Papers

The supercurrent diode effect (SDE), characterized by nonreciprocal critical currents, represents a promising building block for future dissipationless electronics and quantum circuits. Realizing SDE requires breaking both time-reversal and inversion symmetry in the device. Here we use conductive atomic force microscopy (c-AFM) lithography to pattern reconfigurable superconducting weak links (WLs) at the LaAlO3/KTaO3 (LAO/KTO) interface. By deliberately engineering the WL geometry at the nanoscale, we realize SDE in these devices in the presence of modest out-of-plane magnetic fields. The SDE polarity can be reversed by simply changing the WL position, and the rectification efficiency reaches up to 13% under optimal magnetic field conditions. Time-dependent Ginzburg-Landau simulations reveal that the observed SDE originates from asymmetric vortex motion in the inversion-symmetry-breaking device geometry. This demonstration of SDE in the LAO/KTO system establishes a versatile platform for investigating and engineering vortex dynamics, forming the basis for engineered quantum circuit elements.

We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission eigenvalues. We analyze the distribution's shape, bounds, moments, and asymptotic behaviors. In the large n limit, the distribution converges to a Gaussian whose mean and variance depend solely on those of the eigenvalues. This result resolves the apparent paradox between bimodal eigenvalue distribution and unimodal transmissivity distribution.

We propose an improved Path Integral Monte Carlo (PIMC) algorithm called Harmonic PIMC (H-PIMC) and its generalization, Mixed PIMC (M-PIMC). PIMC is a powerful tool for studying quantum condensed phases. However, it often suffers from a low acceptance ratio for solids and dense confined liquids. We develop two sampling schemes especially suited for such problems by dividing the potential into its harmonic and anharmonic contributions. In H-PIMC, we generate the imaginary time paths for the harmonic part of the potential exactly and accept or reject it based on the anharmonic part. In M-PIMC, we restrict the harmonic sampling to the vicinity of local minimum and use standard PIMC otherwise, to optimize efficiency. We benchmark H-PIMC on systems with increasing anharmonicity, improving the acceptance ratio and lowering the auto-correlation time. For weakly to moderately anharmonic systems, at $\beta \hbar \omega=16$, H-PIMC improves the acceptance ratio by a factor of 6-16 and reduces the autocorrelation time by a factor of 7-30. We also find that the method requires a smaller number of imaginary time slices for convergence, which leads to another two- to four-fold acceleration. For strongly anharmonic systems, M-PIMC converges with a similar number of imaginary time slices as standard PIMC, but allows the optimization of the auto-correlation time. We extend M-PIMC to periodic systems and apply it to a sinusoidal potential. Finally, we combine H- and M-PIMC with the worm algorithm, allowing us to obtain similar efficiency gains for systems of indistinguishable particles.

We experimentally investigate the superfluid properties of a two-dimensional, weakly interacting Bose-Einstein condensate in the zero-temperature regime, when it is subjected to a triangular optical lattice potential. We implement an original method, which involves solving the hydrodynamic continuity equation to extract the superfluid fraction tensor from the measured in situ density distribution of the fluid at rest. In parallel, we apply an independent dynamical approach that combines compressibility and sound velocity measurements to determine the superfluid fraction. Both methods yield consistent results in good agreement with simulations of the Gross-Pitaevskii equation as well as with the Leggett bounds determined from the measured density profiles.

We introduce quantum-enhanced memetic tabu search (QE-MTS), a non-variational hybrid algorithm that achieves state-of-the-art scaling for the low-autocorrelation binary sequence (LABS) problem. By seeding the classical MTS with high-quality initial states from digitized counterdiabatic quantum optimization (DCQO), our method suppresses the empirical time-to-solution scaling to $\mathcal{O}(1.24^N)$ for sequence length $N \in [27,37]$. This scaling surpasses the best-known classical heuristic $\mathcal{O}(1.34^N)$ and improves upon the $\mathcal{O}(1.46^N)$ of the quantum approximate optimization algorithm, achieving superior performance with a $6\times$ reduction in circuit depth. A two-stage bootstrap analysis confirms the scaling advantage and projects a crossover point at $N \gtrsim 47$, beyond which QE-MTS outperforms its classical counterpart. These results provide evidence that quantum enhancement can directly improve the scaling of classical optimization algorithms for the paradigmatic LABS problem.

