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On a compact Riemann surface $\Sigma$ of genus $g>1$, equipped with a complex vector bundle $E$ of rank $2$ and degree zero let $M_H$ be the moduli space of Higgs bundles. $M_H$ admits a $\mathbb C^{\star}$-action and to each stable $\mathbb C^{\star}$-fixed point $[(\bar\partial_0,\Phi_0)]$ is associated a holomorphic Lagrangian submanifold $W^1(\bar\partial_0,\Phi_0)$ inside the de Rham moduli space $M_{dR}$ of complex flat connections. In this note we prove a conjecture of Simpson stating that $W^1(\bar\partial_0,\Phi_0)$ is closed inside $M_{dR}$.

We present compact integrated speckle spectrometers based on monofractal and multifractal scattering media in a silicon-on-insulator platform. Through both numerical and experimental studies we demonstrate enhanced optical throughput, and hence signal-to-noise ratio, for a number of random structures with tailored multifractal geometries without affecting the spectral decay of the speckle correlation functions. Moreover, we show that the developed multifractal media outperform traditional scattering spectrometers based on uniform random distributions of scattering centers. Our findings establish the potential of low-density random media with multifractal correlations for integrated on-chip applications beyond what is possible with uncorrelated random disorder.

Novel photonic nanowires were fabricated using low-index materials and tested in the near-infrared spectrum to assess their nonlinear optical properties. In this work, we argue the need to redefine the standard nonlinear figure of merit in terms of nonlinear phase shift and optical transmission for a given propagation distance. According to this new metric, our devices largely outperform all established platforms for devices with a linear footprint in the range of 50 to 500 um, which is demonstrated to be an outstanding technological gap. For 85 fs pulses, with carrier wavelength at 1480nm and sub-uW power levels, a spectral broadening exceeding 80% of the initial bandwidth was recorded over a propagation length of just 50 um. Leveraging on CMOS-compatible processes and well-established materials such as silicon, silica, and indium tin oxide, our devices bring great promise for developing alternative all-optical devices with unparalleled nonlinear performances within the aforementioned range.

We demonstrate temperature-controlled spectral tunability of a partially-pumped single-wavelength random laser in a solid-state random laser based on DCM (4-dicyanomethylene-2-methyl-6-(p-dimethylaminostyryl)-4H-pyran) doped PMMA (polymethyl methacrylate) dye. By carefully shaping the spatial profile of the pump, we first achieve low-threshold, single-mode random lasing with excellent side lobes rejection. Notably, we show how temperature-induced changes in the refractive index of the PMMA-DCM layer result in a blue-shift of this single lasing mode. Continuous tunability of the lasing wavelength is demonstrated over an 8nm-wide bandwidth., Comment: 7 pages, 4 figure

We utilize the theory of local amplitude transfers (LAT) to gain insights into quantum walks (QWs) and quantum annealing (QA) beyond the adiabatic theorem. By representing the eigenspace of the problem Hamiltonian as a hypercube graph, we demonstrate that probability amplitude traverses the search space through a series of local Rabi oscillations. We argue that the amplitude movement can be systematically guided towards the ground state using a time-dependent hopping rate based solely on the problem's energy spectrum. Building upon these insights, we extend the concept of multi-stage QW by introducing the guided quantum walk (GQW) as a bridge between QW-like and QA-like procedures. We assess the performance of the GQW on exact cover, traveling salesperson and garden optimization problems with 9 to 30 qubits. Our results provide evidence for the existence of optimal annealing schedules, beyond the requirement of adiabatic time evolutions. These schedules might be capable of solving large-scale combinatorial optimization problems within evolution times that scale linearly in the problem size.

