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Highly periodic structures are often said to convey the beauty of nature. However, most material properties are strongly influenced by the defects they contain. On the mesoscopic scale, molecular self-assembly exemplifies this interplay; thermodynamic principles determine short-range order, but long-range order is mainly impeded by the kinetic history of the material and by thermal fluctuations. For the development of self-assembly technologies, it is imperative to characterise and understand the interplay between self-assembled order and defect-induced disorder. Here we used synchrotron-based hard X-ray nanotomography to reveal a pair of extended topological defects within a self-assembled single-diamond network morphology. These defects are morphologically similar to the comet and trefoil patterns of equal and opposite half-integer topological charges observed in liquid crystals and appear to maintain a constant separation across the thickness of the sample, resembling pairs of full vortices in superconductors and other hard condensed matter systems. These results are expected to open new windows to study defect formation in soft condensed matter, particularly in biological systems where most structures are formed by self-assembly., Comment: Nat. Nanotechnol. (2024)

Block copolymers are recognised as a valuable platform for creating nanostructured materials with unique properties. Morphologies formed by block copolymer self-assembly can be transferred into a wide range of inorganic materials, enabling applications including energy storage and metamaterials. However, imaging of the underlying, often complex, nanostructures in large volumes has remained a challenge, limiting progress in materials development. Taking advantage of recent advances in X-ray nanotomography, we non-invasively imaged exceptionally large volumes of nanostructured soft materials at high resolution, revealing a single diamond morphology in a triblock terpolymer composite network. This morphology, which is ubiquitous in nature, has so far remained elusive in block copolymers, despite its potential to create materials with large photonic bandgaps. The discovery was made possible by the precise analysis of distortions in a large volume of the self-assembled diamond network, which are difficult to unambiguously assess using traditional characterisation tools. We anticipate that high-resolution X-ray nanotomography, which allows imaging of much larger sample volumes than electron-based tomography, will become a powerful tool for the quantitative analysis of complex nanostructures and that structures such as the triblock terpolymer-directed single diamond will enable the generation of advanced multicomponent composites with hitherto unknown property profiles., Comment: updated reference 38; added reference 40; corrected name of one author; corrected one affiliation; corrected legend in Extended Data Fig. 3

Solid polymer electrolytes for lithium batteries promise improvements in safety and energy density if their conductivity can be increased. Nanostructured block copolymer electrolytes specifically have the potential to provide both good ionic conductivity and good mechanical properties. This study shows that the previously neglected nanoscale composition of the polymer electrolyte close to the electrode surface has an important effect on impedance measurements, despite its negligible extent compared to the bulk electrolyte. Using standard stainless steel blocking electrodes, the impedance of lithium salt-doped poly(isoprene-b-styrene-b-ethylene oxide) (ISO) exhibited a marked decrease upon thermal processing of the electrolyte. In contrast, covering the electrode surface with a low molecular weight poly(ethylene oxide) (PEO) brush resulted in higher and more reproducible conductivity values, which were insensitive to the thermal history of the device. A qualitative model of this effect is based on the hypothesis that ISO surface reconstruction at the different electrode surfaces leads to a change in the electrostatic double layer, affecting electrochemical impedance spectroscopy measurements. As a main result, PEO-brush modification of electrode surfaces is beneficial for the robust electrolyte performance of PEO-containing block-copolymers and may be crucial for their accurate characterization and use in Li-ion batteries.

Direct UV-written waveguides are fabricated in silica-on-silicon with birefringence of $(4.9 \pm 0.2) \times 10^{-4}$, much greater than previously reported in this platform. We show that these waveguides are suitable for the generation of heralded single photons at telecommunication wavelengths by spontaneous four-wave mixing. A pulsed pump field at 1060 nm generates pairs of photons in highly detuned, spectrally uncorrelated modes near 1550 nm and 800 nm. Waveguide-to-fiber coupling efficiencies of 78-91% are achieved for all fields. Waveguide birefringence is controlled through dopant concentration of $\mathrm{GeCl_4}$ and $\mathrm{BCl_3}$ using the flame hydrolysis deposition process. The technology provides a route towards the scalability of silica-on-silicon integrated components for photonic quantum experiments., Comment: 9 pages, 5 figures

The resonant enhancement of both mechanical and optical response in microcavity optomechanical devices allows exquisitely sensitive measurements of stimuli such as acceleration, mass and magnetic fields. In this work, we show that quantum correlated light can improve the performance of such sensors, increasing both their sensitivity and their bandwidth. Specifically, we develop a silicon-chip based cavity optomechanical magnetometer that incorporates phase squeezed light to suppress optical shot noise. At frequencies where shot noise is the dominant noise source this allows a 20% improvement in magnetic field sensitivity. Furthermore, squeezed light broadens the range of frequencies at which thermal noise dominates, which has the effect of increasing the overall sensor bandwidth by 50%. These proof-of-principle results open the door to apply quantum correlated light more broadly in chip-scale sensors and devices., Comment: 8 pages, 5 figures

We determine the theoretical limits to squeezing-enhanced measurement sensitivity of mechanical motion in a cavity optomechanical system. The motion of a mechanical resonator is transduced onto quadrature fluctuations of a cavity optical field and a measurement is performed on the optical field exiting the cavity. We compare measurement sensitivities obtained with coherent probing and quantum-enhanced probing of the mechanical motion, i.e. the coherent probe field carries vacuum states and quadrature squeezed vacuum states at sideband frequencies, respectively. We find that quantum-enhanced probing provides little to no improvement in motion sensing for resonators in the unresolved sideband regime but may significantly increase measurement sensitivities for resonators in the resolved sideband regime.

