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Bacterial communities are pivotal to maintaining ecological function and preserving the rich tapestry of biological diversity. The rapid development of environmental sequencing technologies, such as metagenomics, has revolutionized our capacity to probe such diversity. However, despite these advances, a theoretical understanding connecting empirical data with ecosystem modelling, in particular in the framework of disordered systems akin to spin glasses, is still in its infancy. Here, we present a comprehensive framework using theories of disordered systems to decode microbiome data, which offers insight into the ecological forces that shape macroecological states. By employing the quenched disordered generalized Lotka-Volterra model, we analyze species abundance data in healthy and diseased human gut microbiomes. Results reveal the emergence of two distinct patterns of species-interaction networks, elucidating the pathways through which dysbiosis may drive microbiome instability. Interaction patterns thus provide a window into the systemic shifts accompanying the transition from health to disease, offering a new perspective on the dynamics of the microbial community. Our findings suggest the potential of disordered systems theory to characterize microbiomes by capturing the essence of ecological interactions and their consequences on stability and functioning, leveraging our understanding of the linkages of dysbiosis and microbial dynamics., Comment: 10 pages, 4 figures

Speckle patterns are a powerful tool for high-precision metrology, as they allow remarkable performance in relatively simple setups. Nonetheless, researchers in this field follow rather distinct paths due to underappreciated general principles underlying speckle phenomena. Here, we advise on a universal metric of intrinsic speckle sensitivity, and on the advantages and disadvantages of multiple scattering. This will catalyse progress in speckle metrology but will also translate to other domains of disordered optics which are undergoing rapid developments at present., Comment: 15 pages, 4 figures

Future actively cooled space-borne observatories for the far-infrared, loosely defined as a 1--10 THz band, can potentially reach a sensitivity limited only by background radiation from the Universe. This will result in an increase in observing speed of many orders of magnitude. A spectroscopic instrument on such an observatory requires large arrays of detectors with a sensitivity expressed as a noise equivalent power NEP = 3 $\times 10^{-20}$ $W\surd{Hz}$. We present the design, fabrication, and characterisation of microwave kinetic inductance detectors (MKIDs) for this frequency range reaching the required sensitivity. The devices are based on thin-film NbTiN resonators which use lens-antenna coupling to a submicron-width aluminium transmission line at the shorted end of the resonator where the radiation is absorbed. We optimised the MKID geometry for a low NEP by using a small aluminium volume of $\approx$ 1$\mu m^3$ and fabricating the aluminium section on a very thin (100 nm) SiN membrane. Both methods of optimisation also reduce the effect of excess noise by increasing the responsivity of the device, which is further increased by reducing the parasitic geometrical inductance of the resonator. We measure the sensitivity of eight MKIDs with respect to the power absorbed in the detector using a thermal calibration source filtered in a narrow band around 1.55 THz. We obtain a NEP$_{exp}(P_{abs})\:=\:3.1\pm0.9\times10^{-20}\:W\surd{Hz}$ at a modulation frequency of 200 Hz averaged over all measured MKIDs. The NEP is limited by quasiparticle trapping. The measured sensitivity is sufficient for spectroscopic observations from future, actively cooled space-based observatories. Moreover, the presented device design and assembly can be adapted for frequencies up to $\approx$ 10 THz and can be readily implemented in kilopixel arrays., Comment: 12 pages, 7 figures (including appendices). This work is accepted for publication in Astronomy and Astrophysics and will be published there shortly

As the fields of optical microscopy, semiconductor technology and fundamental science increasingly aim for precision at or below the nanoscale, there is a burgeoning demand for sub-nanometric displacement and position sensing. We show that the speckle patterns produced by multiple reflections of light inside an integrating sphere provide an exceptionally sensitive probe of displacement. We use an integrating sphere split into two equal and independent hemispheres, one of which is free to move in any given direction. The relative motion of the two hemispheres produces a change in the speckle pattern from which we can analytically infer the amplitude of the displacement. The method allows displacement measurement with uncertainty as small as 40 pm ($\lambda/20,000$) in a facile implementation. We show how, under realistic experimental parameters, the uncertainty in displacement could be improved to tens of femtometres, or $\lambda/10^{7}$., Comment: 17 pages, 5 figures

