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We numerically and experimentally investigate the phononic loss for superconducting resonators fabricated on a piezoelectric substrate. With the help of finite element method simulations, we calculate the energy loss due to electromechanical conversion into bulk and surface acoustic waves. This sets an upper limit for the resonator internal quality factor $Q_i$. To validate the simulation, we fabricate quarter wavelength coplanar waveguide resonators on GaAs and measure $Q_i$ as function of frequency, power and temperature. We observe a linear increase of $Q_i$ with frequency, as predicted by the simulations for a constant electromechanical coupling. Additionally, $Q_i$ shows a weak power dependence and a negligible temperature dependence around 10$\,$mK, excluding two level systems and non-equilibrium quasiparticles as the main source of losses at that temperature.

Most earthquake ruptures propagate at speeds below the shear wave velocity within the crust, but in some rare cases, ruptures reach supershear speeds. The physics underlying the transition of natural subshear earthquakes to supershear ones is currently not fully understood. Most observational studies of supershear earthquakes have focused on determining which fault segments sustain fully-grown supershear ruptures. Experimentally cross-validated numerical models have identified some of the key ingredients required to trigger a transition to supershear speed. However, the conditions for such a transition in nature are still unclear, including the precise location of this transition. In this work, we provide theoretical and numerical insights to identify the precise location of such a transition in nature. We use fracture mechanics arguments with multiple numerical models to identify the signature of supershear transition in coseismic off-fault damage. We then cross-validate this signature with high-resolution observations of fault zone width and early aftershock distributions. We confirm that the location of the transition from subshear to supershear speed is characterized by a decrease in the width of the coseismic off-fault damage zone. We thus help refine the precise location of such a transition for natural supershear earthquakes.

Spins confined in quantum dots are considered as a promising platform for quantum information processing. While many advanced quantum operations have been demonstrated, experimental as well as theoretical efforts are now focusing on the development of scalable spin quantum bit architectures. One particularly promising method relies on the coupling of spin quantum bits to microwave cavity photons. This would enable the coupling of distant spins via the exchange of virtual photons for two qubit gate applications, which still remains to be demonstrated with spin qubits. Here, we use a circuit QED spin-photon interface to drive a single electronic spin in a carbon nanotube based double quantum dot using cavity photons. The microwave spectroscopy allows us to identify an electrically controlled spin transition with a decoherence rate which can be tuned to be as low as $250kHz$. We show that this value is consistent with the expected hyperfine coupling in carbon nanotubes. These coherence properties, which can be attributed to the use of pristine carbon nanotubes stapled inside the cavity, should enable coherent spin-spin interaction via cavity photons and compare favourably to the ones recently demonstrated in Si-based circuit QED experiments.

The interplay of superconductivity with a non-trivial spin texture holds promises for the engineering of non-abelian Majorana quasi-particles. A wide class of systems expected to exhibit exotic correlations are based on nanoscale conductors with strong spin-orbit interaction, subject to a strong external magnetic field. The strength of the spin-orbit coupling is a crucial parameter for the topological protection of Majorana modes as it forbids other trivial excitations at low energy. The spin-orbit interaction is in principle intrinsic to a material. As a consequence, experimental efforts have been recently focused on semiconducting nano-conductors or spin-active atomic chains contacted to a superconductor. Alternatively, we show how both a spin-orbit and a Zeeman effect can be autonomously induced by using a magnetic texture coupled to any low dimensional conductor, here a carbon nanotube. Transport spectroscopy through superconducting contacts reveals oscillations of Andreev like states under a change of the magnetic texture. These oscillations are well accounted for by a scattering theory and are absent in a control device with no magnetic texture. A large synthetic spin-orbit energy of about 1.1 meV, larger than the intrinsic spin orbit energy in many other platforms, is directly derived from the number of oscillations. Furthermore, a robust zero energy state, the hallmark of devices hosting localized Majorana modes, emerges at zero magnetic field. Our findings synthetize all the features for the emergence of Majorana modes at zero magnetic field in a controlled, local and autonomous fashion. It could be used for advanced experiments, including microwave spectroscopy and braiding operations, which are at the heart of new schemes of topological quantum computation.

