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Since the birth of quantum optics, the measurement of quantum states of nonclassical light has been of tremendous importance for advancement in the field. To date, conventional detectors such as photomultipliers, avalanche photodiodes, and superconducting nanowires, all rely at their core on linear excitation of bound electrons with light, posing fundamental restrictions on the detection. In contrast, the interaction of free electrons with light in the context of quantum optics is highly nonlinear and offers exciting possibilities. The first experiments that promoted this direction appeared over the past decade as part of photon-induced nearfield electron microscopy (PINEM), wherein free electrons are capable of high-order multi-photon absorption and emission. Here we propose using free electrons for quantum-optical detection of the complete quantum state of light. We show how the precise control of the electron before and after its interaction with quantum light enables to extract the photon statistics and implement full quantum state tomography using PINEM. This technique can reach sub-attosecond time resolutions, measure temporal coherence of any degree (e.g., g(1), g(2)), and simultaneously detect large numbers of photons with each electron. Importantly, the interaction of the electron with light is non-destructive, thereby leaving the photonic state (modified by the interaction) intact, which is conceptually different from conventional detectors. By using a pulse of multiple electrons, we envision how PINEM quantum detectors could achieve a single-shot measurement of the complete state of quantum light, even for non-reproducible emission events. Altogether, our work paves the way to novel kinds of photodetectors that utilize the ultrafast duration, high nonlinearity, and non-destructive nature of electron-light interactions., Comment: 5 figs, 20 pages + Supplementary Material

Gamma-ray bursts (GRBs) are highly variable and exhibit strong spectral evolution. In particular, the emission properties vary from pulse to pulse in multipulse bursts. Here we present a time-resolved Bayesian spectral analysis of a compilation of GRB pulses observed by the {\it Fermi}/Gamma-ray Burst Monitor. The pulses are selected to have at least four timebins with a high statistical significance, which ensures that the spectral fits are well determined and that spectral correlations can be established. The sample consists of 39 bursts, 117 pulses, and 1228 spectra. We confirm the general trend that pulses become softer over time, with mainly the low-energy power-law index $\alpha$ becoming smaller. A few exceptions to this trend exist, with the hardest pulse occurring at late times. The first pulse in a burst is clearly different from the later pulses; three-fourths of them violate the synchrotron line of death, while around half of them significantly prefer photospheric emission. These fractions decrease for subsequent pulses. We also find that in two-thirds of the pulses, the spectral parameters ($\alpha$ and peak energy) track the light-curve variations. This is a larger fraction compared to what is found in previous samples. In conclusion, emission compatible with the GRB photosphere is typically found close to the trigger time, while the chance of detecting synchrotron emission is greatest at late times. This allows for the coexistence of emission mechanisms at late times., Comment: 112 pages, 17 figures including 318 panels, 46 tables. Published in ApJS on 2021 June 7. Data release at this Zenodo link ( [\href{https://zenodo.org/record/4746267}{this https URL}])

We study large networks of parametric oscillators as heuristic solvers of random Ising models. In these networks, known as coherent Ising machines, the model to be solved is encoded in the coupling between the oscillators, and a solution is offered by the steady state of the network. This approach relies on the assumption that mode competition steers the network to the ground-state solution of the Ising model. By considering a broad family of frustrated Ising models, we show that the most-efficient mode does not correspond generically to the ground state of the Ising model. We infer that networks of parametric oscillators close to threshold are intrinsically not Ising solvers. Nevertheless, the network can find the correct solution if the oscillators are driven sufficiently above threshold, in a regime where nonlinearities play a predominant role. We find that for all probed instances of the model, the network converges to the ground state of the Ising model with a finite probability., Comment: 5 pages and 5 figures for the main text, 4 pages and 3 figures for the supplemental material. Updated version after publication in Physical Review Letters

