Decoherence of flux qubits due to 1/f flux noise

We have investigated decoherence in Josephson-junction flux qubits. Based on the measurements of decoherence at various bias conditions, we discriminate contributions of different noise sources. We present a Gaussian decay function extracted from the echo signal as evidence of dephasing due to 1/f flux noise whose spectral density is evaluated to be about (10(-6)Phi0)2/Hz at 1 Hz. We also demonstrate that, at an optimal bias condition where the noise sources are well decoupled, the coherence observed in the echo measurement is limited mainly by energy relaxation of the qubit.     

Liouville Results for <Emphasis Type="Italic">m</Emphasis>-Laplace Equations in Half-Space and Strips with Mixed Boundary Value Conditions and Finite Morse Index

We consider sign-changing solutions of the equation \(-\Delta _m u= |u|^{p-1}u\) where \(m\ge 2\) and \(p>1\) in half-space and strips with nonlinear mixed boundary value conditions. We prove Liouville type theorems for stable solutions or for solutions which are stable outside a compact set. The main methods used are the integral estimates, the Pohozaev-type identity and the monotonicity formula.     

Characterization of the current-induced resistive spots in superconducting \hbox {YBa}_{2} \hbox {Cu}_{3} \hbox {O}_{7} strips

For over a decade, ultrathin superconducting films have been developed for the detection of single photons at optical or near infrared frequencies, with competitive performances in terms of quantum efficiency, speed, and low dark count rate. In order to avoid the requirement of helium refrigeration, we consider here the use of high temperature materials, known to achieve very fast responsiveness to laser irradiation. We excite thin filaments of the cuprate \(\hbox {YBa}_{2} \hbox {Cu}_{3} \hbox {O}_{7}\) by rectangular pulses of supercritical current so as to produce either a phase-slip centre (PSC) or a normal hot spot (HS), according to the temperature and the current amplitude selected. That procedure provides information about the maximum bias current to be used in a particle detector, about the return current back to the quiescent state after excitation, and about the rate of growth and decay of a HS. We also measure the time of PSC nucleation. A unique feature of that approach is to provide the rate of heat transfer between the film and its substrate at whatever temperature, in the superconducting state, in the practical conditions of operation.     

Driven dynamics and rotary echo of a qubit tunably coupled to a harmonic oscillator

We have investigated the driven dynamics of a superconducting flux qubit that is tunably coupled to a microwave resonator. We find that the qubit experiences an oscillating field mediated by off-resonant driving of the resonator, leading to strong modifications of the qubit Rabi frequency. This opens an additional noise channel, and we find that low-frequency noise in the coupling parameter causes a reduction of the coherence time during driven evolution. The noise can be mitigated with the rotary-echo pulse sequence, which, for driven systems, is analogous to the Hahn-echo sequence.     

Fabrication and characterization of Al nanomechanical resonators for coupling to nanoelectronic devices

We report on a suspension technique for Al doubly clamped beams. The technique is based on two consecutive reactive ion etching processes in CF₄ plasma, anisotropic and isotropic, of SiO _x on which Al layer is deposited. With this technique, Al doubly clamped beams were fabricated. One of the beams was characterized using a magnetomotive measurement scheme at low temperatures. The developed suspension technique is suitable for the fabrication of Al nanoelectronic devices with a mechanical degree of freedom, in particular, superconducting flux qubits with partly suspended loops.     

A priori estimates for superlinear and subcritical elliptic equations: the Neumann boundary condition case

We consider here solutions of a nonlinear Neumann elliptic equation Δu +?f (x, u) =?0 in Ω, ?u/?ν =?0 on ?Ω, where Ω is a bounded open smooth domain in ${\mathbb{R}^N, N\geq2}$ and f satisfies super-linear and subcritical growth conditions. We prove that L ^∞?bounds on solutions are equivalent to bounds on their Morse indices.     

On the Palais–Smale condition

We present a new sufficient assumption weaker than the classical Ambrosetti–Rabinowitz condition which guarantees the boundedness of (PS) sequences. Moreover, we relax the standard subcritical polynomial growth condition ensuring the compactness of a bounded (PS) sequences. We also revise the Costa–Magalhaes condition [8] to obtain Cerami condition. As a consequence, some existence results derived by minimax methods were proved. Finally, we establish the existence of positive solution under the subcritical polynomial growth condition, while the strong superlinear condition is only required along an unbounded sequence. In other words, a certain degraded oscillation is allowed.     

Criteria determination to choose piezoelectric materials for BAW resonator applications via colored picosecond acoustics

A great number of piezoelectric materials which could be used in the fabrication of BAW resonators were investigated via colored picosecond acoustics technique in order to study the required parameters for designing and fabricating improved devices. These parameters concerns acoustic longitudinal velocity, v_L, elastic stiffness constant, C^D₃₃, intrinsic mechanical loss, tanδ, and electromechanical coupling coefficient, k²_t. We first quantify the effect of the ratio between the wavelength pulse of a femtosecond laser and the period of Brillouin oscillations, λ_p/T. It is found that C^D₃₃ depends linearly on λ_p/T. Then, we deduced novel relations for stiffness constant and mechanical coupling coefficient. Moreover, the determination of different parameters (density, refractive index and v_L) of piezoelectric film is achieved, with good agreement with literature. The optimized conditions for the parameter choice of BAW resonators are found to be: 300?GPa?<?C^D₃₃?<?500?GPa and 1.7?GPa?<?e²₃₃/ε^s₃₃?<?28.5?GPa with λ_p/T?>?37 10³?m/s where e₃₃ and ε^s₃₃ are the piezoelectric constant and the materials permittivity in the direction 3, respectively.     

Existence of radial solutions with prescribed number of zeros for elliptic equations and their Morse index

In this paper we consider radially symmetric solutions of the nonlinear Dirichlet problem Δu+f(|x|,u)=0 in Ω, where Ω is a ball in RN, N?3 and f satisfies some appropriate assumptions. We prove existence of radially symmetric solutions with k prescribed number of zeros. Moreover, when f(|x|,u)=K(|x|)|u|^p−1u, using the uniqueness result due to Tanaka (2008) [21], we verify that these solutions are non-degenerate and we prove that their radial Morse index is exactly k.