The data on spectroscopic galaxy clustering collected by the Dark Energy Spectroscopic Instrument (DESI) will allow the significant detection of subtle features in the galaxy two-point correlation in redshift space, beyond the "standard" redshift-space distortions. Here we present an independent assessment of the detectability of the relativistic dipole in the cross-correlation of two populations of galaxies if they would be selected from the Bright Galaxy Survey (BGS) of DESI. We build synthetic galaxy catalogues with the characteristics of the BGS using the light cone of a relativistic $N$-body simulation. Exploring different ways of splitting the populations of galaxies we find that with an unequal split with more bright galaxies than faint galaxies the detectability is significantly boosted, reaching 19 $\sigma$ in the redshift bin $0.2 \lesssim z \lesssim 0.3$ and expected to be even higher at lower redshift. Moreover, we find that the measured dipole agrees very well with the prediction of relativistic effects from linear theory down to separations of $\sim$ 30 Mpc/$h$., Comment: version matching publication

We introduce grlic, a publicly available Python tool for generating glass-like point distributions with a radial density profile $n(r)$ as it is observed in large-scale surveys of galaxy distributions on the past light cone. Utilising these glass-like catalogues, we assess the bias and variance of the Landy-Szalay (LS) estimator of the first three two-point correlation function (2PCF) multipoles in halo and particle catalogues created with the cosmological N-body code gevolution. Our results demonstrate that the LS estimator calculated with the glass catalogues is biased by less than $10^{-4}$ with respect to the estimate derived from Poisson-sampled random catalogues, for all multipoles considered and on all but the smallest scales. Additionally, the estimates derived from glass-like catalogues exhibit significantly smaller standard deviation $\sigma$ than estimates based on commonly used Poisson-sampled random catalogues of comparable size. The standard deviation of the estimate depends on a power of the number of objects $N_R$ in the random catalogue; we find a power law $\sigma \propto N_R^{-0.9}$ for glass-like random catalogues as opposed to $\sigma \propto N_R^{-0.48}$ using Poisson-sampled random catalogues. Given a required precision, this allows for a much reduced number of objects in the glass-like random catalogues used for the LS estimate of the 2PCF multipoles, significantly reducing the computational costs of each estimate., Comment: 16 pages, 14 figures

We report on two major hybrid applications of quantum computing, namely, the quantum approximate optimisation algorithm (QAOA) and the variational quantum eigensolver (VQE). Both are hybrid quantum classical algorithms as they require incremental communication between a classical central processing unit and a quantum processing unit to solve a problem. We find that the QAOA scales much better to larger problems than random guessing, but requires significant computational resources. In contrast, a coarsely discretised version of quantum annealing called approximate quantum annealing (AQA) can reach the same promising scaling behaviour using much less computational resources. For the VQE, we find reasonable results in approximating the ground state energy of the Heisenberg model when suitable choices of initial states and parameters are used. Our design and implementation of a general quasi-dynamical evolution further improves these results., Comment: This article is a book contribution. The book is freely available at http://hdl.handle.net/2128/31840

We present the halo number counts and its two-point statistics, the observable angular power spectrum, extracted for the first time from relativistic N-body simulations. The halo catalogues used in this work are built from the relativistic N-body code gevolution, and the observed redshift and angular positions of the sources are computed using a non-perturbative ray-tracing method, which includes all relativistic scalar contributions to the number counts. We investigate the validity and limitations of the linear bias prescription to describe our simulated power spectra. In particular, we assess the consistency of different bias measurements on large scales, and we estimate up to which scales a linear bias is accurate in modelling the data, within the statistical errors. We then test a second-order perturbative bias expansion for the angular statistics, on a range of redshifts and scales previously unexplored in this context, that is $0.4 \le \bar{z} \le 2$ up to scales $\ell_\mathrm{max} \sim 1000$. We find that the angular power spectra at equal redshift can be modelled with high accuracy with a minimal extension of the number of bias parameters, that is using a two-parameter model comprising linear bias and tidal bias. We show that this model performs significantly better than a model without tidal bias but with quadratic bias as extra degree of freedom, and that the latter is inaccurate at $\bar{z} \ge 0.7$. Finally, we extract from our simulations the cross-correlation of halo number counts and lensing convergence. We show that the estimate of the linear bias from this cross-correlation is consistent with the measurements based on the clustering statistics alone, and that it is crucial to take into account the effect of magnification in the halo number counts to avoid systematic shifts in the computed bias., Comment: 28 pages, 16 figures

We investigate $\mathbb{C}^\times$-families of flat connections whose leading term is a nilpotent Higgs field. Examples of such families include real twistor lines and families arising from the conformal limit. We show that these families have the same monodromy as families whose leading term is a regular Higgs bundle and use this to deduce that traces of holonomies are asymptotically exponential in rational powers of the parameter of the family., Comment: 41 pages. Comments welcome