In their seminal paper, Caves and Schumaker presented a new formalism for quantum optics, intended to serve as a building block for describing two-photon processes, in terms of new, generalized qudratures. The important, revolutionary concept in their formalism was that it was fundamentally two-mode, i.e. the related observables could not be attributed to any single one of the comprising modes, but rather to a generalized complex quadrature that could only be attributed to both of them. Here, we propose a subtle, but fundamentally meaningful modification to their important work. Unlike the above proposal, we deliberately choose a frequency-agnostic definition of the two-mode quadrature, that we motivate on physical grounds. This simple modification has far-reaching implications to the formalism -- the real and imaginary parts of the quadratures now coincide with the famous EPR variables, and our two-mode operators transform trivially under two-mode and single-mode squeezing operations. Their quadratic forms, which we call the "quadrature power" are shown to succinctly generate the $SU(1,1)$ algebra of squeezing Hamiltonians, and correspond directly to important, broadband physical observables, that have been directly measured in experiment and are explicitly related to properties like squeezing and entanglement. This new point of view gives a fresh perspective on two-mode processes that is completely agnostic to the bandwidth, and reveals intriguing new ways for understanding and measuring broadband two-mode squeezing.

As gamma-ray burst (GRB) jet drills its way through the collapsing star, it traps a baryonic cork ahead of it. Here we explore a prompt emission model for GRBs in which the jet does not cross the cork, but rather photons that are emitted deep in the flow largely by pair annihilation are scattered inside the expanding cork and escape largely from the back end of it as they push it from behind. Due to the relativistic motion of the cork, these photons are easily seen by an observer close to the jet axis peaking at $\varepsilon_{peak}\sim~few \times 100 keV$. We show that this model naturally explains several key observational features including: (1) High energy power law index $\beta_1 \sim -2 {~\rm to~} -5$ with an intermediate thermal spectral region; (2) decay of the prompt emission light curve as $\sim t^{-2}$; (3) Delay of soft photons; (4) peak energy - isotropic energy (the so-called Amati) correlation, $\varepsilon_{peak} \sim \varepsilon_{iso}^m$, with $m\sim 0.45$, resulting from different viewing angles. At low luminosities, our model predicts an observable turn off in the Amati relation. (4) An anti-correlation between the spectral full width half maxima (FWHM) and time as $t^{-1}$. (5) Temporal evolution $\varepsilon_{peak} \sim t^{-1}$, accompanied by an increase of the high energy spectral slope with time. (6) Distribution of peak energies $\varepsilon_{peak}$ in the observed GRB population. The model is applicable for a single pulse GRB lightcurves and respective spectra. We discuss the consequence of our model in view of the current and future prompt emission observations., Comment: Accepted for publication in ApJ, 20 pages, 17 Figures

The Cherenkov Telescope Array (CTA), the new-generation ground-based observatory for $\gamma$-ray astronomy, provides unique capabilities to address significant open questions in astrophysics, cosmology, and fundamental physics. We study some of the salient areas of $\gamma$-ray cosmology that can be explored as part of the Key Science Projects of CTA, through simulated observations of active galactic nuclei (AGN) and of their relativistic jets. Observations of AGN with CTA will enable a measurement of $\gamma$-ray absorption on the extragalactic background light with a statistical uncertainty below 15% up to a redshift $z=2$ and to constrain or detect $\gamma$-ray halos up to intergalactic-magnetic-field strengths of at least 0.3pG. Extragalactic observations with CTA also show promising potential to probe physics beyond the Standard Model. The best limits on Lorentz invariance violation from $\gamma$-ray astronomy will be improved by a factor of at least two to three. CTA will also probe the parameter space in which axion-like particles could constitute a significant fraction, if not all, of dark matter. We conclude on the synergies between CTA and other upcoming facilities that will foster the growth of $\gamma$-ray cosmology., Comment: 71 pages (including affiliations and references), 13 figures, 6 tables. Accepted in JCAP; matches published version. Corresponding authors: Jonathan Biteau, Julien Lefaucheur, Humberto Martinez-Huerta, Manuel Meyer, Santiago Pita, Ievgen Vovk