Highly-resolved determination of refractive index is vital in fields ranging from biosensing through to laser range-finding. Laser speckle is known to be a sensitive probe of the properties of the light and the environment, but to date speckle-based refractive index measurements have been restricted to $10^{-6}$ resolution. In this work we identify a strategy to optimise the sensitivity of speckle to refractive index changes, namely by maximising the width of the distribution of optical path lengths in the medium. We show that this can be realised experimentally by encapsulating the medium of interest within an integrating sphere. We demonstrate that variations of the refractive index of air as small as $4.5\times10^{-9}$ can be resolved with an uncertainty of $7\times10^{-10}$. This is an improvement of three orders of magnitude when compared to previous speckle-based methods., Comment: 7 pages, 5 figures

Speckle metrology is a powerful tool in the measurement of wavelength and spectra. Recently, speckle produced by multiple reflections inside an integrating sphere has been proposed and showed high performance. However, to our knowledge, a complete characterisation of speckle sensitivity to wavelength in that geometry has not been performed to date. In this work, we derive a general model predicting the variation in a speckle pattern as a result of a generic transformation. Applying this to a shift in the incident wavelength, we show that the speckle sensitivity is mainly governed by the radius and surface reflectivity of the sphere. We show that integrating spheres offer sensitivity three orders of magnitude above that of multimode fibres of a similar size, and discuss analogies with the transmission line of a Fabry-P\'erot interferometer., Comment: 7 pages, 4 figures

Laser speckle is generated by the multiple interference of light through a disordered medium. Here we study the premise that the speckle pattern retains information about the polarisation state of the incident field. We analytically verify that a linear relation exists between the Stokes vector of the light and the resulting speckle pattern. As a result, the polarisation state of a beam can be measured from the speckle pattern using a transmission matrix approach. We perform a quantitative analysis of the accuracy of the transmission matrix method to measure randomly time-varying polarisation states. In experiment, we find that the Stokes parameters of light from a diode laser can be retrieved with an uncertainty of 0.05 using speckle images of 150$\times$150 pixels and 17 training states. We show both analytically and in experiment that this approach may be extended to the case of more than one laser field, demonstrating the measurement of the Stokes parameters of two laser beams simultaneously from a single speckle pattern and achieving the same uncertainty of 0.05., Comment: 7 pages, 7 figures

Many areas of optical science require an accurate measurement of optical spectra. Devices based on laser speckle promise compact wavelength measurement, with attometer-level sensitivity demonstrated for single wavelength laser fields. The measurement of multimode spectra using this approach would be attractive, yet this is currently limited to picometer resolution. Here, we present a method to improve the resolution and precision of speckle-based multi-wavelength measurements. We measure multiple wavelengths simultaneously, in a device comprising a single 1 m-long step-index multimode fiber and a fast camera. Independent wavelengths separated by as little as 1 fm are retrieved with 0.2 fm precision using Principal Component Analysis. The method offers a viable way to measure sparse spectra containing multiple individual lines and is likely to find application in the tracking of multiple lasers in fields such as portable quantum technologies and optical telecommunications., Comment: 5 pages, 6 figures

Aims: To study the presence of superoscillations in coronal magnetoacoustic waves and its possible role in heating coronal loops through the strong and localized gradients they generate on the wave. Methods: An analytic model is built for the transition between a sausage and a kink wave modes propagating along field lines in the corona. We compute in this model the local frequencies, the wave gradients and the associated heating rates due to compressive viscosity. Results: We find superoscillations associated with the transition between wave modes accompanying the wave dislocation that shifts through the wave domain. Frequencies 10 times higher than the normal frequency are found. This means that a typical 3-minute coronal wave will locally oscillate in 10 to 20 seconds. Such high frequencies bring up strong gradients that efficiently dissipate the wave through compressive viscosity. We compute the associated heating rates. Locally, they are very strong, largely compensating typical radiative losses. Conclusions: We find a new heating mechanism associated to magnetoacoustic waves in the corona. Heating due to superoscillations only happens along particular field lines with small cross sections, comparable in size to coronal loops, inside the much larger magnetic flux tubes and wave propagation domain., Comment: Accepted for publication in A&A