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We establish a spectral gap for resonances of the Laplacian of random Schottky surfaces, which is optimal according to a conjecture of Jakobson and Naud.

Neuroscience and artificial intelligence are closely intertwined, but so are the physics of dynamical system, philosophy and psychology. Each of these fields try in their own way to relate observations at the level of molecules, synapses, neurons or behavior, to a function. An influential conceptual approach to this end was popularized by David Marr, which focused on the interaction between three theoretical 'levels of analysis'. With the convergence of simulation-based approaches, algorithm-oriented Neuro-AI and high-throughput data, we currently see much research organized around four levels of analysis: observations, models, algorithms and functions. Bidirectional interaction between these levels influences how we undertake interdisciplinary science., Comment: neuroscience, cognitive neuroscience, computational neuroscience, machine learning, artificial intelligence, philosophy

When a neuron breaks silence, it can emit action potentials in a number of patterns. Some responses are so sudden and intense that electrophysiologists felt the need to single them out, labeling action potentials emitted at a particularly high frequency with a metonym -- bursts. Is there more to bursts than a figure of speech? After all, sudden bouts of high-frequency firing are expected to occur whenever inputs surge. The burst coding hypothesis advances that the neural code has three syllables: silences, spikes and bursts. We review evidence supporting this ternary code in terms of devoted mechanisms for burst generation, synaptic transmission and synaptic plasticity. We also review the learning and attention theories for which such a triad is beneficial., Comment: 15 pages, 4 figures

We investigate the behaviour of the regularized determinant of the Laplace-Beltrami operator on compact hyperbolic surfaces when the genus goes to infinity. We show that for all popular models of random surfaces, with high probability as the genus goes to infinity, the determinant has an exponential growth with a universal exponent. Limit results for some moments of the logarithm of the determinant are then derived., Comment: 20 pages, revised version

We demonstrate a transmon qubit readout based on the nonlinear response to a drive of polaritonic meters in-situ coupled to the qubit. Inside a 3D readout cavity, we place a transmon molecule consisting of a transmon qubit and an ancilla mode interacting via non-perturbative cross-Kerr coupling. The cavity couples strongly only to the ancilla mode, leading to hybridized lower and upper polaritonic meters. Both polaritons are anharmonic and dissipative, as they inherit a self-Kerr nonlinearity $U$ from the ancilla and effective decay $\kappa$ from the open cavity. Via the ancilla, the polariton meters also inherit the non-perturbative cross-Kerr coupling to the qubit. This results in a high qubit-dependent displacement $2\chi > \kappa, ~U$ that can be read out via the cavity without causing Purcell decay. Moreover, the polariton meters, being nonlinear resonators, present bistability, and bifurcation behavior when the probing power increases. In this work, we focus on the bifurcation at low power in the few-photon regime, called the mesoscopic regime, which is accessible when the self-Kerr and decay rates of the polariton meter are similar $U\sim \kappa$. Capitalizing on a latching mechanism by bifurcation, the readout is sensitive to transmon qubit relaxation error only in the first tens of nanoseconds. We thus report a single-shot fidelity of 98.6 $\%$ while having an integration time of a 500 ns and no requirement for an external quantum-limited amplifier.

We consider random n-covers $X_n$ of an arbitrary compact hyperbolic surface $X$. We show that in the large n regime and small window limit, the variance of the smooth spectral statistics of the Laplacian twisted by a unitary abelian character, obey the universal laws of GOE and GUE random matrices, depending on wether the character preserves or breaks the time reversal symmetry. We also prove a generalization for higher dimensional twists valued in compact linear groups. These results confirm a conjecture of Berry and is a discrete analog of a recent work of Rudnick for the Weil-Petersson model of random surfaces., Comment: 22 pages