We provide an updated assessment of the power of the Cherenkov Telescope Array (CTA) to search for thermally produced dark matter at the TeV scale, via the associated gamma-ray signal from pair-annihilating dark matter particles in the region around the Galactic centre. We find that CTA will open a new window of discovery potential, significantly extending the range of robustly testable models given a standard cuspy profile of the dark matter density distribution. Importantly, even for a cored profile, the projected sensitivity of CTA will be sufficient to probe various well-motivated models of thermally produced dark matter at the TeV scale. This is due to CTA's unprecedented sensitivity, angular and energy resolutions, and the planned observational strategy. The survey of the inner Galaxy will cover a much larger region than corresponding previous observational campaigns with imaging atmospheric Cherenkov telescopes. CTA will map with unprecedented precision the large-scale diffuse emission in high-energy gamma rays, constituting a background for dark matter searches for which we adopt state-of-the-art models based on current data. Throughout our analysis, we use up-to-date event reconstruction Monte Carlo tools developed by the CTA consortium, and pay special attention to quantifying the level of instrumental systematic uncertainties, as well as background template systematic errors, required to probe thermally produced dark matter at these energies. "Full likelihood tables complementing our analysis are provided here [ https://doi.org/10.5281/zenodo.4057987 ]", Comment: 68 pages (including references) and 26 figures; text identical to the version published in JCAP

Mode locking in lasers is a collective effect, where due to a weak coupling a large number of frequency modes lock their phases to oscillate in unison, forming an ultrashort pulse in time. We demonstrate an analogous collective effect in coupled parametric oscillators, which we term "pairwise mode-locking", where many pairs of modes with twin frequencies (symmetric around the center carrier) oscillate simultaneously with a locked phase-sum, while the phases of individual modes remain undefined. Thus, despite being broadband and multimode, the emission is not pulsed and lacks first-order coherence, while possessing a very high degree of second-order coherence. Our configuration is comprised of two coupled parametric oscillators within identical multimode cavities, where the coupling between the oscillators is modulated in time at the repetition rate of the cavity modes, with some analogy to active mode-locking in lasers. We demonstrate pairwise mode-locking in a radio-frequency (RF) experiment, covering over an octave of bandwidth with approximately 20 resonant mode-locked pairs, filling most of the available bandwidth between DC and the pump frequency. We accompany our experiment with an analytic model that accounts for the properties of the coupled parametric oscillators near threshold., Comment: 6 pages, 5 figures

We examine with particle-in-cell (PIC) simulations how a parallel shock in pair plasma reacts to upstream waves, which are driven by escaping downstream particles. Initially, the shock is sustained in the two-dimensional simulation by a magnetic filamentation (beam-Weibel) instability. Escaping particles drive an electrostatic beam instability upstream. Modifications of the upstream plasma by these waves hardly affect the shock. In time, a decreasing density and increasing temperature of the escaping particles quench the beam instability. A larger thermal energy along than perpendicular to the magnetic field destabilizes the pair-Alfv\'en mode. In the rest frame of the upstream plasma, the group velocity of the growing pair-Alfv\'en waves is below that of the shock and the latter catches up with the waves. Accumulating pair-Alfv\'en waves gradually change the shock in the two-dimensional simulation from a Weibel-type shock into an Alfv\'enic shock with a Mach number that is about 6 for our initial conditions., Comment: 11 pages, 10 figures, accepted for publication in Physics of Plasmas

Passive mode-locking critically relies on a saturable loss mechanism to form ultrashort pulses. However, in Kerr-lens mode-locking (KLM), no actual absorption takes place, but rather losses appear due to diffraction, and actual light must escape the cavity. The Kerr-lens effect works to generate through diffraction an effective instantaneous saturable absorber that delicately depends on the interplay between the spatial and temporal profiles of the pulse. Despite the importance of KLM as a technique for generating ultrafast pulses and the fundamental role of the diffraction losses in its operation, these losses were never directly observed. Here, we measure the light that leaks out due to diffraction losses in a hard-aperture Kerr-lens mode-locked Ti:Sapphire laser, and compare the measured results with a numerical theory that explicitly calculates the spatio-temporal behavior of the pulse.