The Free-Electron Laser (FEL) FLASH offers the worldwide still unique capability to study ultrafast processes with high-flux, high-repetition rate XUV and soft X-ray pulses. The vast majority of experiments at FLASH are of pump-probe type. Many of them rely on optical ultrafast lasers. Here, a novel FEL facility laser is reported which combines high average power output from Yb:YAG amplifiers with spectral broadening in a Herriott-type multi-pass cell and subsequent pulse compression to sub-100 fs durations. Compared to other facility lasers employing optical parametric amplification, the new system comes with significantly improved noise figures, compactness, simplicity and power efficiency. Like FLASH, the optical laser operates with 10 Hz burst repetition rate. The bursts consist of 800 $\mu$s long trains of up to 800 ultrashort pulses being synchronized to the FEL with femtosecond precision. In the experimental chamber, pulses with up to 50 $\mu$J energy, 60 fs FWHM duration and 1 MHz rate at 1.03 $\mu$m wavelength are available and can be adjusted by computer-control. Moreover, nonlinear polarization rotation is implemented to improve laser pulse contrast. First cross-correlation measurements with the FEL at the plane-grating monochromator photon beamline are demonstrated, exhibiting the suitability of the laser for user experiments at FLASH., Comment: 28 pages, 13 figures

We present predictions for the extent of the dust-continuum emission of thousands of main-sequence galaxies drawn from the TNG50 simulation between $z=1-5$. To this aim, we couple the radiative transfer code SKIRT to the output of the TNG50 simulation and measure the dust-continuum half-light radius of the modeled galaxies, assuming a Milky Way dust type and a metallicity dependent dust-to-metal ratio. The dust-continuum half-light radius at observed-frame 850 $\mu$m is up to $\sim$75 per cent larger than the stellar half-mass radius, but significantly more compact than the observed-frame 1.6 $\mu$m (roughly corresponding to H-band) half-light radius, particularly towards high redshifts: the compactness compared to the 1.6 $\mu$m emission increases with redshift. This is driven by obscuration of stellar light from the galaxy centres, which increases the apparent extent of 1.6 $\mu$m disk sizes relative to that at 850 $\mu$m. The difference in relative extents increases with redshift because the observed-frame 1.6 $\mu$m emission stems from ever shorter wavelength stellar emission. These results suggest that the compact dust-continuum emission observed in $z>1$ galaxies is not (necessarily) evidence of the buildup of a dense central stellar component. We also find that the dust-continuum half-light radius very closely follows the radius containing half the star formation in galaxies, indicating that single band dust-continuum emission is a good tracer of the location of (obscured) star formation. The dust-continuum emission is more compact than the H2 mass (for galaxies at $z\geq 2$) and the underlying dust mass. The dust emission strongly correlates with locations with the highest dust temperatures, which do not need to be the locations where most H$_2$ and/or dust is located. The presented results are a common feature of main-sequence galaxies., Comment: Submitted to MNRAS

Controlling the optical response of a medium through suitably tuned coherent electromagnetic fields is highly relevant in a number of potential applications, from all-optical modulators to optical storage devices. In particular, electromagnetically induced transparency (EIT) is an established phenomenon in which destructive quantum interference creates a transparency window over a narrow spectral range around an absorption line, which, in turn, allows to slow and ultimately stop light due to the anomalous refractive index dispersion. Here we report on the observation of a new form of either induced transparency or amplification of a weak probe beam in a strongly driven silicon photonic crystal resonator at room temperature. The effect is based on the oscillating temperature field induced in a nonlinear optical cavity, and it reproduces many of the key features of EIT while being independent of either atomic or mechanical resonances. Such thermo-optically induced transparency (TOIT) will allow a versatile implementation of EIT-analogues in an integrated photonic platform, at almost arbitrary wavelength of interest, room temperature and in a practical, low cost and scalable system.

Through the triality of ${\rm SO}(8,\mathbb{C})$, we study three interrelated homogeneous basis of the ring of invariant polynomials of Lie algebras, which give the basis of three Hitchin fibrations, and identify the explicit automorphisms that relate them.