We propose Néel antiferromagnetic (AF) Mott insulators with a buckled honeycomb structure as potential candidates to host a high-temperature AF Chern insulator (AFCI). Using a generalized Kondo lattice model we show that the staggered potential induced by a perpendicular electric field due to the buckling can drive the AF Mott insulator to an AFCI phase. We address the temperature evolution of the Hall conductance and the chiral edge states. The quantization temperature $T_q$, below which the Hall conductance is quantized, depends essentially on the strength of the spin-orbit coupling and the hopping parameter, independent of the specific details of the model. The deviation of the Hall conductance from the quantized value $e^2/h$ above $T_q$ is found to be accompanied by a spectral broadening of the chiral edge states, reflecting a finite life-time, i.e., a decay. Using parameters typical for heavy transition-metal elements we predict that the AFCI can survive up to room temperature. We suggest Sr$_3$CaOs$_2$O$_9$ as a potential compound to realize a high-$T$ AFCI phase.

In this work we introduce an ansatz for continuous matrix product operators for quantum field theory. We show that (i) they admit a closed-form expression in terms of finite number of matrix-valued functions without reference to any lattice parameter; (ii) they are obtained as a suitable continuum limit of matrix product operators; (iii) they preserve the entanglement area law directly in the continuum, and in particular they map continuous matrix product states (cMPS) to another cMPS. As an application, we use this ansatz to construct several families of continuous matrix product unitaries beyond quantum cellular automata.

Donor spin qubits in silicon offer one- and two-qubit gates with fidelities beyond 99%, coherence times exceeding 30 seconds, and compatibility with industrial manufacturing methods. This motivates the development of large-scale quantum processors using this platform, and the ability to automatically tune and operate such complex devices. In this work, we present the first machine learning algorithm with the ability to automatically locate the charge transitions of an ion-implanted donor in a silicon device, tune single-shot charge readout, and identify the gate voltage parameters where tunnelling rates in and out the donor site are the same. The entire tuning pipeline is completed on the order of minutes. Our results enable both automatic characterisation and tuning of a donor in silicon devices faster than human experts.

Freeze-thaw cycles can be regularly observed in nature in water and are essential in industry and science. Objects present in the medium will interact with either an advancing solidification front during freezing or a retracting solidification front, i.e., an advancing melting front, during thawing. It is well known that objects show complex behaviours when interacting with the advancing solidification front, but the extent to which they are displaced during the retraction of the solid-liquid interface is less well understood. To study potential hysteresis effects during freeze-thaw cycles, we exploit experimental model systems of oil-in-water emulsions and polystyrene (PS) particle suspensions, in which a water-ice solidification front advances and retracts over an individual immiscible (and deformable) oil droplet or over a solid PS particle. We record several interesting hysteresis effects, resulting in non-zero relative displacements of the objects between freezing and thawing. PS particles tend to migrate further and further away from their initial position, whereas oil droplets tend to return to their starting positions during thawing. We rationalize our experimental findings by comparing them to our prior theoretical model of Meijer, Bertin & Lohse, Phys. Rev. Fluids (2025), yielding a qualitatively good agreement. Additionally, we look into the reversibility of how the droplet deforms and re-shapes throughout one freeze-thaw cycle, which will turn out to be remarkably robust.

Understanding charge transfer at oxide interfaces is crucial for designing materials with emergent electronic and magnetic properties, especially in systems where strong electron correlations and spin-orbit coupling coexist. SrIrO$_3$/SrCoO$_3$ (SIO/SCO) superlattices offer a unique platform to explore these effects due to their contrasting electronic structures and magnetic behaviors. Building on past theory based on continuity of O 2p band alignment, we employ density functional theory (DFT) to model electron transfer from Ir to Co across the SIO/SCO interface. To characterize these effects, we synthesized epitaxial SIO/SCO superlattices via molecular beam epitaxy. Structural and transport measurements confirmed high crystallinity, metallic behavior, and suppression of Kondo scattering that has been reported in uniform SIO films. Further characterization via X-ray absorption spectroscopy (XAS) revealed orbital anisotropy and valence changes consistent with interfacial charge transfer. Co K- and L$_{2,3}$-edge and Ir L$_2$-edge spectra verified electron donation from Ir to Co, stabilizing the perovskite SCO phase and tuning the electronic structure of SIO via hole-doping. O K-edge XAS showed band alignment shifts in the SIO layer consistent with DFT predictions. Our work here provides a pathway for engineering oxide heterostructures with tailored magnetic and electronic properties.