We explore the coherent dynamics in a small network of three coupled parametric oscillators and demonstrate the effect of frustration on the persistent beating between them. Since a single-mode parametric oscillator represents an analog of a classical Ising spin, networks of coupled parametric oscillators are considered as simulators of Ising spin models, aiming to efficiently calculate the ground state of an Ising network - a computationally hard problem. However, the coherent dynamics of coupled parametric oscillators can be considerably richer than that of Ising spins, depending on the nature of the coupling between them (energy preserving or dissipative), as was recently shown for two coupled parametric oscillators. In particular, when the energy-preserving coupling is dominant, the system displays everlasting coherent beats, transcending the Ising description. Here, we extend these findings to three coupled parametric oscillators, focusing in particular on the effect of frustration of the dissipative coupling. We theoretically analyze the dynamics using coupled nonlinear Mathieu's equations, and corroborate our theoretical findings by a numerical simulation that closely mimics the dynamics of the system in an actual experiment. Our main finding is that frustration drastically modifies the dynamics. While in the absence of frustration the system is analogous to the two-oscillator case, frustration reverses the role of the coupling completely, and beats are found for small energy-preserving couplings., Comment: 22 pages, 9 figures. Updated version after publication in New J. Phys

We study the connection between low-luminosity gamma-ray bursts (llGRBs) and ultra-high-energy cosmic rays (UHECRs) using the canonical low-luminosity GRB 060218 as a proxy. We focus on the consequential synchrotron emission from electrons that are coaccelerated in the UHECR acceleration region, comparing this emission to observations. Both the prompt and afterglow phases are considered. For the prompt phase, we assume the coaccelerated electrons are injected with a power law distribution instantaneously (without additional heating or reacceleration), which results in bright optical-UV emission in tension with observations. For the afterglow phase, we constrain the total kinetic energy of the blast wave by comparing electron thermal synchrotron radiation to available radio data at $\sim~3$ days. Considering mildly relativistic outflows with bulk Lorentz factor $\Gamma \gtrsim 2$ (slower trans-relativistic outflows are not treated), we find that the limited available energy does not allow for GRB 060218-like afterglows to be the main origin of UHECRs. This analysis independently constrains the prompt phase as a major UHECR source as well, given that the prompt energy budget is comparable to that of the afterglow kinetic energy. More generally, our study demonstrates that synchrotron emission from thermal electrons is a powerful diagnostic of the physics of mildly relativistic shocks., Comment: Published as ApJ 902:148 (2020). Updated to match published version. Discussion added on inverse Compton effects during the prompt phase. Main conclusions unchanged

There is no complete description of the emission physics during the prompt phase in gamma-ray bursts. Spectral analyses, however, indicate that many spectra are narrower than what is expected for non-thermal emission models. Here, we reanalyse the sample of 37 bursts in \citet{Yu2019}, by fitting the narrowest time-resolved spectrum in each burst. We perform model comparison between a photospheric and a synchrotron emission model based on Bayesian evidence. We choose to compare the shape of the narrowest expected spectra: emission from the photosphere in a non-dissipative flow and slow-cooled synchrotron emission from a narrow electron distribution. We find that the photospheric spectral shape is preferred by $54 \pm 8 \%$ of the spectra (20/37), while $38 \pm 8 \%$ of the spectra (14/37) prefer the synchrotron spectral shape; three spectra are inconclusive. We hence conclude that GRB spectra are indeed very narrow and that more than half of the bursts have a photospheric emission episode. We also find that a third of all analysed spectra, not only prefer, but are also compatible with a non-dissipative photosphere, confirming previous similar findings. Furthermore, we notice that the spectra, that prefer the photospheric model, all have a low-energy power-law indices $\alpha > -0.5$. This means that $\alpha$ is a good estimator of which model is preferred by the data. Finally, we argue that the spectra which statistically prefer the synchrotron model, could equally well be caused by subphotospheric dissipation. If that is the case, photospheric emission during the early, prompt phase would be even more dominant., Comment: Accepted: ApJ