We present a novel, highly versatile, and self-referenced arrival time monitor for measuring the femtosecond time delay between a hard X-ray pulse from a free-electron laser and an optical laser pulse, measured directly on the same sample used for pump-probe experiments. Two chirped and picosecond long optical supercontinuum pulses traverse the sample with a mutually fixed time delay of 970 fs, while a femtosecond X-ray pulse arrives at an instant in between both pulses. Behind the sample the supercontinuum pulses are temporally overlapped to yield near-perfect destructive interference in the absence of the X-ray pulse. Stimulation of the sample with an X-ray pulse delivers non-zero contributions at certain optical wavelengths, which serve as a measure of the relative arrival time of the X-ray pulse with an accuracy of better than 25 fs. We find an excellent agreement of our monitor with the existing timing diagnostics at the SACLA XFEL with a Pearson correlation value of 0.98. We demonstrate a high sensitivity to measure X-ray pulses with pulse energies as low as 30 $\mu$J. Using a free-flowing liquid jet as interaction sample ensures the full replacement of the sample volume for each X-ray/optical event, thus enabling its utility even at MHz repetition rate XFEL sources.

In haemoglobin (consisting of four globular myoglobin-like subunits), the change from the low-spin (LS) hexacoordinated haem to the high spin (HS) pentacoordinated domed form upon ligand detachment and the reverse process upon ligand binding, represent the transition states that ultimately drive the respiratory function. Visible-ultraviolet light has long been used to mimic the ligand release from the haem by photodissociation, while its recombination was monitored using time-resolved infrared to ultraviolet spectroscopic tools. However, these are neither element- nor spin-sensitive. Here we investigate the transition state in the case of Myoglobin-NO (MbNO) using femtosecond Fe Kalpha and Kbeta non-resonant X-ray emission spectroscopy (XES) at an X-ray free-electron laser upon photolysis of the Fe-NO bond. We find that the photoinduced change from the LS (S = 1/2) MbNO to the HS (S = 2) deoxy-myoglobin (deoxyMb) haem occurs in ca. 800 fs, and that it proceeds via an intermediate (S = 1) spin state. The XES observables also show that upon NO recombination to deoxyMb, the return to the planar MbNO ground state is an electronic relaxation from HS to LS taking place in ca. 30 ps. Thus, the entire ligand dissociation-recombination cycle in MbNO is a spin cross-over followed by a reverse spin cross-over process.

Nonlinear metasurfaces that dynamically manipulate the phase of a passing light beam are of interest for a wide range of applications. The controlled operation of such devices requires accurate measurements of the optical transmission phase in both the linear and nonlinear regime, an experimentally challenging task. In this paper we show that this phase information can be extracted directly from simple transmission measurements, using a Hilbert transform approach, removing the need for complicated, interferometric experimental set-ups, and enabling direct measurements of the phase in conditions not suitable for other traditional approaches, such Z-scan measurements., Comment: 13 pages, 4 figure, underlying data to be shared upon publication

We study the relation between the UV-slope, $\beta$, and the ratio between the infrared- and UV-luminosities (IRX) of galaxies from TNG50, the latest installment of the IllustrisTNG galaxy formation simulations. We select 7280 star-forming main-sequence (SFMS) galaxies with stellar mass $10^9M_\odot$ at redshifts $0 \leq z \leq 4$ and perform radiative transfer with SKIRT to model effects of interstellar medium dust on the emitted stellar light. Assuming a Milky Way (MW) dust type and a dust-to-metal ratio of 0.3, we find that TNG50 SFMS galaxies generally agree with observationally-derived IRX-$\beta$ relations at $z \lesssim 1$. However, we find a redshift-dependent systematic offset with respect to empirically-derived local relations, with the TNG50 IRX-$\beta$ relation shifting towards lower $\beta$ and steppening at higher redshifts. This is partially driven by variations in the dust-uncorrected UV-slope of galaxies, due to different star-formation histories of galaxies selected at different cosmic epochs; we suggest the remainder of the effect is caused by differences in the effective dust attenuation curves (EDACs) of galaxies as a function of redshift. We find a typical galaxy-to-galaxy variation of 0.3 dex in IRX at fixed $\beta$, correlated with intrinsic galaxy properties: galaxies with higher star-formation rates, star-formation efficiencies, gas metallicities and stellar masses exhibit larger IRX values. We demonstrate a degeneracy between stellar age, dust geometry and dust composition: $z=4$ galaxies with a Small Magellanic Cloud dust type follow the same IRX-$\beta$ relation as low-redshift galaxies with MW dust. We provide a redshift-dependent fitting function for the IRX-$\beta$ relation for MW dust based on our models., Comment: The paper has been accepted for publishing in MNRAS