The ability to control electronic states at the nanoscale has contributed to our modern understanding of condensed matter. In particular, quantum dot circuits represent model systems for the study of strong electronic correlations, epitomized by the Kondo effect. Here, we show that circuit Quantum Electrodynamics architectures can be used to study the internal degrees of freedom of such a many-body phenomenon. We couple a quantum dot to a high finesse microwave cavity to measure with an unprecedented sensitivity the dot electronic compressibility i.e. the ability of the dot to accommodate charges. Because it corresponds solely to the charge response of the electronic system, this quantity is not equivalent to the conductance which involves in general other degrees of freedom such as spin. By performing dual conductance/compressibility measurements in the Kondo regime, we uncover directly the charge dynamics of this peculiar mechanism of electron transfer. Strikingly, the Kondo resonance, visible in transport measurements, is transparent to microwave photons trapped in the high finesse cavity. This reveals that, in such a many body resonance, finite conduction is achieved from a charge frozen by Coulomb interaction. This previously elusive freezing of charge dynamics is in stark contrast with the physics of a free electron gas. Our setup highlights the power of circuit quantum electrodynamics architectures to study condensed matter problems. The tools of cavity quantum electrodynamics could be used in other types of mesoscopic circuits with many-body correlations and bring a promising platform to perform quantum simulation of fermion-boson problems., Comment: minor differences with published version

Driving a quantum system at finite frequency allows one to explore its dynamics. This has become a well mastered resource for controlling the quantum state of two level systems in the context of quantum information processing. However, this can also be of fundamental interest, especially with many-body systems which display an intricate finite frequency behavior. In condensed matter, the Kondo effect epitomizes strong electronic correlations, but the study of its dynamics and the related scaling laws has remained elusive so far. Here, we fill this gap by studying a carbon nanotube based Kondo quantum dot driven by a microwave signal. Our findings not only confirm long-standing theoretical predictions, but also allow us to establish a simple ansatz for the scaling laws on the Kondo problem at finite frequency. More generally, our technique opens a new path for understanding the dynamics of complex quantum dot circuits in the context of quantum simulation of strongly correlated electron fluids.

Circuit QED techniques have been instrumental to manipulate and probe with exquisite sensitivity the quantum state of superconducting quantum bits coupled to microwave cavities. Recently, it has become possible to fabricate new devices where the superconducting quantum bits are replaced by hybrid mesoscopic circuits combining nanoconductors and metallic reservoirs. This mesoscopic QED provides a new experimental playground to study the light-matter interaction in electronic circuits. Here, we present the experimental state of the art of Mesoscopic QED and its theoretical description. A first class of experiments focuses on the artificial atom limit, where some quasiparticles are trapped in nanocircuit bound states. In this limit, the Circuit QED techniques can be used to manipulate and probe electronic degrees of freedom such as confined charges, spins, or Andreev pairs. A second class of experiments consists in using cavity photons to reveal the dynamics of electron tunneling between a nanoconductor and fermionic reservoirs. For instance, the Kondo effect, the charge relaxation caused by grounded metallic contacts, and the photo-emission caused by voltage-biased reservoirs have been studied. The tunnel coupling between nanoconductors and fermionic reservoirs also enable one to obtain split Cooper pairs, or Majorana bound states. Cavity photons represent a qualitatively new tool to study these exotic condensed matter states., Comment: 34 pages, 18 figures, 1 table, minor differences with the published version to appear in Journal of Physics: Condensed Matter as a topical review

Circuit quantum electrodynamics allows one to probe, manipulate and couple superconducting quantum bits using cavity photons at an exquisite level. One of its cornerstones is the possibility to achieve the strong coupling which allows one to hybridize coherently light and matter. Its transposition to quantum dot circuits could offer the opportunity to use new degrees of freedom such as individual charge or spin. However, the strong coupling of quantum dot circuits to cavity photons remains to be observed. Here, we demonstrate a hybrid superconductor-quantum dot circuit which realizes the strong coupling of an individual electronic excitation to microwave photons. We observe a vacuum Rabi splitting 2g~10 MHz which exceeds by a factor of 3 the linewidth of the hybridized light-matter states. Our findings open the path to ultra-long distance entanglement of quantum dot based qubits. They could be adapted to many other circuit designs, shedding new light on the roadmap for scalability of quantum dot setups.

Cavity quantum electrodynamics allows one to study the interaction between light and matter at the most elementary level. The methods developed in this field have taught us how to probe and manipulate individual quantum systems like atoms and superconducting quantum bits with an exquisite accuracy. There is now a strong effort to extend further these methods to other quantum systems, and in particular hybrid quantum dot circuits. This could turn out to be instrumental for a noninvasive study of quantum dot circuits and a realization of scalable spin quantum bit architectures. It could also provide an interesting platform for quantum simulation of simple fermion-boson condensed matter systems. In this short review, we discuss the experimental state of the art for hybrid circuit quantum electrodynamics with quantum dots, and we present a simple theoretical modeling of experiments., Comment: Minor differences with published version