In order to better understand the physical origin of short duration gamma-ray bursts (GRBs), we perform time-resolved spectral analysis on a sample of 70 pulses in 68 short GRBs with burst duration $T_{90}\lesssim2$ s detected by the \textit{Fermi}/GBM. We apply a Bayesian analysis to all spectra that have statistical significance $S\ge15$ within each pulse and apply a cut-off power law (CPL) model. We then select in each pulse the timebin that has the maximal value of the low energy spectral index, %$\alpha_{\rm max}$, for further analysis. Under the assumption that the main emission mechanism is the same throughout each pulse, such an analysis is indicative of pulse emission. We find that $\sim$1/3 of short GRBs are consistent with a pure, non-dissipative photospheric model, at least, around the peak of the pulse. This fraction is larger compare to the corresponding one (1/4) obtained for long GRBs. For these bursts, we find (i) a bi-modal distribution in the values of the Lorentz factors and the hardness ratios; (ii) an anti-correlation between $T_{90}$ and the peak energy, $E_{\rm pk}$: $T_{90} \propto E_{\rm pk}^{-0.50\pm0.19}$. This correlation disappears when we consider the entire sample. Our results thus imply that the short GRB population may in fact be composed of two separate populations: one being a continuation of the long GRB population to shorter durations, and the other one being distinctly separate with different physical properties. Furthermore, thermal emission is initially ubiquitous, but is accompanied at longer times by additional radiation (likely synchrotron)., Comment: 24 pages, 20 figures, one table, accepted for publication in Ap.J. on the 4th of June 2020

We propose and fully analyze the simplest technique to date to generate light-based universal quantum computing resources, namely 2D, 3D and, in general, n-hypercubic cluster states. The technique uses two standard optical components: first, a single optical parametric oscillator pumped below threshold by a monochromatic field, which generates Einstein-Podolsky-Rosen entangled states, a.k.a. two-mode-squeezed states, over the quantum optical frequency comb; second, phase modulation at frequencies multiple of the comb spacing (via RF or optical means). The unprecedented compactness of this technique paves the way to implementing quantum computing on chip using quantum nanophotonics., Comment: 11 pages, 10 figures, submitted for publication

Proteins are the major building blocks of life, and actuators of almost all chemical and biophysical events in living organisms. Their native structures in turn enable their biological functions which have a fundamental role in drug design. This motivates predicting the structure of a protein from its sequence of amino acids, a fundamental problem in computational biology. In this work, we demonstrate state-of-the-art protein structure prediction (PSP) results using embeddings and deep learning models for prediction of backbone atom distance matrices and torsion angles. We recover 3D coordinates of backbone atoms and reconstruct full atom protein by optimization. We create a new gold standard dataset of proteins which is comprehensive and easy to use. Our dataset consists of amino acid sequences, Q8 secondary structures, position specific scoring matrices, multiple sequence alignment co-evolutionary features, backbone atom distance matrices, torsion angles, and 3D coordinates. We evaluate the quality of our structure prediction by RMSD on the latest Critical Assessment of Techniques for Protein Structure Prediction (CASP) test data and demonstrate competitive results with the winning teams and AlphaFold in CASP13 and supersede the results of the winning teams in CASP12. We make our data, models, and code publicly available.

A body of recent work has focused on constructing a variational family of filtered distributions using Sequential Monte Carlo (SMC). Inspired by this work, we introduce Particle Smoothing Variational Objectives (SVO), a novel backward simulation technique and smoothed approximate posterior defined through a subsampling process. SVO augments support of the proposal and boosts particle diversity. Recent literature argues that increasing the number of samples K to obtain tighter variational bounds may hurt the proposal learning, due to a signal-to-noise ratio (SNR) of gradient estimators decreasing at the rate $\mathcal{O}(1/\sqrt{K})$. As a second contribution, we develop theoretical and empirical analysis of the SNR in filtering SMC, which motivates our choice of biased gradient estimators. We prove that introducing bias by dropping Categorical terms from the gradient estimate or using Gumbel-Softmax mitigates the adverse effect on the SNR. We apply SVO to three nonlinear latent dynamics tasks and provide statistics to rigorously quantify the predictions of filtered and smoothed objectives. SVO consistently outperforms filtered objectives when given fewer Monte Carlo samples on three nonlinear systems of increasing complexity., Comment: 13 pages, 5 figures