The precise identification of neurotransmitters is essential for comprehending cerebral function, detecting neurological conditions, and formulating successful therapeutic approaches. The present work investigates the electrochemical detection of serotonin with the excellent hybrid electrocatalyst $Cu_2S/H{\beta}cd-rGO$. $Cu_2S$, with its significant features as improved catalytic activity and enhanced charge transfer when combined with $H{\beta}cd-rGO$, will enhance the performance. The integration of $Cu_2S$ with $H{\beta}cd-rGO$, regulated by the van der Waals force and the electrostatic interaction, makes it a stable catalyst without disrupting the composite structure. Also, the aggregation of the $Cu_2S/H{\beta}cd$ with the layered sheets of rGO can be highly reduced and resulting in the improvement of the conductivity. Thus, the above features resulted in the improved oxidation response current when fabricated over the glassy carbon electrode (GCE). The SR showed sensitive response at a broad linear range of 0.019 to 0.299 $\mu$M and 4.28 to 403.14 $\mu$M, resulting in a lower limit of detection (LOD) of 1.2 nM or 0.0012 $\mu$M and a sensitivity of about 15.9 $\mu$A ${\mu}M^{-1}$ $cm^{-2}$. The sensor demonstrated excellent selectivity against common interferents, including aminophenol, dopamine, epinephrine, hydroquinone, melatonin, and chlorine. The real sample studies in the biological samples show good recovery values, showing the effectiveness of the as-fabricated sensor. Thus, the cost-efficient and straightforward integration of $Cu_2S/H{\beta}cd-rGO$ will be an outstanding electrocatalyst for detecting SR.

The study of the interplay of applied external magnetic field and superconductivity has been invigorated by recent works on Bernal bilayer and rhombohedral multilayer graphene. These studies, with and without proximitized spin-orbit coupling, have opened up a new frontier in the exploration of unconventional superconductors as they offer a unique platform to investigate superconductivity with high degree of in-plane magnetic field resilience and even magnetic field-induced superconductivity. Here, we present a framework for analyzing the upper critical in-plane magnetic field data in multilayer superconductors. Our framework relies on an analytically tractable superconducting pairing model that captures the normal state phenomenology of these systems and applies it to calculate the relationship between the upper critical field $H_{c2}$ and the corresponding critical temperature $T_{c}$. We study the $H_{c2}-T_{c}$ critical curve as a function of experimental parameters (Ising and Rashba spin-orbit coupling) and depairing mechanisms (Zeeman and orbital coupling) for both spin-singlet and spin-triplet pairing. By applying our framework to analyze four recent Bernal bilayer graphene-WSe$_2$ experiments [1-4], we identify an apparent discrepancy between fitted and measured spin-orbit parameters, which we propose can be explained by an enhancement of the Landé g factor in the Bernal bilayer graphene experiments.

We study the correlated electronic structure and local spin behaviour of the copper-substituted lead-vanadium bromine apatite Pb$_9$Cu(VO$_4$)$_6$Br$_2$ using DFT+DMFT with a two-orbital Cu-centred low-energy model. Simulations are done for several temperatures (20, 60, 100 K) and a broad range of band fillings 2.46 $\leq$ n $\leq$ 3.54. We find that the present compound stays metallic even once correlations are treated dynamically around the stoichiometric filling (n $\simeq$ 3). Away from n $\simeq$ 3, both hole and electron doping drive the system toward non-Fermi-liquid behaviour, and spectral weight is transferred from the low-energy peak into upper and lower Hubbard-like features. By analysing the low-frequency self-energy exponent and the dynamical part of the local spin susceptibility, we identify a narrow window of enhanced spin fluctuations on the slightly hole-doped side (n $\simeq$ 2.94), i.e. a spin-freezing-crossover regime of the kind reported in the literature for multiorbital Hund metals. This places Pb$_9$Cu(VO$_4$)$_6$Br$_2$ among the promising members of the Cu-substituted apatite family.