Microwave cavities have been widely used to investigate the behavior of closed few-level systems. Here, we show that they also represent a powerful probe for the dynamics of charge transfer between a discrete electronic level and fermionic continua. We have combined experiment and theory for a carbon nanotube quantum dot coupled to normal metal and superconducting contacts. In equilibrium conditions, where our device behaves as an effective quantum dot-normal metal junction, we approach a universal photon dissipation regime governed by a quantum charge relaxation effect. We observe how photon dissipation is modified when the dot admittance turns from capacitive to inductive. When the fermionic reservoirs are voltage biased, the dot can even cause photon emission due to inelastic tunneling to/from a Bardeen-Cooper-Schrieffer peak in the density of states of the superconducting contact. We can model these numerous effects quantitatively in terms of the charge susceptibility of the quantum dot circuit. This validates an approach that could be used to study a wide class of mesoscopic QED devices., Comment: 15 pages, 8 figures, minor differences with published version

Brief account of results on the Cauchy problem for the Einstein equations starting with early the works of Darmois and Lichnerowicz and going up to the proofs of the existence and uniqueness of solutions global in space and local in time, in Sobolev spaces, for the general equations either in vacuum or with classical sources., Comment: 19 pages

Engineering the interaction between light and matter is an important goal in the emerging field of quantum opto-electronics. Thanks to the use of cavity quantum electrodynamics architectures, one can envision a fully hybrid multiplexing of quantum conductors. Here, we use such an architecture to couple two quantum dot circuits . Our quantum dots are separated by 200 times their own size, with no direct tunnel and electrostatic couplings between them. We demonstrate their interaction, mediated by the cavity photons. This could be used to scale up quantum bit architectures based on quantum dot circuits or simulate on-chip phonon-mediated interactions between strongly correlated electrons.

We show how to solve the Cauchy problem for the Einstein-Vlasov equations with geometric initial data on a light-cone., Comment: 14 pages

We present a streamlined, complete proof, valid in arbitrary space dimension $n$, and using only spinors on the oriented Riemannian space $(M^{n};g),$ of the positive energy theorem in General Relativity.

We prove that analytic initial data on a light cone arising from a metric satisfying a "near-roundness" condition near the vertex lead to a solution of the vacuum Einstein equations to the future of the light-cone., Comment: 33 pages. Contribution to the proceedings of the "Petrov 2010 Anniversary Symposium on General Relativity and Gravitation", held in Kazan, Nov 2010

The Einstein equations in wave map gauge are a geometric second order system for a Lorentzian metric. To study existence of solutions of this hyperbolic quasi diagonal system with initial data on a characteristic cone which are not zero in a neighbourhood of the vertex one can appeal to theorems due to Cagnac and Dossa, proved for a scalar wave equation, for initial data in functional spaces relevant for their proofs. It is difficult to check that the initial data that we have constructed as solutions of the Einstein wave-map gauge constraints satisfy the more general of the Cagnac-Dossa hypotheses which uses weighted energy estimates. In this paper we start a new study of energy estimates using on the cone coordinates adapted to its null structure which are precisely the coordinates used to solve the constraints, following work of Rendall who considered the Cauchy problem for Einstein equations with data on two intersecting characteristic surfaces., Comment: 11 pages. Contribution to the proceedings of the conference "New Developments in Lorentzian Geometry", held in Berlin, Nov 2009

We prove an existence theorem for the Cauchy problem on a characteristic cone for the vacuum Einstein equations., Comment: 9 pages, to be published in the proceedings of the conference "Complex Analysis & Dynamical Systems IV'', held in Nahariya, May 2009

We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime solution of the Cauchy problem on a characteristic cone for the hyperbolic system of the reduced Einstein equations in wave-map gauge also satisfies the full Einstein equations. We prove a geometric uniqueness theorem for this Cauchy problem in the vacuum case., Comment: 83 pages, 1 figure

We analyse the Cauchy problem on a characteristic cone, including its vertex, for the Einstein equations in arbitrary dimensions. We use a wave map gauge, solve the obtained constraints and show gauge conservation., Comment: 10 pages, to be published in the Proceedings of the 15th International Conference on Waves and Stability in Continuous Media, held in Palermo, 28th June to 1st July 2009

We prove that the area of cross-sections of light-cones, in space-times satisfying suitable energy conditions, is smaller than or equal to that of the corresponding cross-sections in Minkowski, or de Sitter, or anti-de Sitter space-time. The equality holds if and only if the metric coincides with the corresponding model in the domain of dependence of the light-cone., Comment: 24 pages, 1 figure. Minor changes to match published version

The Einstein-scalar field theory can be used to model gravitational physics with scalar field matter sources. We discuss the initial value formulation of this field theory, and show that the ideas of Leray can be used to show that the Einstein-scalar field system of partial differential equations is well-posed as an evolutionary system. We also show that one can generate solutions of the Einstein-scalar field constraint equations using conformal methods.