Quantum impurities are ubiquitous in condensed matter physics and constitute the most stripped-down realization of many-body problems. While measuring their finite-frequency response could give access to key characteristics such as excitations spectra or dynamical properties, this goal has remained elusive despite over two decades of studies in nanoelectronic quantum dots. Conflicting experimental constraints of very strong coupling and large measurement bandwidths must be met simultaneously. We get around this problem using cQED tools, and build a precisely characterized quantum simulator of the boundary sine-Gordon model, a non-trivial bosonic impurity problem. We succeeded to fully map out the finite frequency linear response of this system. Its reactive part evidences a strong renormalisation of the nonlinearity at the boundary in agreement with non-perturbative calculations. Its dissipative part reveals a dramatic many-body broadening caused by multi-photon conversion. The experimental results are matched quantitatively to a resummed diagrammatic calculation based on a microscopically calibrated model. Furthermore, we push the device into a regime where diagrammatic calculations break down, which calls for more advanced theoretical tools to model many-body quantum circuits. We also critically examine the technological limitations of cQED platforms to reach universal scaling laws. This work opens exciting perspectives for the future such as quantifying quantum entanglement in the vicinity of a quantum critical point or accessing the dynamical properties of non-trivial many-body problems., Comment: 39 pages, 14 figures. The final version clarifies the position of our study w.r.t previous works

The modern primary voltage standard is based on the AC Josephson effect and the ensuing Shapiro steps, where a microwave tone applied to a Josephson junction yields a constant voltage $hf/2e$ ($h$ is Planck's constant and $e$ the electron charge) determined by only the microwave frequency $f$ and fundamental constants. Duality arguments for current and voltage have long suggested the possibility of dual Shapiro steps -- that a Josephson junction device could produce current steps with heights determined only on the applied frequency. In this report, we embed an ultrasmall Josephson junction in a high impedance array of larger junctions to reveal dual Shapiro steps. For multiple frequencies, we detect that the AC response of the circuit is synchronised with the microwave tone at frequency $f$, and the corresponding emergence of flat steps in the DC response with current $2ef$, equal to the tunnelling of a Cooper pair per tone period. This work sheds new light on phase-charge duality, omnipresent in condensed matter physics, and extends it to Josephson circuits. Looking forward, it opens a broad range of possibilities for new experiments in the field of circuit quantum electrodynamics and is an important step towards the long-sought closure of the quantum metrology electrical triangle., Comment: 14 pages, 11 figures

We consider Laplacians with non unitary twists acting on sections of flat vector bundles over compact hyperbolic surfaces. These non self-adjoint Laplacians have discrete spectrum inside a parabola in the complex plane. For representations of the fundamental group of the base surface which are of Teichm\"uller type, we investigate the high energy limit and give a precise description of the bulk of the spectrum where Weyl's law is satisfied in terms of critical exponents of the representations which are completely determined by the Manhattan curve associated to the Teichm\"uller deformation. Our main result provides a counting estimate for the eigenvalues outside the bulk with a polynomial improvement over Weyl's law., Comment: 33 pages, 4 figures. Added more relevant references and comments

X-ray binaries provide exceptional laboratories for understanding the physics of matter under the most extreme conditions. Until recently, there were few, if any, observational constraints on the circumbinary environments of X-ray binaries at $\sim$ 100-5000 AU scales; it remains unclear how the accretion onto the compact objects or the explosions giving rise to the compact objects interact with their immediate surroundings. Here, we present the first high-contrast adaptive optics images of X-ray binaries. These observations target all X-ray binaries within $\sim$ 3 kpc accessible with the Keck/NIRC2 vortex coronagraph. This paper focuses on one of the first key results from this campaign: our images reveal the presence of 21 sources potentially associated with the $\gamma$ Cassiopeiae analog high-mass X-ray binary RX J1744.7$-$2713. By conducting different analyses - a preliminary proper motion analysis, a color-magnitude diagram and a probability of chance alignment calculation - we found that three of these 21 sources have a high probability of being bound to the system. If confirmed, they would be in wide orbits ($\sim$ 450 AU to 2500 AU). While follow-up astrometric observations will be needed in $\sim$ 5-10 years to confirm further the bound nature of these detections, these discoveries emphasize that such observations may provide a major breakthrough in the field. In fact, they would be useful not only for our understanding of stellar multiplicity but also for our understanding of how planets, brown dwarfs and stars can form even in the most extreme environments., Comment: Accepted for publication in AJ

