Entanglement in fermionic chains with finite range coupling and broken symmetries

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Renyi entropy of a partial observation to a subsystem consisting of $X$ contiguous sites in the limit of large $X$. The present work generalizes similar results due to Its, Jin, Korepin and Its, Mezzadri, Mo. A striking new feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size of $X$. This logarithmic behaviour originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyse the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long range pairing.Comment: 27 pages, 5 figure

On the M\"obius transformation in the entanglement entropy of fermionic chains

There is an intimate relation between entanglement entropy and Riemann surfaces. This fact is explicitly noticed for the case of quadratic fermionic Hamiltonians with finite range couplings. After recollecting this fact, we make a comprehensive analysis of the action of the M\"obius transformations on the Riemann surface. We are then able to uncover the origin of some symmetries and dualities of the entanglement entropy already noticed recently in the literature. These results give further support for the use of entanglement entropy to analyse phase transition.Comment: 29 pages, 5 figures. Final version published in JSTAT. Two new figures. Some comments and references added. Typos correcte

Characterization of a two-transmon processor with individual single-shot qubit readout

We report the characterization of a two-qubit processor implemented with two capacitively coupled tunable superconducting qubits of the transmon type, each qubit having its own non-destructive single-shot readout. The fixed capacitive coupling yields the \sqrt{iSWAP} two-qubit gate for a suitable interaction time. We reconstruct by state tomography the coherent dynamics of the two-bit register as a function of the interaction time, observe a violation of the Bell inequality by 22 standard deviations after correcting readout errors, and measure by quantum process tomography a gate fidelity of 90%

A MEMS-based solid propellant microthruster array for space and military applications

Since combustion is an easy way to achieve large quantities of energy from a small volume, we developed a MEMS based solid propellant microthruster array for small spacecraft and micro-air-vehicle applications. A thruster is composed of a fuel chamber layer, a top-side igniter with a micromachined nozzle in the same silicon layer. Layers are assembled by adhesive bonding to give final MEMS array. The thrust force is generated by the combustion of propellant stored in a few millimeter cube chamber. The micro-igniter is a polysilicon resistor deposited on a low stress SiO2/SiNx thin membrane to ensure a good heat transfer to the propellant and thus a low electric power consumption. A large range of thrust force is obtained simply by varying chamber and nozzle geometry parameters in one step of Deep Reactive Ion Etching (DRIE). Experimental tests of ignition and combustion employing home made (DB+x% BP) propellant composed of a Double-Base and Black-Powder. A temperature of 250 therefore degrees C, enough to propellant initiation, is reached for 40 mW of electric power. A combustion rate of about 3.4 mm/s is measured for DB+20% BP propellant and thrust ranges between 0.1 and 3,5 mN are obtained for BP ratio between 10% and 30% using a microthruster of 100 mu m of throat wide

Quantum Heating of a nonlinear resonator probed by a superconducting qubit

We measure the quantum fluctuations of a pumped nonlinear resonator, using a superconducting artificial atom as an in-situ probe. The qubit excitation spectrum gives access to the frequency and temperature of the intracavity field fluctuations. These are found to be in agreement with theoretical predictions; in particular we experimentally observe the phenomenon of quantum heating

Circuit QED with a Nonlinear Resonator : ac-Stark Shift and Dephasing

We have performed spectroscopic measurements of a superconducting qubit dispersively coupled to a nonlinear resonator driven by a pump microwave field. Measurements of the qubit frequency shift provide a sensitive probe of the intracavity field, yielding a precise characterization of the resonator nonlinearity. The qubit linewidth has a complex dependence on the pump frequency and amplitude, which is correlated with the gain of the nonlinear resonator operated as a small-signal amplifier. The corresponding dephasing rate is found to be close to the quantum limit in the low-gain limit of the amplifier.Comment: Paper : 4 pages, 3 figures; Supplementary material : 1 page, 1 figur

Coulomb charging energy for arbitrary tunneling strength

The Coulomb energy of a small metallic island coupled to an electrode by a tunnel junction is investigated. We employ Monte Carlo simulations to determine the effective charging energy for arbitrary tunneling strength. For small tunneling conductance, the data agree with analytical results based on a perturbative treatment of electron tunneling, while for very strong tunneling recent semiclassical results for large conductance are approached. The data allow for an identification of the range of validity of various analytical predictions.Comment: 4 pages REVTeX, incl 3 figures, to appear in Europhys.Let

Estimation of the mechanical properties of the eye through the study of its vibrational modes

Measuring the eye's mechanical properties in vivo and with minimally invasive techniques can be the key for individualized solutions to a number of eye pathologies. The development of such techniques largely relies on a computational modelling of the eyeball and, it optimally requires the synergic interplay between experimentation and numerical simulation. In Astrophysics and Geophysics the remote measurement of structural properties of the systems of their realm is performed on the basis of (helio-)seismic techniques. As a biomechanical system, the eyeball possesses normal vibrational modes encompassing rich information about its structure and mechanical properties. However, the integral analysis of the eyeball vibrational modes has not been performed yet. Here we develop a new finite difference method to compute both the spheroidal and, specially, the toroidal eigenfrequencies of the human eye. Using this numerical model, we show that the vibrational eigenfrequencies of the human eye fall in the interval 100 Hz - 10 MHz. We find that compressible vibrational modes may release a trace on high frequency changes of the intraocular pressure, while incompressible normal modes could be registered analyzing the scattering pattern that the motions of the vitreous humour leave on the retina. Existing contact lenses with embebed devices operating at high sampling frequency could be used to register the microfluctuations of the eyeball shape we obtain. We advance that an inverse problem to obtain the mechanical properties of a given eye (e.g., Young's modulus, Poisson ratio) measuring its normal frequencies is doable. These measurements can be done using non-invasive techniques, opening very interesting perspectives to estimate the mechanical properties of eyes in vivo. Future research might relate various ocular pathologies with anomalies in measured vibrational frequencies of the eye.Comment: Published in PLoS ONE as Open Access Research Article. 17 pages, 5 color figure