Quantum Electrodynamics predicts that the vacuum must behave as a nonlinear optical medium: the vacuum optical index should increase when it is stressed by intense electromagnetic fields. The DeLLight (Deflection of Light by Light) project aims to measure it by using intense and ultra-short laser pulses. The experiment uses a Sagnac interferometer to amplify the tiny deflection signal of a low-intensity probe pulse crossing the vacuum refractive-index gradient produced by an external high-intensity pump pulse. The measurement of the amplified signal by a CCD camera requires a high spatial resolution, which is limited by the ultimate quantum noise of the CCD. However, interferometric phase noise induced by the mechanical vibrations of the interferometer is also amplified and degrades spatial resolution. To overcome this, we propose a new method named High-Frequency Phase Noise Suppression (HFPNS), based on the addition of a delayed replica (5 ns) of the probe pulse. The delayed pulse, which is not affected by the pump but is subject to the same vibration noise, enables offline subtraction of correlated phase noise. In this work, we present an experimental proof-of-concept on a prototype interferometer operating with a limited amplification factor (𝒜≃25), about 10 times smaller than the required value of the final experiment. We have succeeded in reducing phase noise by a factor of 40, resulting in a residual noise level 2.3 times higher than the expected quantum noise. The residual noise is linked to delay-line instabilities and incident beam pointing fluctuations present during these tests. This result validates HFPNS as a robust method for future quantum-noise-limited interferometric measurements of vacuum optical nonlinearity, though additional stabilization and higher interferometric amplification are still needed.

It is proven each ring $R$ for which every indecomposable right module is pure-projective is right pure-semisimple. Each commutative ring $R$ for which every indecomposable module is pure-injective is a clean ring and for each maximal ideal $P$, $R_P$ is a maximal valuation ring. Complete discrete valuation domain of rank one are examples of non-artinian semi-perfect rings with pure-injective indecomposable modules.

In Quantum Electrodynamics, vacuum becomes a nonlinear optical medium: its optical index should be modified in the presence of intense external electromagnetic fields. The DeLLight project (Deflection of Light by Light) aims to observe this effect using intense focused femtosecond laser pulses delivered by LASERIX. The principle is to measure with a Sagnac interferometer the deflection of a low-intensity focused pulse (probe) crossing the vacuum index gradient induced by a high-intensity pulse (pump). A Sagnac interferometer working with femtosecond laser pulses has been developed for the DeLLight project. Compared to previous prototypes, the interferometer now includes the focusing of the probe beam in the interaction area. In this article, we measure and characterize the critical experimental parameters limiting the sensitivity of the interferometer, namely the extinction factor, the spatial resolution, and the waist at focus of the probe pulse. We discuss future improvements.

The aim of the DeLLight (Deflection of Light by Light) experiment is to observe for the first time the optical nonlinearity in vacuum, as predicted by Quantum Electrodynamics, by measuring the refraction of a low-intensity focused laser pulse (probe) when crossing the effective vacuum index gradient induced by a high-intensity focused laser pulse (pump). The deflection signal is amplified by using a Sagnac interferometer. Here, we report the first measurement performed with the DeLLight pilot interferometer, of the deflection of light by light in air, with a low-intensity pump. We show that the deflection signal measured by the interferometer is amplified, and is in agreement with the expected signal induced by the optical Kerr effect in air. Moreover, we verify that the signal varies as expected as a function of the pump intensity, the temporal delay between the pump and the probe, and their relative polarisation. These results represent a proof of concept of the DeLLight experimental method based on interferometric amplification.

We present a model that builds ``dark matter"-like halo density profiles from free-falling zero-point vacuum fluctuations. It does not require a modification of Newton's laws, nor the existence of as-yet-undiscovered dark matter particles. The 3D halos predicted by our model are fully constrained by the baryonic mass distribution, and are generally far from spherical. The model introduces a new fundamental constant of vacuum, T, having the dimensions of time. We deduce the associated formalism from some basic assumptions, and adjust the model successfully on several spiral galaxy rotation data while comparing our results to the existing analyses. We believe our approach opens up a new paradigm that is worth further exploration, and that would benefit from checks relating to other phenomena attributed to dark matter at all time and distance scales. Following such a program would allow the present model to evolve, and if successful it would make vacuum fluctuations responsible for the typical manifestations of dark matter.