In arXiv:1408.4708, Xu defines the dlt motivic zeta function associated to a regular function $f$ on a smooth variety $X$ over a field of characteristic zero. This is an adaptation of the classical motivic zeta function that was introduced by Denef and Loeser. The dlt motivic zeta function is defined on a dlt modification via a Denef-Loeser-type formula, replacing classes of strata in the Grothendieck ring of varieties by stringy motives. We provide explicit examples that show that the dlt motivic zeta function depends on the choice of dlt modification, contrary to what is claimed in arXiv:1408.4708, and that it is therefore not well-defined.

Traveling wave parametric amplifiers (TWPAs) have recently emerged as essential tools for broadband near quantum-limited amplification. However, their use to generate microwave quantum states still misses an experimental demonstration. In this letter, we report operation of a TWPA as a source of two-mode squeezed microwave radiation. We demonstrate broadband entanglement generation between two modes separated by up to 400 MHz by measuring logarithmic negativity between 0.27 and 0.51 and collective quadrature squeezing below the vacuum limit between 1.5 and 2.1 dB. This work opens interesting perspectives for the exploration of novel microwave photonics experiments with possible applications in quantum sensing and continuous variable quantum computing., Comment: version accepted for publication

Let $X=\Lambda\backslash\mathbb{H}$ be a Schottky surface, that is, a conformally compact hyperbolic surface of infinite area. Let $\delta$ denote the Hausdorff dimension of the limit set of $\Lambda$. We prove that for any compact subset $\mathcal{K} \subset\{\,s\,:\,\Re(s)>\frac{\delta}{2}\,\}$, if one picks a random degree $n$ cover $X_{n}$ of $X$ uniformly at random, then with probability tending to one as $n\to\infty$, there are no resonances of $X_{n}$ in $\mathcal{K}$ other than those already belonging to $X$ (and with the same multiplicity). This result is conjectured to be the optimal one for bounded frequency resonances and is analogous to both Alon's and Friedman's conjectures for random graphs, which are now theorems due to Friedman and Bordenave-Collins, respectively., Comment: 34 pages, this version: fixed typos and minor change to Introduction

Josephson meta-materials have recently emerged as very promising platform for superconducting quantum science and technologies. Their distinguishing potential resides in ability to engineer them at sub-wavelength scales, which allows complete control over wave dispersion and nonlinear interaction. In this article we report a versatile Josephson transmission line with strong third order nonlinearity which can be tuned from positive to negative values, and suppressed second order non linearity. As an initial implementation of this multipurpose meta-material, we operate it to demonstrate reversed Kerr phase-matching mechanism in traveling wave parametric amplification. Compared to previous state of the art phase matching approaches, this reversed Kerr phase matching avoids the presence of gaps in transmission, can reduce gain ripples, and allows in situ tunability of the amplification band over an unprecedented wide range. Besides such notable advancements in the amplification performance with direct applications to superconducting quantum computing and generation of broadband squeezing, the in-situ tunability with sign reversal of the nonlinearity in traveling wave structures, with no counterpart in optics to the best of our knowledge, opens exciting experimental possibilities in the general framework of microwave quantum optics, single-photon detection and quantum limited amplification.

