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Abstract The physics of recombination lines in the Heisinglet system is expected to be relatively simple, supported by accurate atomic models. We examine the intensities of Heisingletsλ3614, λ3965, λ5016, λ6678, and λ7281 and the triplet Heiλ5876 in various types of ionized nebulae and compare them with theoretical predictions to test the validity of the “Case B” recombination scenario and the assumption of thermal homogeneity. Our analysis includes 85 spectra from Galactic and extragalactic Hiiregions, 90 from star-forming galaxies, and 218 from planetary nebulae, all compiled by the Deep Spectra of Ionized Regions Database Extended (DESIRED-E) project. By evaluating the ratios Heiλ7281/λ6678 and Heiλ7281/λ5876, we determineT_e(Hei) and compare it with direct measurements ofT_e([Oiii]λ4363/λ5007). We find thatT_e(Hei) is systematically lower thanT_e([Oiii]) across most objects and nebula types. Additionally, we identify a correlation between the abundance discrepancy factor (ADF(O²⁺)) and the differenceT_e([Oiii]) –T_e(Hei) for planetary nebulae. We explore two potential explanations: photon loss fromn¹P → 1¹Stransitions and temperature inhomogeneities. Deviations from “Case B” may indicate photon absorption by Hirather than Heiand/or generalized ionizing photon escape, highlighting the need for detailed consideration of radiative transfer effects. If temperature inhomogeneities are widespread, identifying a common physical phenomenon affecting all ionized nebulae is crucial. Our results suggest that both scenarios can contribute to the observed discrepancies. 

Phase estimation plays a central role in communications, sensing, and information processing. Quantum correlated states, such as squeezed states, enable phase estimation beyond the shot-noise limit, and in principle approach the ultimate quantum limit in precision, when paired with optimal quantum measurements. However, physical realizations of optimal quantum measurements for optical phase estimation with quantum-correlated states are still unknown. Here we address this problem by introducing an adaptive Gaussian measurement strategy for optical phase estimation with squeezed vacuum states that, by construction, approaches the quantum limit in precision. This strategy builds from a comprehensive set of locally optimal POVMs through rotations and homodyne measurements and uses the Adaptive Quantum State Estimation framework for optimizing the adaptive measurement process, which, under certain regularity conditions, guarantees asymptotic optimality for this quantum parameter estimation problem. As a result, the adaptive phase estimation strategy based on locally-optimal homodyne measurements achieves the quantum limit within the phase interval of $[0,\pi /2)$. Furthermore, we generalize this strategy by including heterodyne measurements, enabling phase estimation across the full range of phases from $[0,\pi )$, where squeezed vacuum allows for unambiguous phase encoding. Remarkably, for this phase interval, which is the maximum range of phases that can be encoded in squeezed vacuum, this estimation strategy maintains an asymptotic quantum-optimal performance, representing a significant advancement in quantum metrology. 

Abstract Physical realizations of the canonical phase measurement for the optical phase are unknown. Single-shot phase estimation, which aims to determine the phase of an optical field in a single shot, is critical in quantum information processing and metrology. Here we present a family of strategies for single-shot phase estimation of coherent states based on adaptive non-Gaussian, photon counting, measurements with coherent displacements that maximize information gain as the measurement progresses, which have higher sensitivities over the best known adaptive Gaussian strategies. To gain understanding about their fundamental characteristics and demonstrate their superior performance, we develop a comprehensive statistical analysis based on Bayesian optimal design of experiments, which provides a natural description of these non-Gaussian strategies. This mathematical framework, together with numerical analysis and Monte Carlo methods, allows us to determine the asymptotic limits in sensitivity of strategies based on photon counting designed to maximize information gain, which up to now had been a challenging problem. Moreover, we show that these non-Gaussian phase estimation strategies have the same functional form as the canonical phase measurement in the asymptotic limit differing only by a scaling factor, thus providing the highest sensitivity among physically-realizable measurements for single-shot phase estimation of coherent states known to date. This work shines light into the potential of optimized non-Gaussian measurements based on photon counting for optical quantum metrology and phase estimation. 

Context.Dark gamma-ray bursts (GRBs) constitute a significant fraction of the GRB population. In this paper, we present a multi-wavelength analysis (both prompt emission and afterglow) of an intense (3.98  ×  10⁻⁵erg cm⁻²usingFermi-Gamma-Ray Burst Monitor) two-episodic GRB 150309A observed early on until ∼114 days post burst. Despite the strong gamma-ray emission, no optical afterglow was detected for this burst. However, we discovered near-infrared (NIR) afterglow (K_S-band), ∼5.2 h post burst, with the CIRCE instrument mounted at the 10.4 m Gran Telescopio Canarias (hereafter, GTC). Aims.We aim to examine the characteristics of GRB 150309A as a dark burst and to constrain other properties using multi-wavelength observations. Methods.We usedFermiobservations of GRB 150309A to understand the prompt emission mechanisms and jet composition. We performed early optical observations using the BOOTES robotic telescope and late-time afterglow observations using the GTC. A potential faint host galaxy was also detected in the optical wavelength using the GTC. We modelled the potential host galaxy of GRB 150309A in order to explore the environment of the burst. Results.The time-resolved spectral analysis ofFermidata indicates a hybrid jet composition consisting of a matter-dominated fireball and magnetic-dominated Poynting flux. The GTC observations of the afterglow revealed that the counterpart of GRB 150309A was very red, withH − K_S > 2.1 mag (95% confidence). The red counterpart was not discovered in any bluer filters ofSwiftUVOT/BOOTES, which would be indicative of a high redshift origin. Therefore we discarded this possibility based on multiple arguments, such as spectral analysis of the X-ray afterglow constrainz < 4.15 and a moderate redshift value obtained using the spectral energy distribution (SED) modelling of the potential galaxy. The broadband (X-ray to NIR bands) afterglow SED implies a very dusty host galaxy with a deeply embedded GRB (suggestingA_V ≳ 35 mag). Conclusions.The environment of GRB 150309A demands a high extinction towards the line of sight. Demanding dust obscuration is the most probable origin of optical darkness as well as the very red afterglow of GRB 150309A. This result establishes GRB 150309A as the most extinguished GRB known to date. 