Laser cooling is a fundamental technique used in primary atomic frequency standards, quantum computers, quantum condensed matter physics and tests of fundamental physics, among other areas. It has been known since the early 1990s that laser cooling can, in principle, be improved by using squeezed light as an electromagnetic reservoir; while quantum feedback control using a squeezed light probe is also predicted to allow improved cooling. Here, we implement quantum feedback control of a micro-mechanical oscillator for the first time with a squeezed probe field. This allows quantum-enhanced feedback cooling with a measurement rate greater than it is possible with classical light, and a consequent reduction in the final oscillator temperature. Our results have significance for future applications in areas ranging from quantum information networks, to quantum-enhanced force and displacement measurements and fundamental tests of macroscopic quantum mechanics., Comment: 6 pages, 3 figures

We present a novel proposal for generating quantum superpositions of macroscopically distinct states of a bulk mechanical oscillator, compatible with existing optomechanical devices operating in the readily achievable bad-cavity limit. The scheme is based on a pulsed cavity optomechanical quantum non-demolition (QND) interaction, driven by displaced non-Gaussian states, and measurement-induced feedback, avoiding the need for strong single-photon optomechanical coupling. Furthermore, we show that single-quadrature cooling of the mechanical oscillator is sufficient for efficient state preparation, and we outline a three-pulse protocol comprising a sequence of QND interactions for squeezing-enhanced cooling, state preparation, and tomography., Comment: 7 pages, 5 figures

An integrated silicon nitride resonator is proposed as an ultra-compact source of bright single-mode quadrature squeezed light at 850 nm. Optical properties of the device are investigated and tailored through numerical simulations, with particular attention paid to loss associated with interfacing the device. An asymmetric double layer stack waveguide geometry with inverse vertical tapers is proposed for efficient and robust fibre-chip coupling, yielding a simulated total loss of -0.75 dB/facet. We assess the feasibility of the device through a full quantum noise analysis and derive the output squeezing spectrum for intra-cavity pump self-phase modulation. Subject to standard material loss and detection efficiencies, we find that the device holds promises for generating substantial quantum noise squeezing over a bandwidth exceeding 1 GHz. In the low-propagation loss regime, approximately -7 dB squeezing is predicted for a pump power of only 50 mW., Comment: 23 pages, 12 figures

We report on a hitherto unexplored application of squeezed light: for quantum-enhancement of mechanical transduction sensitivity in microcavity optomechanics. Using a toroidal silica microcavity, we experimentally demonstrate measurement of the transduced phase modulation signal with a sensitivity $-0.72(\pm 0.01)$\,dB below the shot noise level. This is achieved for resonant probing in the highly under-coupled regime, by preparing the probe in a weak coherent state with phase squeezed vacuum states at sideband frequencies.

We provide a framework for understanding recent experiments on squeezing of a collective atomic pseudo-spin, induced by a homodyne measurement on off-resonant probe light interrogating the atoms. The detection of light decimates the atomic state distribution and we discuss the conditions under which the resulting reduced quantum fluctuations are metrologically relevant. In particular, we consider a dual probe scheme which benefits from a cancelation of classical common mode noise sources such that quantum fluctuations from light and atoms are the main contributions to the detected signal., Comment: Submitted to Journal of Modern Optics

We used Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) to investigate the decay of Ne$_2$ after K-shell photoionization. The breakup into Ne$^{1+}$ / Ne$^{2+}$ shows interatomic Coulombic decay (ICD) occurring after a preceding atomic Auger decay. The molecular frame angular distributions of the photoelectron and the ICD electron show distinct, asymmetric features, which imply localization of the K-vacancy created at one of the two atomic sites of the Ne$_2$ and an emission of the ICD electron from a localized site. The experimental results are supported by calculations in frozen core Hartree-Fock approach., Comment: 4 pages, 4 figures

We prove that the integral closedness of any ideal of height at least two is compatible with specialization by a generic element. This opens the possibility for proofs using induction on the height of an ideal. Also, with additional assumptions, we show that an element is integral over a module if it is integral modulo a generic element of the module. This turns questions about integral closures of modules into problems about integral closures of ideals, by means of a construction known as Bourbaki ideal.

\noindent We study the Zariski tangent cone $T_X\stackrel{\pi}{\lar} X$ to an affine variety $X$ and the closure $\bar{T}_X$ of $\pi^{-1}({\rm Reg}(X))$ in $T_X$. We focus on the comparison between $T_X$ and $\bar{T}_X$, giving sufficient conditions on $X$ in order that $T_X=\bar{T}_X$. One aspect of the results is to understand when this equality takes place in the presence of the reducedness of the Zariski tangent cone. Our other interest is to consider conditions on $X$ in order that $\bar{T}_X$ be normal or/and Cohen--Macaulay, and to prove that they are met by several classes of affine varieties including complete intersection, Cohen--Macaulay codimension two and Gorenstein codimension three singularities. In addition, when $X$ is the affine cone over a smooth arithmetically normal Calabi--Yau projective variety, we establish when $\bar{T}_X$ is also (the affine cone over) an arithmetically normal Calabi--Yau like (projective) variety.