Semiconductor-superconductor hybrid systems have outstanding potential for emerging high-performance nanoelectronics and quantum devices. However, critical to their successful application is the fabrication of high-quality and reproducible semiconductor-superconductor interfaces. Here, we realize and measure axial Al-Ge-Al nanowire heterostructures with atomically precise interfaces, enwrapped by an ultrathin epitaxial Si layer further denoted as Al-Ge/Si-Al nanowire heterostructures. The heterostructures were synthesized by a thermally induced exchange reaction of single-crystalline Ge/Si core/shell nanowires and lithographically defined Al contact pads. Applying this heterostructure formation scheme enables self-aligned quasi one-dimensional crystalline Al leads contacting ultrascaled Ge/Si segments with contact transparencies greater than 96%. Integration into back-gated field-effect devices and continuous scaling beyond lithographic limitations allows us to exploit the full potential of the highly transparent contacts to the 1D hole gas at the Ge-Si interface. This leads to the observation of ballistic transport as well as quantum confinement effects up to temperatures of 150 K. Low-temperature measurements reveal proximity-induced superconductivity in the Ge/Si core/shell nanowires. The realization of a Josephson field-effect transistor allows us to study the subgap structure caused by multiple Andreev reflections. Most importantly, the absence of a quantum dot regime indicates a hard superconducting gap originating from the highly transparent contacts to the 1D hole gas, which is potentially interesting for the study of Majorana zero modes. Moreover, underlining the importance of the proposed thermally induced Al-Ge/Si-Al heterostructure formation technique, our system could contribute to the development of key components of quantum computing such as gatemon or transmon qubits

Extreme pressures and high magnetic fields can affect materials in profound and fascinating ways. However, large pressures and fields are often mutually incompatible; the rapidly changing fields provided by pulsed magnets induce eddy currents in the metallic components used in conventional pressure cells, causing serious heating, forces and vibration. Here we report a diamond-anvil-cell made mainly out of insulating composites that minimizes inductive heating while retaining sufficient strength to apply pressures of up to 9 GPa. Any residual metallic components are made of low-conductivity metals and patterned to reduce eddy currents. The simple design enables rapid sample or pressure changes, desired by pulsed-magnetic-field-facility users. The pressure cell has been used in pulsed magnetic fields of up to 65 T with no noticeable heating at cryogenic temperatures. Several measurement techniques are possible inside the cell at temperatures as low as 500 mK.

Anomalies are by definition rare, thus labeled examples are very limited or nonexistent, and likely do not cover unforeseen scenarios. Unsupervised learning methods that don't necessarily encounter anomalies in training would be immensely useful. Generative vision models can be useful in this regard but do not sufficiently represent normal and abnormal data distributions. To this end, we propose constant curvature manifolds for embedding data distributions in unsupervised visual anomaly detection. Through theoretical and empirical explorations of manifold shapes, we develop a novel hyperspherical Variational Auto-Encoder (VAE) via stereographic projections with a gyroplane layer - a complete equivalent to the Poincar\'e VAE. This approach with manifold projections is beneficial in terms of model generalization and can yield more interpretable representations. We present state-of-the-art results on visual anomaly benchmarks in precision manufacturing and inspection, demonstrating real-world utility in industrial AI scenarios. We further demonstrate the approach on the challenging problem of histopathology: our unsupervised approach effectively detects cancerous brain tissue from noisy whole-slide images, learning a smooth, latent organization of tissue types that provides an interpretable decisions tool for medical professionals.

Let $X$ be a compact connected hyperbolic surface, that is, a closed connected orientable smooth surface with a Riemannian metric of constant curvature -1. For each $n\in\mathbf{N}$, let $X_{n}$ be a random degree-$n$ cover of $X$ sampled uniformly from all degree-$n$ Riemannian covering spaces of $X$. An eigenvalue of $X$ or $X_{n}$ is an eigenvalue of the associated Laplacian operator $\Delta_{X}$ or $\Delta_{X_{n}}$. We say that an eigenvalue of $X_n$ is new if it occurs with greater multiplicity than in $X$. We prove that for any $\varepsilon>0$, with probability tending to 1 as $n\to\infty$, there are no new eigenvalues of $X_n$ below $\frac{3}{16}-\varepsilon$. We conjecture that the same result holds with $\frac{3}{16}$ replaced by $\frac{1}{4}$., Comment: 54 pages, 5 figures. Accepted for publication in GAFA. This version: journal version, incorporated referees' comments and added figures