We present post-jet-break \textit{HST}, VLA and \textit{Chandra} observations of the afterglow of the long $\gamma$-ray bursts GRB 160625B (between 69 and 209 days) and GRB 160509A (between 35 and 80 days). We calculate the post-jet-break decline rates of the light curves, and find the afterglow of GRB 160625B inconsistent with a simple $t^{-3/4}$ steepening over the break, expected from the geometric effect of the jet edge entering our line of sight. However, the favored optical post-break decline ($f_{\nu} \propto t^{-1.96 \pm 0.07}$) is also inconsistent with the $f_{\nu} \propto t^{-p}$ decline (where $p \approx 2.3$ from the pre-break light curve), which is expected from exponential lateral expansion of the jet; perhaps suggesting lateral expansion that only affects a fraction of the jet. The post-break decline of GRB 160509A is consistent with both the $t^{-3/4}$ steepening and with $f_{\nu} \propto t^{-p}$. We also use {\sc boxfit} to fit afterglow models to both light curves and find both to be energetically consistent with a millisecond magnetar central engine, although the magnetar parameters need to be extreme (i.e. $E \sim 3 \times 10^{52}$ erg). Finally, the late-time radio light curves of both afterglows are not reproduced well by {\sc boxfit} and are inconsistent with predictions from the standard jet model; instead both are well represented by a single power law decline (roughly $f_{\nu} \propto t^{-1}$) with no breaks. This requires a highly chromatic jet break ($t_{j,\mathrm{radio}} > 10 \times t_{j,\mathrm{optical}}$) and possibly a two-component jet for both bursts., Comment: 19 pages, 9 figures. Revised version; accepted for publication in ApJ

The jet photosphere has been proposed as the origin for the gamma-ray burst (GRB) prompt emission. In many such models, characteristic features in the spectra appear below the energy range of the $\textit{Fermi}$ GBM detectors, so joint fits with X-ray data are important in order to assess the photospheric scenario. Here we consider a particular photospheric model which assumes localized subphotospheric dissipation by internal shocks in a non-magnetized outflow. We investigate it using Bayesian inference and a sample of 8 GRBs with known redshifts which are observed simultaneously with $\textit{Fermi}$ GBM and $\textit{Swift}$ XRT. This provides us with an energy range of $0.3$~keV to $40$~MeV and much tighter parameter constraints. We analyze 32 spectra and find that 16 are well described by the model. We also find that the estimates of the bulk Lorentz factor, $\Gamma$, and the fireball luminosity, $L_{0,52}$, decrease while the fraction of dissipated energy, $\varepsilon_{\mathrm{d}}$, increase in the joint fits compared to GBM only fits. These changes are caused by a small excess of counts in the XRT data, relative to the model predictions from fits to GBM only data. The fact that our limited implementation of the physical scenario yields 50\% accepted spectra is promising, and we discuss possible model revisions in the light of the new data. Specifically, we argue that the inclusion of significant magnetization, as well as removing the assumption of internal shocks, will provide better fits at low energies., Comment: 20 pages, 11 figures

The Cherenkov Telescope Array (CTA) is the major next-generation observatory for ground-based very-high-energy gamma-ray astronomy. It will improve the sensitivity of current ground-based instruments by a factor of five to twenty, depending on the energy, greatly improving both their angular and energy resolutions over four decades in energy (from 20 GeV to 300 TeV). This achievement will be possible by using tens of imaging Cherenkov telescopes of three successive sizes. They will be arranged into two arrays, one per hemisphere, located on the La Palma island (Spain) and in Paranal (Chile). We present here the optimised and final telescope arrays for both CTA sites, as well as their foreseen performance, resulting from the analysis of three different large-scale Monte Carlo productions., Comment: 48 pages, 16 figures, accepted for publication in Astroparticle Physics