We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new conformal invariant, which is sensitive to the presence of the initial data for the scalar field, we are able to divide the set of free conformal data into subclasses depending on the possible signs for the coefficients of terms in the resulting Einstein-scalar field Lichnerowicz equation. For many of these subclasses we determine whether or not a solution exists. In contrast to other well studied field theories, there are certain cases, depending on the mean curvature and the potential of the scalar field, for which we are unable to resolve the question of existence of a solution. We consider this system in such generality so as to include the vacuum constraint equations with an arbitrary cosmological constant, the Yamabe equation and even (all cases of) the prescribed scalar curvature problem as special cases., Comment: Minor changes, final version. To appear: Classical and Quantum Gravity

We consider the Einstein-Maxwell equations in space-dimension $n$. We point out that the Lindblad-Rodnianski stability proof applies to those equations whatever the space-dimension $n\ge 3$. In even space-time dimension $n+1\ge 6$ we use the standard conformal method on a Minkowski background to give a simple proof that the maximal globally hyperbolic development of initial data sets which are sufficiently close to the data for Minkowski space-time and which are Schwarzschildian outside of a compact set lead to geodesically complete space-times, with a complete Scri, with smooth conformal structure, and with the gravitational field approaching the Minkowski metric along null directions at least as fast as $r^{-(n-1)/2}$., Comment: minor corrections

It is shown that sufficiently smooth initial data for the Einstein-dust or the Einstein-Maxwell-dust equations with non-negative density of compact support develop into solutions representing isolated bodies in the sense that the matter field has spatially compact support and is embedded in an exterior vacuum solution.

In this article, dedicated to one of the best specialist of the FOSH systems, we couple the Bianchi equations with the equations satisfied by the dynamical acceleration of a charged fluid and the derivatives of the associated Maxwell field., Comment: submitted for special issue of Circolo Matematico di Palermo in honor of Guy Boilla

We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because the scalar field introduces three extra terms into the Lichnerowicz equation, rather than just one. Our proofs are constructive and allow for arbitrary dimension (>2) as well as low regularity initial data., Comment: 31 pages

In a previous work, we used a polarization condition to show that there is a family of U(1) symmetric solutions of the vacuum Einstein equations such that each exhibits AVTD (Asymptotic Velocity Term Dominated) behavior in the neighborhood of its singularity. Here we consider the general case of U(1) bundles and determine a condition, called the half polarization condition, necessary and sufficient in our context, for AVTD behavior near the singularity.

We use Fuchsian methods to show that, for any two dimensional manifold $\Sigma^2$, there is a large family of U(1) symmetric solutions of the vacuum Einstein equations on the manifold $\Sigma \times S^1 \times \mathbb{R}$, each of which has AVTD behavior in the neighborhood of its singularity., Comment: proceedings of conference in Elba to appear in Nuovo Cimento

We extend to the Einstein Maxwell Higgs system results first obtained previously in collaboration with V. Moncrief for Einstein equations in vacuum., Comment: to appear in proceedings of the greek relativity meeting 2004

We give a general survey of the solution of the Einstein constraints by the conformal method on n dimensional compact manifolds. We prove some new results about solutions with low regularity (solutions in $H_{2}$ when n=3), and solutions with unscaled sources., Comment: Article for the volume "Space time safari" in honor of Vincent Moncrief

I prove the existence of vacuum $S^{1}$ symmetric Einsteinian, unpolarized, space times which are complete in the direction of the expansion, for small initial data, without supposing that the $S^{1}$ orbits are orthogonal to the 3-manifolds, as was done in previous work in collaboration with V. Moncrief., Comment: 67 pages, text for the volume of the Cargese meeting "50 years of the Cauchy problem in General Relativity"

We prove global completeness in the expanding direction of spacetimes satisfying the vacuum Einstein equations on a manifold of the form $\Sigma \times S^{1}\times R$ where $\Sigma $ is a compact surface of genus $G>1.$ The Cauchy data are supposed to be invariant with respect to the group $S^{1}$ and sufficiently small, but we do not impose a restrictive hypothesis made in gr-qc 0112049 on the lowest eigenvalue of a relevant Laplacian. The total energy decay still holds, but its rate depends of the asymptotic value of this eigenvalue., Comment: Conference in honor of J. Leray, Tokyo 2001, Kajitani and Vaillant ed. to appear Birkhauser

We write a first order symmetric hyperbolic system coupling the Riemann with the dynamical acceleration of a relativistic fluid. W determine the associated, coupled, Bel - Robinson energy, and the integral equality that it satisfies., Comment: 10 pages

We review some old and new results about strict and non strict hyperbolic formulations of the Einstein equations., Comment: To appear in the proceedings of the first Aegean summer school in General Relativity, S. Cotsakis ed. Springer Lecture Notes in Physics

We establish a variant, which has the advantage of introducing only physical characteristics, of the symmetric quasi linear first order system given by H.\ Friedrich for the evolution equations of gravitating fluid bodies in General Relativity which can be important to solve realistic problems. We explicit the conditions under which the system is hyperbolic and admits a well posed Cauchy problem., Comment: To appear in TMNA, volume in honor of A. Granas