Electromagnetic fields possess zero point fluctuations (ZPF) which lead to observable effects such as the Lamb shift and the Casimir effect. In the traditional quantum optics domain, these corrections remain perturbative due to the smallness of the fine structure constant. To provide a direct observation of non-perturbative effects driven by ZPF in an open quantum system we wire a highly non-linear Josephson junction to a high impedance transmission line, allowing large phase fluctuations across the junction. Consequently, the resonance of the former acquires a relative frequency shift that is orders of magnitude larger than for natural atoms. Detailed modelling confirms that this renormalization is non-linear and quantum. Remarkably, the junction transfers its non-linearity to about 30 environmental modes, a striking back-action effect that transcends the standard Caldeira-Leggett paradigm. This work opens many exciting prospects for longstanding quests such as the tailoring of many-body Hamiltonians in the strongly non-linear regime, the observation of Bloch oscillations, or the development of high-impedance qubits., Comment: 10 pages, 4 figures and Supplementary Material

We present the first statistical analysis of exoplanet direct imaging surveys combining adaptive optics imaging at small separations with deep seeing-limited observations at large separations allowing us to study the entire orbital separation domain from 5 to 5000~au simultaneously. Our sample of 344 stars includes only confirmed members of nearby young associations and is based on all AO direct-imaging detection limits readily available online, with addition of our own previous seeing limited surveys. Assuming that the companion distribution in mass and semi-major axis follows a power law distribution and adding a dependence on the mass of the host star, such as $d^2n\propto fM^{\alpha}a^{\beta} (M_\star/M_{\odot})^{\gamma}$d$ M $d$a$, we constrain the parameters to obtained $\alpha=-0.18^{+0.77}_{-0.65}$, $\beta=-1.43^{+0.23}_{-0.24}$, and $\gamma=0.62^{+0.56}_{-0.50}$,at a 68\% confidence level, and we obtain $f=0.11^{+0.11}_{-0.05}$, for the overall planet occurrence rate for companions with masses between 1 to 20~\mj\ in the range 5--5000~au. Thus, we find that occurrence of companions is negatively correlated with semi-major axis and companion mass (marginally) but is positively correlated with the stellar host mass. Our inferred mass distribution is in good agreement with other distributions found previously from direct imaging surveys for planets and brown dwarfs, but is shallower as a function of mass than the distributions inferred by radial velocity surveys of gas giants in the 1--3\,au range. This may suggest that planets at these wide and very-wide separations represent the low-mass tail of the brown dwarfs and stellar companion distribution rather than an extension of the distribution of the inner planets., Comment: 26 pages, 8 figures Accepted to Astronomical Journal Updated Table 4

We report on the fabrication and characterization of 50 Ohms, flux-tunable, low-loss, SQUID-based transmission lines. The fabrication process relies on the deposition of a thin dielectric layer (few tens of nanometers) via Atomic Layer Deposition (ALD) on top of a SQUID array, the whole structure is then covered by a non-superconducting metallic top ground plane. We present experimental results from five different samples. We systematically characterize their microscopic parameters by measuring the propagating phase in these structures. We also investigate losses and discriminate conductor from dielectric losses. This fabrication method offers several advantages. First, the SQUID array fabrication does not rely on a Niobium tri-layer process but on a simpler double angle evaporation technique. Second, ALD provides high quality dielectric leading to low-loss devices. Further, the SQUID array fabrication is based on a standard, all-aluminum process, allowing direct integration with superconducting qubits. Moreover, our devices are in-situ flux tunable, allowing mitigation of incertitude inherent to any fabrication process. Finally, the unit cell being a single SQUID (no extra ground capacitance is needed), it is straightforward to modulate the size of the unit cell periodically, allowing band-engineering. This fabrication process can be directly applied to traveling wave parametric amplifiers., Comment: 9 pages, 9 figures, Appendixes