Inorganic crystal materials have broad application potential due to excellent physical and chemical properties, with elastic properties (shear modulus, bulk modulus) crucial for predicting materials' electrical conductivity, thermal conductivity and mechanical properties. Traditional experimental measurement suffers from high cost and low efficiency, while theoretical simulation and graph neural network-based machine learning methods–especially crystal graph convolutional neural networks (CGCNNs)–have become effective alternatives, achieving remarkable results in predicting material elastic properties. This study trained two CGCNN models using shear modulus and bulk modulus data of 10987 materials from the Matbench v0.1 dataset, which exhibit high accuracy (mean absolute error <13, coefficient of determination R-squared close to 1) and good generalization ability. Materials were screened to retain those with band gaps between 0.1-3.0 eV and exclude radioactive element-containing compounds. The final predicted dataset comprises two parts: 54359 crystal structures from the Materials Project database and 26305 crystal structures discovered by Merchant et al. (2023 Nature 624 80). Ultimately, this study completed the prediction of shear modulus and bulk modulus for 80664 inorganic crystals. This work enriches existing material elastic data resources and provides robust support for material design, with all data openly available at https://doi.org/10.57760/sciencedb.j00213.00104.

Understanding the interactions between microstructure, strain, phase, and material behavior is crucial in many scientific fields. However, quantifying these correlations is challenging, as it requires the use of multiple instruments and techniques, often separated by space and time. The Dual Imaging And Diffraction (DIAD) beamline at Diamond is designed to address this challenge. DIAD allows its users to visualize internal structures, identify compositional/phase changes, and measure strain. DIAD provides two independent beams combined at one sample position, allowing quasi-simultaneous X-ray Computed Tomography and X-ray Powder Diffraction. A unique functionality of the DIAD configuration is the ability to perform image-guided diffraction, where the micron-sized diffraction beam is scanned over the complete area of the imaging field of view without moving the specimen. This moving beam diffraction geometry enables the study of fast-evolving and motion-susceptible processes and samples. Here, we discuss the novel moving beam diffraction geometry presenting the latest findings on the reliability of both geometry calibration and data reduction routines used. Our measures confirm diffraction is most sensitive to the moving geometry for the detector position downstream normal to the incident beam. The observed data confirm that the motion of the KB mirror coupled with a fixed aperture slit results in a rigid translation of the beam probe, without affecting the angle of the incident beam path to the sample. Our measures demonstrate a nearest-neighbour calibration can achieve the same accuracy as a self-calibrated geometry when the distance between calibrated and probed sample region is smaller or equal to the beam spot size. We show the absolute error of the moving beam diffraction geometry remains below 0.0001, which is the accuracy we observe for the beamline with stable beam operation.

This study presents a method for deterministic Er3+ doping of x-cut TFLN using focused ion beam (FIB) implantation with sub-100 nm spatial precision, enabling seamless integration of active rare-earth ions into this technologically relevant platform for lithium niobate integrated nanophotonics. Photoluminescence (PL) measurements from implanted regions reveal Stark-split 4f-4f transitions consistent with bulk Er-doped lithium niobate, indicating similar lattice occupation. Temperature-dependent PL measurements from 300 K to 5 K exhibit conventional behaviour down to approximately 50 K, followed by a marked decrease in the emission intensity and lifetime. This anomaly is attributed to a suppression of the pyroelectric response in LiNbO3 at low temperatures, which affects local electric fields and, consequently, Er3+ emission. The sensitivity of the PL response to the modulation frequency and polarization of the 980 nm excitation light is also consistent with possible mechanisms linking thermal effects and internal fields arising in the thin film. The results demonstrate a method for the targeted doping with Er3+ ions into the most widely used cut of TFLN for integrated photonic devices and provide further important considerations for their exploitation in cryogenic quantum devices.

Accurately determining ground-state properties of quantum many-body systems remains one of the major challenges of quantum simulation. In this work, we present a protocol for estimating the ground-state energy using only global time evolution under a target Hamiltonian. This avoids the need for controlled operations that are typically required in conventional quantum phase estimation and extends the algorithm applicability to analog simulators. Our method extracts energy differences from measurements of the Loschmidt echo over an initial ground-state approximation, combines them with direct energy measurements, and solves a set of equations to infer the individual eigenenergies. We benchmark this protocol on free-fermion systems, showing orders-of-magnitude precision gains over direct energy measurements on the initial state, with accuracy improving rapidly with initial-state fidelity and persisting for hundreds of modes. We further demonstrate applicability to the 2D Ising and Fermi-Hubbard models and show that the approach extends naturally to other observables such as order parameters. Finally, we analyze the effect of experimental imperfections and propose error-mitigation strategies. These results establish a practical route to compute physically relevant quantities with high precision using globally controlled quantum simulators.