The field of optical metrology with its high precision position, rotation and wavefront sensors represents the basis for lithography and high resolution microscopy. However, the on-chip integration - a task highly relevant for future nanotechnological devices - necessitates the reduction of the spatial footprint of sensing schemes by the deployment of novel concepts. A promising route towards this goal is predicated on the controllable directional emission of the fundamentally smallest emitters of light, i.e. dipoles, as an indicator. Here we realize an integrated displacement sensor based on the directional emission of Huygens dipoles excited in an individual dipolar antenna. The position of the antenna relative to the excitation field determines its directional coupling into a six-way crossing of photonic crystal waveguides. In our experimental study supported by theoretical calculations, we demonstrate the first prototype of an integrated displacement sensor with a standard deviation of the position accuracy below $\lambda$/300 at room temperature and ambient conditions., Comment: Ankan and Martin contributed equally, 6 pages, 5 figures

Most present-day resonant systems, throughout physics and engineering, are characterized by a strict time-reversal symmetry between the rates of energy coupled in and out of the system, which leads to a trade-off between how long a wave can be stored in the system and the system bandwidth. Any attempt to reduce the losses of the resonant system, and hence store a (mechanical, acoustic, electronic, optical, atomic, or of any other nature) wave for more time, will inevitably also reduce the bandwidth of the system. Until recently, this time-bandwidth limit has been considered fundamental, arising from basic Fourier reciprocity. A recent theory suggested that it might in fact be overcome by breaking Lorentz reciprocity in the resonant system, reinvigorated a debate about whether (or not) this was indeed the case. Here, we report an experimental realization of a cavity where, inducing nonreciprocity by breaking the time invariance, we do overcome the fundamental time-bandwidth limit of ordinary resonant systems by a factor of 30, in full agreement with accompanying numerical simulations. We show that, although in practice experimental constraints limit our scheme, the time bandwidth product can be arbitrarily large, simply dictated by the finesse of the cavity. Our experimental realization uses a simple macroscopic, time-variant, fiber-optic cavity, where we break Lorentz reciprocity by non-adiabatically opening the cavity, injecting a pulse of large bandwidth, and then closing the cavity, storing the pulse which can be released on-demand at a later time. Our results open the path for designing resonant systems, ubiquitous in physics and engineering, that can simultaneously be broadband (i.e., ultrafast) and possessing long storage times, thereby unleashing fundamentally new functionalities in wave physics and wave-matter interactions.

We experimentally demonstrate that the spectral sensitivity of a Mach-Zehnder (MZ) interferometer can be enhanced through structural slow light. We observe a 20 times enhancement by placing a dispersion-engineered-slow-light photonic-crystal waveguide in one arm of a fibre-based MZ interferometer. The spectral sensitivity of the interferometer increases roughly linearly with the group index, and we have quantified the resolution in terms of the spectral density of interference fringes. These results show promise for the use of slow-light methods for developing novel tools for optical metrology and, specifically, for compact high-resolution spectrometers.

Light localization due to random imperfections in periodic media is paramount in photonics research. The group index is known to be a key parameter for localization near photonic band edges, since small group velocities reinforce light interaction with imperfections. Here, we show that the size of the smallest localized mode that is formed at the band edge of a one-dimensional periodic medium is driven instead by the effective photon mass, i.e. the flatness of the dispersion curve. Our theoretical prediction is supported by numerical simulations, which reveal that photonic-crystal waveguides can exhibit surprisingly small localized modes, much smaller than those observed in Bragg stacks thanks to their larger effective photon mass. This possibility is demonstrated experimentally with a photonic-crystal waveguide fabricated without any intentional disorder, for which near-field measurements allow us to distinctly observe a wavelength-scale localized mode despite the smallness ($\sim 1/1000$ of a wavelength) of the fabrication imperfections.