We say that a ring R is a right RDV-ring if each simple right R-module is RD-injective. In this paper, we study the notion of RDV-rings which is a non-trivial generalization of V-rings and Köthe rings. For instance, commutative RD-rings, serial rings and right duo right uniserial rings are RDV-rings. Several characterizations of right RDV-rings are given. Also, it is shown that over a semilocal ring R with Jacobson radical J, each simple right R-module is RD-flat if and only if R is a left RDV-ring, if and only if R(R/J) is RD-injective, if and only if (R/J)R is RD-flat. As a consequence, we show that a local ring R is a principal ideal ring if and only if R satisfies the ascending chain condition on principal left ideals and R(R/J) is RD-injective. In the case of R being either a local left perfect ring or a normal left perfect ring, we have obtained results which state that to check whether every left R-module is RD-injective (or, R is Köthe), it suffices to test only the RD-injectivity of the simple left R-modules. Finally, we give some characterizations of quasi-Frobenius rings by using these concepts.

Electro-thermal coupling in semiconductor bolometers is known to create nonlinearities in transient detector response, particularly when such detectors are biased outside of their ideal regions (i.e. past the turnover point in their IV curves). This effect is further compounded in the case where a stray capacitance in the bias circuit is present, for example in long cryogenic cabling. We present a physical model of the influence of such electro-thermal coupling and stray capacitance in a composite NTD germanium bolometer, in which previous experimental data at high V-bias resulted in oscillations of the impulse response of the detector to irradiation by alpha particles. The model reproduces the transient oscillations seen in the experimental data, depending both on electro-thermal coupling and stray capacitance. This is intended as an experimental and simulated example of such oscillations, demonstrated for the specific case of this bolometric detector.

The polarized thermal emission from diffuse Galactic dust is the main foreground present in measurements of the polarization of the cosmic microwave background (CMB) at frequencies above 100 GHz. In this paper we exploit the uniqueness of the Planck HFI polarization data from 100 to 353 GHz to measure the polarized dust angular power spectra CEE ` and C BB ` over the multipole range 40 < ` < 600 well away from the Galactic plane. These measurements will bring new insights into interstellar dust physics and allow a precise determination of the level of contamination for CMB polarization experiments. Despite the non-Gaussian and anisotropic nature of Galactic dust, we show that general statistical properties of the emission can be characterized accurately over large fractions of the sky using angular power spectra. The polarization power spectra of the dust are well described by power laws in multipole, C` ∝ `, with exponents αEE,BB = −2.42± 0.02. The amplitudes of the polarization power spectra vary with the average brightness in a way similar to the intensity power spectra. The frequency dependence of the dust polarization spectra is consistent with modified blackbody emission with βd = 1.59 and Td = 19.6 K down to the lowest Planck HFI frequencies. We find a systematic difference between the amplitudes of the Galactic Band E-modes, CBB ` /C EE ` = 0.5. We verify that these general properties are preserved towards high Galactic latitudes with low dust column densities. We show that even in the faintest dust-emitting regions there are no “clean” windows in the sky where primordial CMB B-mode polarization measurements could be made without subtraction of foreground emission. Finally, we investigate the level of dust polarization in the specific field recently targeted by the BICEP2 experiment. Extrapolation of the Planck 353 GHz data to 150 GHz gives a dust powerDBB ` ≡ `(`+ 1)CBB ` /(2π) of 1.32× 10−2 μKCMB over the multipole range of the primordial recombination bump (40 < ` < 120); the statistical uncertainty is ±0.29 × 10−2 μKCMB and there is an additional uncertainty (+0.28,−0.24) × 10−2 μKCMB from the extrapolation. This level is the same magnitude as reported by BICEP2 over this ` range, which highlights the need for assessment of the polarized dust signal even in the cleanest windows of the sky.

In this paper, we are mainly interested in the two questions “which are the commutative rings on which every finitely presented modules is [Formula: see text]-periodic (respectively, [Formula: see text]-periodic)?”. It is proved that these kinds of rings are particular cases of semiregular rings. So, we call them [Formula: see text]-semiregular and [Formula: see text]-semiregular rings, respectively. We establish characterizations of these rings in terms of various classical notions and we provide several examples of such rings.