We study a broad class of qudit stabilizer codes, termed $\mathbb{Z}_N$ bivariate-bicycle (BB) codes, arising either as two-dimensional realizations of modulated gauge theories or as $\mathbb{Z}_N$ generalizations of binary BB codes. Our central finding, derived from the polynomial representation, is that the essential topological properties of these $\mathbb{Z}_N$ codes can be determined by the properties of their $\mathbb{Z}_p$ counterparts, where $p$ are the prime factors of $N$, even when $N$ contains prime powers ($N = \prod_i p_i^{k_i}$). This result yields a significant simplification by leveraging the well-studied framework of codes with prime qudit dimensions. In particular, this insight directly enables the generalization of the algebraic-geometric methods (e.g., the Bernstein-Khovanskii-Kushnirenko theorem) to determine anyon fusion rules in the general qudit situation. Moreover, we elucidate the symmetry-enriched topological (SET) order underlying the quasifractonic behavior in qudit BB codes (including the Delfino-Chamon-You model), resolving the associated anyon mobility puzzle. We also develop an efficient computational algebraic method, based on Gröbner bases over the ring of integers, to determine both the topological order and its SET properties.

Exactly solvable models of topologically ordered phases with non-abelian anyons typically require complicated many-body interactions which do not naturally appear in nature. This motivates the "inverse problem" of quantum many-body physics: given microscopic systems with experimentally realistic two-body interactions, how to design a Hamiltonian that realizes a desired topological phase? Here we solve this problem on a platform motivated by Rydberg atoms, where elementary two-level systems couple via simple blockade interactions. Within this framework, we construct Hamiltonians that realize topological orders described by non-abelian quantum double models. We analytically prove the existence of topological order in the ground state, and present efficient schemes to prepare these states. We also introduce protocols for the controlled adiabatic braiding of anyonic excitations to probe their non-abelian statistics. Our construction is generic and applies to quantum doubles $\mathcal{D}(G)$ for arbitrary finite groups $G$. We illustrate braiding for the simplest non-abelian quantum double $\mathcal{D}(S_3)$.

Motivated by the ubiquity of decoherence in quantum hardware and the growing role of imaginary-time evolution (ITE) in quantum algorithms, we investigate how many-body correlations generated by imaginary-time filtering are modified by local decoherence. We introduce measurement-dressed imaginary-time evolution (MDITE), which alternates ITE with projective-measurement channels, producing a competition between low-energy filtering and local dephasing. By developing a new efficient quantum Monte Carlo method, we uncover MDITE mixed-state transitions with spontaneous-symmetry-breaking signatures in the driving of 1D transverse-field Ising and 2D columnar dimerized Heisenberg Hamiltonians in the resulting density matrices. In the continuous limit, the Choi-Jamiolkowski mapping yields a tractable equilibrium description with conformal criticality that qualitatively captures the phase transitions. At finite protocol parameters, however, the four-point correlator violates the conformal cross-ratio form and the critical exponents deviate from their continuous-limit values, signaling the loss of conformal symmetry and richer nonequilibrium criticality. Our results establish MDITE as a controlled setting for exploring mixed-state phases and critical phenomena driven by the interplay between imaginary-time filtering and decoherence.

We present a combined theoretical and experimental study of angle-dependent parametric pumping of magnons in Yttrium Iron Garnet films, with a focus on the mechanisms that transfer parametrically injected magnons toward the spectral minimum where Bose-Einstein condensation occurs. Using a classical Hamiltonian formalism, we analyze the threshold conditions for parametric instability as a function of the angle between the microwave pumping field and the external magnetic field, continuously tracing the transition between parallel and transverse pumping. We also describe two competing four-magnon scattering mechanisms that transfer parametric magnons toward the bottom of their frequency spectrum: The step-by-step Kolmogorov-Zakharov cascade, which is allowed for all magnetic field values, and the kinetic instability mechanisms that provide a much more efficient single-step channel in transferring magnons directly to the lowest-energy states, but occurs within specific regions of the pumping angle and the external magnetic field where the conservation laws permit it. In the experimental part, we employ microfocused Brillouin light scattering spectroscopy in combination with a vector magnet, allowing for angle-resolved mapping of the magnon population spectrum under controlled pumping angle. We observe that transverse pumping, although characterized by a higher instability threshold, yields a markedly stronger population at the spectral minimum compared to parallel pumping. These observations demonstrate that the kinetic instability channel plays a dominant role in transferring magnons to the spectral minimum under such conditions. These results reveal the crucial role of pumping geometry in shaping the magnon distribution and provide guidelines for optimizing the flux of magnons into the condensate, thereby advancing the control of magnon Bose-Einstein condensation in magnetic insulators.