Abstract We present a detailed prompt emission and early optical afterglow analysis of the two very-high-energy (VHE) detected bursts GRB 201015A and GRB 201216C, and their comparison with a subset of similar bursts. Time-resolved spectral analysis of multistructured GRB 201216C using the Bayesian binning algorithm revealed that during the entire duration of the burst, the low-energy spectral index ( α pt ) remained below the limit of the synchrotron line of death. However, statistically some of the bins supported the additional thermal component. Additionally, the evolution of spectral parameters showed that both the peak energy ( E p ) and α pt tracked the flux. These results were further strengthened using the values of the physical parameters obtained by synchrotron modeling of the data. Our earliest optical observations of both bursts using the F/Photometric Robotic Atmospheric Monitor Observatorio del Roque de los Muchachos and Burst Observer and Optical Transient Exploring System robotic telescopes displayed a smooth bump in their early optical light curves, consistent with the onset of the afterglow due to synchrotron emission from an external forward shock. Using the observed optical peak, we constrained the initial bulk Lorentz factors of GRB 201015A and GRB 201216C to Γ 0 = 204 and Γ 0 = 310, respectively. The present early optical observations are the earliest known observations constraining outflow parameters and our analysis indicate that VHE detected bursts could have a diverse range of observed luminosity within the detectable redshift range of present VHE facilities. 

Abstract Despite the f₀(980) hadron having been discovered half a century ago, the question about its quark content has not been settled: it might be an ordinary quark-antiquark ($${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$) meson, a tetraquark ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}q\overline{q}$) exotic state, a kaon-antikaon ($${{\rm{K}}}\overline{{{\rm{K}}}}$$ $K\overline{K}$) molecule, or a quark-antiquark-gluon ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{g}}}$$ $q\overline{q}g$) hybrid. This paper reports strong evidence that the f₀(980) state is an ordinary$${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$meson, inferred from the scaling of elliptic anisotropies (v₂) with the number of constituent quarks (n_q), as empirically established using conventional hadrons in relativistic heavy ion collisions. The f₀(980) state is reconstructed via its dominant decay channel f₀(980) →π⁺π⁻, in proton-lead collisions recorded by the CMS experiment at the LHC, and itsv₂is measured as a function of transverse momentum (p_T). It is found that then_q= 2 ($${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$state) hypothesis is favored overn_q= 4 ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}q\overline{q}$or$${{\rm{K}}}\overline{{{\rm{K}}}}$$ $K\overline{K}$states) by 7.7, 6.3, or 3.1 standard deviations in thep_T< 10, 8, or 6 GeV/cranges, respectively, and overn_q= 3 ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{g}}}$$ $q\overline{q}g$hybrid state) by 3.5 standard deviations in thep_T< 8 GeV/crange. This result represents the first determination of the quark content of the f₀(980) state, made possible by using a novel approach, and paves the way for similar studies of other exotic hadron candidates. 

ABSTRACT We report on detailed multiwavelength observations and analysis of the very bright and long GRB 210619B, detected by the Atmosphere-Space Interactions Monitor installed on the International Space Station and the Gamma-ray Burst Monitor (GBM) on-board the Fermi mission. Our main goal is to understand the radiation mechanisms and jet composition of GRB 210619B. With a measured redshift of z = 1.937, we find that GRB 210619B falls within the 10 most luminous bursts observed by Fermi so far. The energy-resolved prompt emission light curve of GRB 210619B exhibits an extremely bright hard emission pulse followed by softer/longer emission pulses. The low-energy photon index (αpt) values obtained using the time-resolved spectral analysis of the burst suggest a transition between the thermal (during harder pulse) to non-thermal (during softer pulse) outflow. We examine the correlation between spectral parameters and find that both peak energy and αpt exhibit the flux tracking pattern. The late time broad-band photometric data set can be explained within the framework of the external forward shock model with νm < νc < νx (where νm, νc, and νx are the synchrotron peak, cooling-break, and X-ray frequencies, respectively) spectral regime supporting a rarely observed hard electron energy index (p < 2). We find moderate values of host extinction of E(B − V) = 0.14 ± 0.01 mag for the small magellanic cloud extinction law. In addition, we also report late-time optical observations with the 10.4 m Gran Telescopio de Canarias placing deep upper limits for the host galaxy (z = 1.937), favouring a faint, dwarf host for the burst.