Quantum electrodynamics predicts that the vacuum must behave as a nonlinear optical medium: the speed of light should be modified when the vacuum is stressed by intense electromagnetic fields. This optical phenomenon has not yet been observed. The DeLLight (deflection of light by light) experiment aims to observe the optically induced index change of vacuum, a nonlinear effect which has never been explored. The experiment is installed in the LASERIX facility at IJCLab, which delivers ultrashort intense laser pulses (2.5 J per pulse, each of 30 fs duration, with a 10 Hz repetition rate). The proposal is to measure the refraction of a probe laser pulse when crossing a transverse vacuum index gradient, produced by a very intense pump pulse. The refraction induces a transverse shift in the intensity profile of the probe, whose signal is amplified by a Sagnac interferometer. In this article we describe the experimental method and setup, and present the complete theoretical calculations for the expected signal. With a minimum waist at focus of $5\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{m}$ (corresponding to a maximum intensity of $\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{4pt}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$), and with the nonlinear vacuum index derived from QED, the expected refraction angle is 0.13 prad. First results of the interferometer prototype are presented. It is shown that an extinction factor $\mathcal{F}=0.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ (corresponding to a signal amplification factor of 250) and a spatial resolution ${\ensuremath{\sigma}}_{y}=10\phantom{\rule{4pt}{0ex}}\mathrm{nm}$ are achievable. The expected signal is then about 15 pm, and could be observed at a 5-sigma confidence level with about one month of collected data.

We present three Monte Carlo models for the propagation of athermal phonons in the diamond absorber of a composite semiconducting bolometer `Bolo 184'. Previous measurements of the response of this bolometer to impacts by $\alpha$ particles show a strong dependence on the location of particle incidence, and the shape of the response function is determined by the propagation and thermalisation of athermal phonons. The specific mechanisms of athermal phonon propagation at this time were undetermined, and hence we have developed three models for probing this behaviour by attempting to reproduce the statistical features seen in the experimental data. The first two models assume a phonon thermalisation length determined by a mean free path $\lambda$, where the first model assumes that phonons thermalise at the borders of the disc (with a small $\lambda$) and the second assumes that they reflect (with a $\lambda$ larger than the size of the disc). The third model allows athermal photons to propagate along their geometrical line of sight (similar to ray optics), gradually losing energy. We find that both the reflective model and the geometrical model reproduce the features seen in experimental data, whilst the model assuming phonon thermalisation at the disc border produces unrealistic results. There is no significant dependence on directionality of energy absorption in the geometrical model, and in the schema of this thin crystalline diamond, a reflective absorber law and a geometrical law both produce consistent results.

This paper presents the High Frequency Instrument (HFI) data processing procedures for the Planck 2018 release. Major improvements in mapmaking have been achieved since the previous Planck 2015 release, many of which were used and described already in an intermediate paper dedicated to the Planck polarized data at low multipoles. These improvements enabled the first significant measurement of the reionization optical depth parameter using Planck-HFI data. This paper presents an extensive analysis of systematic effects, including the use of end-to-end simulations to facilitate their removal and characterize the residuals. The polarized data, which presented a number of known problems in the 2015 Planck release, are very significantly improved, especially the leakage from intensity to polarization. Calibration, based on the cosmic microwave background (CMB) dipole, is now extremely accurate and in the frequency range 100-353 GHz reduces intensity-to-polarization leakage caused by calibration mismatch. The Solar dipole direction has been determined in the three lowest HFI frequency channels to within one arc minute, and its amplitude has an absolute uncertainty smaller than 0.35 mu K, an accuracy of order 10(-4). This is a major legacy from the Planck HFI for future CMB experiments. The removal of bandpass leakage has been improved for the main high-frequency foregrounds by extracting the bandpass-mismatch coefficients for each detector as part of the mapmaking process; these values in turn improve the intensity maps. This is a major change in the philosophy of "frequency maps", which are now computed from single detector data, all adjusted to the same average bandpass response for the main foregrounds. End-to-end simulations have been shown to reproduce very well the relative gain calibration of detectors, as well as drifts within a frequency induced by the residuals of the main systematic effect (analogue-to-digital convertor non-linearity residuals). Using these simulations, we have been able to measure and correct the small frequency calibration bias induced by this systematic effect at the 10(-4) level. There is no detectable sign of a residual calibration bias between the first and second acoustic peaks in the CMB channels, at the 10(-3) level.