We present a Bayesian hierarchical multi-view mixture model termed Symphony that simultaneously learns clusters of cells representing cell types and their underlying gene regulatory networks by integrating data from two views: single-cell gene expression data and paired epigenetic data, which is informative of gene-gene interactions. This model improves interpretation of clusters as cell types with similar expression patterns as well as regulatory networks driving expression, by explaining gene-gene covariances with the biological machinery regulating gene expression. We show the theoretical advantages of the multi-view learning approach and present a Variational EM inference procedure. We demonstrate superior performance on both synthetic data and real genomic data with subtypes of peripheral blood cells compared to other methods.

Being the most extreme explosions in the universe, gamma-ray bursts (GRBs) provide a unique laboratory to study various plasma physics phenomena. The complex lightcurve and broad-band, non-thermal spectra indicate a very complicated system on the one hand, but on the other hand provide a wealth of information to study it. In this chapter I focus on recent progress in some of the key unsolved physical problems. These include: (1) Particle acceleration and magnetic field generation in shock waves; (2) Possible role of strong magnetic fields in accelerating the plasmas, and accelerating particles via magnetic reconnection process; (3) Various radiative processes that shape the observed lightcurve and spectra, both during the prompt and the afterglow phases, and finally (4) GRB environments and their possible observational signature., Comment: Invited chapter for a special issue of "galaxies", dedicated to "Cosmic Plasmas and Electromagnetic phenomena"

It has been suggested that the prompt emission in gamma-ray bursts (GRBs) could be described by radiation from the photosphere in a hot fireball. Such models must be tested by directly fitting them to data. In this work we use data from the Fermi Gamma-ray Space Telescope and consider a specific photospheric model, in which kinetic energy of a low-magnetisation outflow is dissipated locally by internal shocks below the photosphere. We construct a table model with a physically motivated parameter space and fit it to time-resolved spectra of the 36 brightest Fermi GRBs with known redshift. We find that about two thirds of the examined spectra cannot be described by the model, as it typically under-predicts the observed flux. However, since the sample is strongly biased towards bright GRBs, we argue that this fraction will be significantly lowered when considering the full population. From the successful fits we find that the model can reproduce the full range of spectral slopes present in the sample. For these cases we also find that the dissipation consistently occurs at a radius of $\sim 10^{12}$ cm and that only a few percent efficiency is required. Furthermore, we find a positive correlation between the fireball luminosity and the Lorentz factor. Such a correlation has been previously reported by independent methods. We conclude that if GRB spectra are due to photospheric emission, the dissipation cannot only be the specific scenario we consider here., Comment: 25 pages, 21 figures, 1 supplementary table

Periodically driven parametric oscillators offer a convenient way to simulate classical Ising spins. When many parametric oscillators are coupled dissipatively, they can be analogous to networks of Ising spins, forming an effective coherent Ising machine (CIM) that efficiently solves computationally hard optimization problems. In the companion paper, we studied experimentally the minimal realization of a CIM, i.e. two coupled parametric oscillators [L. Bello, M. Calvanese Strinati, E. G. Dalla Torre, and A. Pe'er, Phys. Rev. Lett. 123, 083901 (2019)]. We found that the presence of an energy-conserving coupling between the oscillators can dramatically change the dynamics, leading to everlasting beats, which transcend the Ising description. Here, we analyze this effect theoretically by solving numerically and, when possible, analytically the equations of motion of two parametric oscillators. Our main tools include: (i) a Floquet analysis of the linear equations, (ii) a multi-scale analysis based on a separation of time scales between the parametric oscillations and the beats, and (iii) the numerical identification of limit cycles and attractors. Using these tools, we fully determine the phase boundaries and critical exponents of the model, as a function of the intensity and the phase of the coupling and of the pump. Our study highlights the universal character of the phase diagram and its independence on the specific type of nonlinearity present in the system. Furthermore, we identify new phases of the model with more than two attractors, possibly describing a larger spin algebra., Comment: 20 pages, 11 figures. Updated version after publication in Phys. Rev. A