An amplifier combining noise performances as close as possible to the quantum limit with large bandwidth and high saturation power is highly desirable for many solid state quantum technologies such as high fidelity qubit readout or high sensitivity electron spin resonance for example. Here we introduce a new Traveling Wave Parametric Amplifier based on Superconducting QUantum Interference Devices. It displays a 3 GHz bandwidth, a -102 dBm 1-dB compression point and added noise near the quantum limit. Compared to previous state-of-the-art, it is an order of magnitude more compact, its characteristic impedance is in-situ tunable and its fabrication process requires only two lithography steps. The key is the engineering of a gap in the dispersion relation of the transmission line. This is obtained using a periodic modulation of the SQUID size, similarly to what is done with photonic crystals. Moreover, we provide a new theoretical treatment to describe the non-trivial interplay between non-linearity and such periodicity. Our approach provides a path to co-integration with other quantum devices such as qubits given the low footprint and easy fabrication of our amplifier., Comment: 6 pages, 4 figures, Appendixes

We introduce a permutation model for random degree $n$ covers $X_{n}$ of a non-elementary convex-cocompact hyperbolic surface $X=\Gamma\backslash\mathbb{H}$. Let $\delta$ be the Hausdorff dimension of the limit set of $\Gamma$. We say that a resonance of $X_{n}$ is new if it is not a resonance of $X$, and similarly define new eigenvalues of the Laplacian. We prove that for any $\epsilon>0$ and $H>0$, with probability tending to $1$ as $n\to\infty$, there are no new resonances $s=\sigma+it$ of $X_{n}$ with $\sigma\in[\frac{3}{4}\delta+\epsilon,\delta]$ and $t\in[-H,H]$. This implies in the case of $\delta>\frac{1}{2}$ that there is an explicit interval where there are no new eigenvalues of the Laplacian on $X_{n}$. By combining these results with a deterministic `high frequency' resonance-free strip result, we obtain the corollary that there is an $\eta=\eta(X)$ such that with probability $\to1$ as $n\to\infty$, there are no new resonances of $X_{n}$ in the region $\{\,s\,:\,\mathrm{Re}(s)>\delta-\eta\,\}$., Comment: 38 pages, 2 figures. Final revisions based on referee comments: minor corrections and simplification of Section 5

Qubit readout is an indispensable element of any quantum information processor. In this work, we experimentally demonstrate a non-perturbative cross-Kerr coupling between a transmon and a polariton mode which enables an improved quantum non-demolition (QND) readout for superconducting qubits. The new mechanism uses the same experimental techniques as the standard QND qubit readout in the dispersive approximation, but due to its non-perturbative nature, it maximizes the speed, the single-shot fidelity and the QND properties of the readout. In addition, it minimizes the effect of unwanted decay channels such as the Purcell effect. We observed a single-shot readout fidelity of 97.4% for short 50 ns pulses, and we quantified a QND-ness of 99% for long measurement pulses with repeated single-shot readouts.

Let $\Gamma$ be a Zariski dense Kleinian Schottky subgroup of PSL2(C). Let $\Lambda(\Gamma)$ be its limit set, endowed with a Patterson-Sullivan measure $\mu$ supported on $\Lambda(\Gamma)$. We show that the Fourier transform $\widehat{\mu}(\xi)$ enjoys polynomial decay as $\vert \xi \vert$ goes to infinity. This is a PSL2(C) version of the result of Bourgain-Dyatlov [8], and uses the decay of exponential sums based on Bourgain-Gamburd sum-product estimate on C. These bounds on exponential sums require a delicate non-concentration hypothesis which is proved using some representation theory and regularity estimates for stationary measures of certain random walks on linear groups., Comment: 2 figures