Using data from the Planck satellite, we study the statistical properties of interstellar dust polarization at high Galactic latitudes. Our aim is to advance the understanding of the magnetized interstellar medium (ISM), and to provide a modelling framework of the polarized dust foreground for use in cosmic microwave background (CMB) component-separation procedures. Focusing on the southern Galactic cap (b < −60◦), we examine the Stokes I, Q, and U maps at 353 GHz, and particularly the statistical distribution of the polarization fraction (p) and angle (ψ), in order to characterize the ordered and turbulent components of the Galactic magnetic field (GMF) in the solar neighbourhood. The Q and U maps show patterns at large angular scales, which we relate to the mean orientation of the GMF towards Galactic coordinates (l0, b0) = (70◦±5◦, 24◦±5◦). The histogram of the observed p values shows a wide dispersion up to 25 %. The histogram of ψ has a standard deviation of 12◦ about the regular pattern expected from the ordered GMF. We build a phenomenological model that connects the distributions of p and ψ to a statistical description of the turbulent component of the GMF, assuming a uniform effective polarization fraction (p0) of dust emission. To compute the Stokes parameters, we approximate the integration along the line of sight (LOS) as a sum over a set of N independent polarization layers, in each of which the turbulent component of the GMF is obtained from Gaussian realizations of a power-law power spectrum. We are able to reproduce the observed p and ψ distributions using: a p0 value of 26 %; a ratio of 0.9 between the strengths of the turbulent and mean components of the GMF; and a small value of N. The mean value of p (inferred from the fit of the large-scale patterns in the Stokes maps) is 12 ± 1 %. We relate the polarization layers to the density structure and to the correlation length of the GMF along the LOS. We stress the simplicity of our model (involving only a few parameters), which can be easily computed on the celestial sphere to produce simulated maps of dust polarization, and thereby to assess component-separation approaches in CMB experiments.

Nonlinear electrodynamics in vacuum remains a relatively unexplored topic, as the intensities required to reach the nonlinear regime make it difficult to test in the laboratory. There are thus several competing theories of nonlinear electrodynamics, distinct from each other in theory but not yet having been ruled out by experiment [1,2]. The standard theory (derived from QED) is the Heisenberg-Euler model, which treats vacuum as a polarizable medium through the production of virtual electron-positron pairs. This model has had success in explaining (for example) the Lamb shift in hydrogen, but in recent years significant discrepancies (of ~ 7 σ) have appeared when applied to muonic hydrogen and muonic deuterium, where the heavier muon is 200 times closer to the nucleus and thus experiences a much stronger electric field [3,4]. To date, the most sensitive tests of nonlinear electrodynamics, performed by the collaborations PVLAS in Italy [5] and BMV in Toulouse [6], have aimed at detecting the birefringence of vacuum induced by a strong external magnetic field. However, the regime in which these tests are conducted currently lies one to two orders of magnitude above the Heisenberg-Euler regime, and the results are compatible with there being no birefringence at all, as predicted by, e.g., the Born-Infeld model.

In this paper, we study the estimation of the effective number of relativistic species from a combination of cosmic microwave background (CMB) and baryon acoustic oscillations (BAO) data. We vary different ingredients of the analysis: the Planck high-ℓ likelihoods, the Boltzmann solvers, and the statistical approaches. The variation of the inferred values gives an indication of an additional systematic uncertainty, which is of the same order of magnitude as the error derived from each individual likelihood. We show that this systematic uncertainty is essentially associated to the assumptions made in the high-ℓ likelihood implementations, in particular for the foreground residuals modellings. We also compare a subset of likelihoods using only the TE power spectra, expected to be less sensitive to foreground residuals.

