "Preparing for Life after High School: The Characteristics and Experiences of Youth in Special Education. Findings from The National Longitudinal Transition Study 2012. Volume 3: Comparisons over Time. Full Report. NCEE 2018-4007," see ED580934. For "Preparing for Life after High School: The Characteristics and Experiences of Youth in Special Education. Findings from the National Longitudinal Transition Study 2012. Volume 2: Comparisons across Disability Groups. Executive Summary. NCEE 2017-4019," see ED573353.]

For more than 40 years, policymakers have committed to supporting the education of students with disabilities, who have grown as a share of all students in the United States (Snyder, de Brey, & Dillow, 2016). Beginning with landmark legislation in 1975, the U.S. Congress mandated that students with disabilities have access to a free and appropriate public education and provided funds to school districts nationwide to help serve them. Since then, the legislation has been updated six times, most recently in the 2004 Individuals with Disabilities Education Act (IDEA), which emphasized helping youth prepare for postsecondary education, careers, and independent living. These and other changes in the educational, social, and economic landscapes may have affected all youth, raising interest in how the characteristics, experiences, and challenges of youth with disabilities have changed over time. The National Longitudinal Transition Study (NLTS) 2012 provides updated information on youth with disabilities in light of these changes, to inform efforts to address their needs. Sponsored by the U.S. Department of Education under a congressional mandate to study IDEA 2004 and the students it serves, the NLTS 2012 is the third in a series of such studies. It describes the backgrounds of secondary school youth and their functional abilities, activities in school and with friends, academic supports received from schools and parents, and preparation for life after high school. Through surveys in 2012 and 2013, the study collected data on a nationally representative set of nearly 13,000 students--mostly those with an individualized education program (IEP) and expected to receive special education services. The study also includes students without an IEP, who either have no identified disability or who have an impairment that does not qualify them for special education but allows them to receive accommodations through a 504 plan under the Rehabilitation Act, another federal law pertaining to the rights and needs of youth with disabilities. This third volume of findings from the NLTS 2012 uses data from all three studies in the NLTS series to examine how the characteristics and experiences of youth in special education have changed over time, overall and for each of 12 disability groups defined by IDEA 2004. Most of the analyses examine trends for in-school youth ages 15 to 18 from 2003 to 2012, using the NLTS2 and NLTS 2012. When comparable data are available from the NLTS, the volume also examines trends starting in 1987 for youth ages 15 to 18 and youth ages 19 to 21 who were still enrolled in high school. The trends from 2003 to 2012 for youth with an individualized education program (IEP) ages 15 to 18 suggests several key points: (1) Youth with an IEP are more likely than a decade ago to live in households that face economic challenges; (2) Youth with an IEP are about as healthy and able to perform some typical tasks independently as in the past, but they are also more likely to use behavioral medicines and have trouble understanding others; (3) Engagement in school and extracurricular activities among youth with an IEP increased in the past decade, whereas the prevalence of negative events such as grade retention, suspensions, and expulsions was little changed; (4) Youth with an IEP are more likely than in the past to receive supports at school but less likely to get them at home; and (5) Participation in key transition activities by youth with an IEP and their parents has declined, although they are just as likely to have gone to an IEP meeting. [For "Preparing for Life after High School: The Characteristics and Experiences of Youth in Special Education. Findings from The National Longitudinal Transition Study 2012. Volume 3: Comparisons over Time. Executive Summary. NCEE 2018-4008," see ED580936. For "Preparing for Life after High School: The Characteristics and Experiences of Youth in Special Education. Findings from the National Longitudinal Transition Study 2012. Volume 2: Comparisons across Disability Groups. Full Report. NCEE 2017-4018," see ED573334.]

Atomic vacancy defects in single unit cell thick hexagonal boron nitride are of significant interest because of their photophysical properties, including single-photon emission, and promising applications in quantum communication and computation. The spectroscopic assignment of emission energies to specific atomic vacancies within the triangular lattice is confounded by the exponential scaling of defect candidates with the number of removed atoms. Herein, we collect more than 1000 spectra consisting of single, isolated zero-phonon lines between 1.69 and 2.25 eV, observing 6 quantized zero-phonon lines arising from hexagonal boron nitride vacancies. A newly developed computational framework for isomer cataloguing significantly narrows the number of candidate vacancies. Direct lattice imaging of hexagonal boron nitride, electronic structure calculations, and subsequent boric acid etching are used to definitively assign the 6 features. Systematic chemical etching supports the assignment by demonstrating the sequence of growth of successively larger vacancy centres from smaller ones, with the defects including a single B vacancy and a 16-atom triangular defect. These features exhibit a range of emission lifetimes from 1 to 6 ns, and phonon sidebands offset by the dominant lattice phonon in hexagonal boron nitride near 1370 cm-1. This assignment should significantly advance the solid-state chemistry and photophysics of such vacancy emitters., Comment: 28 pages, 5 figures, and 40 pages of supplementary information

The band-gaps of CsPbI$_3$ perovskite nanocrystals are measured by absorption spectroscopy at cryogenic temperatures. Anomalous band-gap shifts are observed in CsPbI$_3$ nanocubes and nanoplatelets, which are modeled accurately by band-gap renormalization due to lattice vibrational modes. We find that decreasing dimensionality of the CsPbI$_3$ lattice in nanoplatelets greatly reduces electron-phonon coupling, and dominant out-of-plane quantum confinement results in a homogeneously broadened absorption lineshape down to cryogenic temperatures. An absorption tail forms at low-temperatures in CsPbI$_3$ nanocubes, which we attribute to shallow defect states positioned near the valence band-edge.