The stability of nonlinear waves on curved surfaces is a problem of widespread interest across physics. Here, we establish the stability criteria for dark solitons on a spherical Bose-Einstein condensate. We demonstrate a sharp instability threshold in the nonlinear parameter, beyond which solitons decay into vortex dipoles via snake instabilities. Analytically and numerically, we prove this decay is dictated by a single unstable mode for each angular momentum $m \geq 2$, which is a universal mechanism that controls the resulting vortex state. Unlike in the full three-dimensional case, where snake instabilities lead to vortex rings, a dark soliton confined to the surface of a bubble can only decay into vortex pairs.

Twisted cylindrical tubes are important model systems for nanostructures, heterostructures, and curved quantum devices. In this work, we investigate the quantum behavior of an electron confined to a twisted cylindrical surface. By first calculating the strain tensor to obtain the induced surface metric, we employ da Costa's formalism to derive the geometry-induced quantum potential. This potential modifies the Schrödinger equation even in the absence of external forces, allowing us to determine the bound states and energy eigenvalues. This was made in the linear and non-linear torsion regime. Furthermore, we analyze two distinct scattering problems: (i) scattering within an infinite cylinder containing a twisted section, and (ii) scattering of a free particle incident upon a finite twisted cylinder. Our goal is to understand how geometry and strain influence the properties of analogous untwisted systems. It turns out that both the linear and non-linear twists yield to a geometric phase into the wave function, while the da Costa potential is kept unchanged. Consequently, the system supports bound states whose energie spectrum is twist independent. For both scattering problems, we find that the transmission probability is insensitive to torsion, whereas it is significantly affected by the particle angular momentum and the cylinder's radius, exhibiting distinct oscillatory behavior. These findings suggest relevant implications for engineering quantum devices based on materials with controlled curvature and twist.

Localization transitions represent a fundamental class of continuous phase transitions, yet they occur without any accompanying symmetry breaking. We resolve this by introducing the concept of dynamical translational symmetry (DTS), which is defined not by the Hamiltonian but by the long-time dynamics of local observables. Its order parameter, the time-averaged local translational contrast (TLTC), quantitatively diagnoses whether evolution restores or breaks translational equivalence. We demonstrate that the TLTC universally captures the Anderson localization transition, the many-body localization transition, and topological phase transitions, revealing that these disparate phenomena are unified by the emergent breaking of DTS. This work establishes a unified dynamical-symmetry framework for phases transitions beyond the equilibrium paradigm.

The Mpemba effect, where a state farther from equilibrium relaxes faster than one closer to it, is a striking phenomenon in both classical and quantum systems. In open quantum systems, however, the quantum Mpemba effect (QME) typically occurs only for specifically chosen initial states, which limits its universality. Here we present a general and experimentally feasible strategy to realize both QME and anti-QME. By applying a temporary bond-dissipation quench, we selectively suppresses or enhances slow relaxation modes, thereby reshaping relaxation pathways independently of both the system and the initial state. We demonstrate this mechanism in systems with dephasing and boundary dissipation, and outline feasible cold-atom implementations. Our results establish controllable dissipation as a versatile tool for quantum control, accelerated relaxation, and efficient nonequilibrium protocols.

I investigate the generic problem of lossy compression of a fluctuating stochastic signal $X$ into a discrete representation $Z$ through optimal thresholding. The signal modulates transition rates of a two-state system described by a binary variable $Y$. Optimising the retained mutual information between $Z$ and $Y$ under a constraint on fixed encoding cost of $Z$ reveals Pareto-optimal trade-offs, determined numerically using genetic algorithms. In the small-noise regime, these fronts are either concave or exhibit piecewise convex “intrusions” separated by first-order transitions in the optimal protocol. An analytical high-rate expansion shows that the optimal threshold density follows a universal cube-root scaling with the product of the prior distribution and the Fisher information associated with the response, which holds qualitatively even for few discrete states. Extending the analysis to non-Gaussian fluctuations reveals that for some parameters optimal encoders can yield strictly better information-cost trade-offs than Gaussian surrogates, meaning the same information content can often be achieved with fewer discrete readout states.