The dust-HI correlation is used to characterize the emission properties of dust in the diffuse interstellar medium. We cross-correlate sky maps from Planck, WMAP, and DIRBE, at 17 frequencies from 23 to 3000 GHz, with the Parkes survey of the 21-cm line emission of neutral atomic hydrogen, over a contiguous area of 7500 deg$^2$ centred on the southern Galactic pole. Our analysis yields four specific results. (1) The dust temperature is observed to be anti-correlated with the dust emissivity and opacity. We interpret this result as evidence for dust evolution within the diffuse ISM. The mean dust opacity is measured to be $(7.1 \pm 0.6) 10^{-27} cm^2/H \times (\nu/353\, GHz)^{1.53\pm0.03}$ for $100 < \nu <353$GHz. (2) We map the spectral index of dust emission at millimetre wavelengths, which is remarkably constant at $\beta_{mm} = 1.51\pm 0.13$. We compare it with the far infrared spectral index beta_FIR derived from greybody fits at higher frequencies, and find a systematic difference, $\beta_{mm}-\beta_{FIR} = -0.15$, which suggests that the dust SED flattens at $\nu < 353\,$GHz. (3) We present spectral fits of the microwave emission correlated with HI from 23 to 353 GHz, which separate dust and anomalous microwave emission. The flattening of the dust SED can be accounted for with an additional component with a blackbody spectrum, which accounts for $(26 \pm 6)$% of the dust emission at 100 GHz and could represent magnetic dipole emission. Alternatively, it could account for an increasing contribution of carbon dust, or a flattening of the emissivity of amorphous silicates, at millimetre wavelengths. These interpretations make different predictions for the dust polarization SED. (4) We identify a Galactic contribution to the residuals of the dust-HI correlation, which we model with variations of the dust emissivity on angular scales smaller than that of our correlation analysis.

H.A. Wilson, then R.H. Dicke, proposed to describe gravitation by a spatial change of the refractive index of the vacuum around a gravitational mass. Dicke extended this formalism in order to describe the apparent expansion of the universe by a cosmological time dependence of the global vacuum index. In this paper, we develop Dicke’s formalism. The metric expansion in standard cosmology (the time-dependent scale factor of the Friedmann–Lemaître curved spacetime metric) is replaced by a flat and static Euclidean metric with a change with time of the vacuum index. We show that a vacuum index increasing with time produces both the cosmological redshift and time dilation, and that the predicted evolution of the energy density of the cosmological microwave background is consistent with the standard cosmology. We then show that the type Ia supernovæ data, from the joint SDSS-II and SNLS SNe-Ia samples, are well modeled by a vacuum index varying exponentially as \(n(t)=exp(t/\tau _0)\), where \(\tau _0=8.0^{+0.2}_{-0.8}\) Gyr. The main consequence of this formalism is that the cosmological redshift should affect any atom, with a relative decrease of the energy levels of about \(-2 \ 10^{-18} \ \mathrm {s}^{-1}\). Possibilities for an experimental investigation of this prediction are discussed.

QUBIC, the QU Bolometric Interferometer for Cosmology, is a novel forthcoming instrument to measure the B-mode polarization anisotropy of the Cosmic Microwave Background. The detection of the B-mode signal will be extremely challenging; QUBIC has been designed to address this with a novel approach, namely bolometric interferometry. The receiver cryostat is exceptionally large and cools complex optical and detector stages to 40 K, 4 K, 1 K and 350 mK using two pulse tube coolers, a novel 4He sorption cooler and a double-stage 3He/4He sorption cooler. We discuss the thermal and mechanical design of the cryostat, modelling and thermal analysis, and laboratory cryogenic testing.

The next generation of cosmology space missions will be sensitive to parasitic signals arising from cosmic rays. Using a composite bolometer, we have investigated pulses produced by α particles in order to understand the movement of energy produced by ionising radiation. Using a series of measurements at 100 mK, we have compared the typical fitting algorithm (a mathematical model) with a second method of pulse interpretation by convolving the detector’s thermal response function with a starting profile of thermalised athermal phonons, taking into account the effects of heat propagation. Using this new fitting method, we have eliminated the need for a non-physical quadratic nonlinearity factor produced using more common methods, and we find a pulse form in good agreement with known aspects of thermal physics. This work is carried forward in the effort to produce a physical model for energy deposition in this detector. The modelling is motivated by the reproduction of statistical features in the experimental dataset, and the new interpretation of α pulse shapes represents an improvement in the current understanding of the energy propagation mechanisms in this detector.