We recast quantum entanglement as a cohomological obstruction to reconstructing a global quantum state from locally compatible information. We address this by considering presheaf cohomologies of states and entanglement witnesses. Sheafification erases the global-from-local signature while leaving within-patch multipartite structure, captured by local entanglement groups introduced here. For smooth parameter families, the obstruction admits a differential-geometric representative obtained by pairing an appropriate witness field with the curvature of a natural unitary connection on the associated bundle of amplitudes. We also introduce a Quantum Entanglement Index (QEI) as an index-theoretic invariant of entangled states and explain its behavior. Finally, we outline a theoretical physics approach to probe these ideas in quantum many-body systems and suggest a possible entanglement-induced correction as an experimental validation. Detailed numerical implementations for concrete quantum many-body models are presented in the companion paper \cite{2026arXiv260113467I}.

We present an analytical theory of second harmonic generation (SHG) in hybrid structures combining a nonlinear 2D crystal with a dielectric metasurface waveguide. The theory describes the excitation spectrum and enhancement of SHG at both leaky mode and quasi-bound state in the continuum (quasi-BIC) resonances in terms of the material parameters. For low-loss systems, the SHG efficiency at leaky resonances is determined by their radiative broadening, governed by the relevant Fourier harmonics of the metasurface polarizability, whereas the SHG enhancement at quasi-BIC resonances is ultimately limited by inhomogeneous broadening and absorption in the system. We also describe the emergence and polarization properties of second harmonic diffracted beams. These beams appear even if both the 2D crystal and the meta-waveguide are centrosymmetric owing to the nonlocal mechanism of SHG. The developed framework provides a systematic theoretical basis for optimizing the resonant nonlinear frequency conversion in hybrid 2D-material-metasurface platforms and identifies the fundamental limitations of the SHG efficiency.

Continuous particle exchange thermal machines require no time-dependent driving, can be realised in solid-state electronic devices, and miniaturised to nanometre scale. Quantum dots, providing a narrow energy filter and allowing to manipulate particle flow between the hot and cold reservoirs are at the heart of such devices. It has been theoretically shown that by mitigating passive heat flow, Carnot efficiency can be approached arbitrarily closely in a quantum dot heat engine, and experimentally, values of 0.7{\eta}C have been reached. However, for practical applications, other parameters of a thermal machine, such as maximum power, efficiency at maximum power, and noise - stability of the power output or heat extraction - take precedence over maximising efficiency. We explore the effect of internal microscopic dynamics of a quantum dot on these quantities and demonstrate that its performance as a thermal machine depends on few parameters - the overall conductance and three inherent asymmetries of the dynamics. These parameters will act as a guide to engineering the quantum states of the quantum dot, allowing to optimise its performance beyond that of the simplest case of a two-fold spin-degenerate transmission level.

The way living tissues respond to external mechanical forces is crucial in physiological processes like embryogenesis, homeostasis or tumor growth. Providing a complete description across length scales which relates the properties of individual cells to the rheological behavior of complex 3D-tissues remains an open challenge. The development of simplified biomimetic tissues capable of reproducing essential mechanical features of living tissues can help achieving this major goal. We report in this work the development of a microfluidic device that enables to achieve the sequential assembly of biomimetic prototissues and their rheological characterization. We synthesize prototissues by the controlled assembly of Giant Unilamellar Vesicles (GUVs) for which we can tailor their sizes and shapes as well as their level of GUV-GUV adhesion. We address a rheological description at multiple scales which comprises an analysis at the local scale of individual GUVs and at the global scale of the prototissue. The flow behavior of prototissues ranges from purely viscous to viscoelastic for increasing levels of adhesion. At low adhesion the flow response is dominated by viscous dissipation, which is mediated by GUV spatial reorganizations at the local scale, whereas at high adhesion the flow is viscoelastic, which results from a combination of internal reorganizations and deformation of individual GUVs. Such multiscale characterization of model biomimetic tissues provides a robust framework to rationalize the role of cell adhesion in the flow dynamics of living tissues.