Relaxation of a qubit measured by a driven Duffing oscillator

We investigate the relaxation of a superconducting qubit for the case when its detector, the Josephson bifurcation amplifier, remains latched in one of its two (meta)stable states of forced vibrations. The qubit relaxation rates are different in different states. They can display strong dependence on the qubit frequency and resonant enhancement, which is due to quasienergy resonances. Coupling to the driven oscillator changes the effective temperature of the qubit.Comment: To appear in Phys. Rev. A (2010

Quantum nondemolition-like, fast measurement scheme for a superconducting qubit

We present a measurement protocol for a flux qubit coupled to a dc-Superconducting QUantum Interference Device (SQUID), representative of any two-state system with a controllable coupling to an harmonic oscillator quadrature, which consists of two steps. First, the qubit state is imprinted onto the SQUID via a very short and strong interaction. We show that at the end of this step the qubit dephases completely, although the perturbation of the measured qubit observable during this step is weak. In the second step, information about the qubit is extracted by measuring the SQUID. This step can have arbitrarily long duration, since it no longer induces qubit errors.Comment: published version, minor correction

Phase-space theory for dispersive detectors of superconducting qubits

Motivated by recent experiments, we study the dynamics of a qubit quadratically coupled to its detector, a damped harmonic oscillator. We use a complex-environment approach, explicitly describing the dynamics of the qubit and the oscillator by means of their full Floquet state master equations in phase-space. We investigate the backaction of the environment on the measured qubit and explore several measurement protocols, which include a long-term full read-out cycle as well as schemes based on short time transfer of information between qubit and oscillator. We also show that the pointer becomes measurable before all information in the qubit has been lost.Comment: 15 pages, 8 figure

Comparative Study Between Solid State Welding and Radiant Energy Welding Processes for Joining Metallic Glassy Ribbons

Amorphous alloys have emerged as an important class of advanced materials that own a combination of properties, such as mechanical strength, hardness, high elasticity modulus and a very good corrosion resistance. Since the number of amorphous structures alloys increased in the last decades, ways of joining such materials were studied in order to produce complex structures or increase their size. Thus, if this kind of complex products are obtained, it will diversify their applicability in multiple and various domains. For this research two ways of joining amorphous ribbons has been studied: solid state welding and radiant energy welding. For the radiant energy welding process, it was selected electron beam welding (EBW) method and for the solid-state welding process, ultrasonic welding (UW) method was chosen. Seeing that these methods have found applicability in industries, a comparative study was done in order to see which one offers the best outcome. Recently, in the last years, such products were embedded in a polymer matrix, creating thus, composite materials that have improved mechanical properties. This raised curiosity for major industries, such as aero-space, medical and automotive. Amorphous ribbons from Ni-Fe-Cr-Si-B and Al-Ni-Nd-Co alloy families were welded by EBW method, and Cu-Zr-Al amorphous ribbons were welded by the UW method. Microstructure characterization has been performed by SEM, EDX, XRD and DSC analyses

Integrability and Transcendentality

We derive the two-loop Bethe ansatz for the sl(2) twist operator sector of N=4 gauge theory directly from the field theory. We then analyze a recently proposed perturbative asymptotic all-loop Bethe ansatz in the limit of large spacetime spin at large but finite twist, and find a novel all-loop scaling function. This function obeys the Kotikov-Lipatov transcendentality principle and does not depend on the twist. Under the assumption that one may extrapolate back to leading twist, our result yields an all-loop prediction for the large-spin anomalous dimensions of twist-two operators. The latter also appears as an undetermined function in a recent conjecture of Bern, Dixon and Smirnov for the all-loop structure of the maximally helicity violating (MHV) n-point gluon amplitudes of N=4 gauge theory. This potentially establishes a direct link between the worldsheet and the spacetime S-matrix approach. A further assumption for the validity of our prediction is that perturbative BMN (Berenstein-Maldacena-Nastase) scaling does not break down at four loops, or beyond. We also discuss how the result gets modified if BMN scaling does break down. Finally, we show that our result qualitatively agrees at strong coupling with a prediction of string theory.Comment: 45 pages LaTeX, 3 postscript figures. v2: Chapter on BMN scaling and transcendentality added. v3: version accepted for publication in JSTA

On one-loop correction to energy of spinning strings in S^5

We revisit the computation (hep-th/0306130) of 1-loop AdS_5 x S^5 superstring sigma model correction to energy of a closed circular string rotating in S^5. The string is spinning around its center of mass with two equal angular momenta J_2=J_3 and its center of mass angular momentum is J_1. We revise the argument in hep-th/0306130 that the 1-loop correction is suppressed by 1/J factor (J= J_1 + 2 J_2 is the total SO(6) spin) relative to the classical term in the energy and use numerical methods to compute the leading 1-loop coefficient. The corresponding gauge theory result is known (hep-th/0405055) only in the J_1=0 limit when the string solution becomes unstable and thus the 1-loop shift of the energy formally contains an imaginary part. While the comparison with gauge theory may not be well-defined in this case, our numerical string theory value of the 1-loop coefficient seems to disagree with the gauge theory one. A plausible explanation should be (as in hep-th/0405001) in the different order of limits taken on the gauge theory and the string theory sides of the AdS/CFT duality.Comment: 21 pages, 8 figure

AdS/CFT duality at strong coupling

We study the strong coupling limit of AdS/CFT correspondence in the framework of a recently proposed fermionic formulation of the Bethe Ansatz equations governing the gauge theory anomalous dimensions. We provide examples of states that do not follow the Gubser-Klebanov-Polyakov law at large 't Hooft coupling $\lambda$, in contrast with recent results on the quantum string Bethe equations valid in that regime. This result indicates that the fermionic construction cannot be trusted at large $\lambda$, although it remains an efficient tool to compute the weak coupling expansion of anomalous dimensions.Comment: Presented at Nonlinear Physics. Theory and Experiment. IV Gallipoli, June 22 - July 1, 2006. To appear in the proceeding

Integrability in QCD and beyond

Yang--Mills theories in four space-time dimensions possess a hidden symmetry which does not exhibit itself as a symmetry of classical Lagrangians but is only revealed on the quantum level. It turns out that the effective Yang--Mills dynamics in several important limits is described by completely integrable systems that prove to be related to the celebrated Heisenberg spin chain and its generalizations. In this review we explain the general phenomenon of complete integrability and its realization in several different situations. As a prime example, we consider in some detail the scale dependence of composite (Wilson) operators in QCD and super-Yang--Mills (SYM) theories. High-energy (Regge) behavior of scattering amplitudes in QCD is also discussed and provides one with another realization of the same phenomenon that differs, however, from the first example in essential details. As the third example, we address the low-energy effective action in a N=2 SYM theory which, contrary to the previous two cases, corresponds to a classical integrable model. Finally, we include a short overview of recent attempts to use gauge/string duality in order to relate integrability of Yang--Mills dynamics with the hidden symmetry of a string theory on a curved background.Comment: 87 pages, 4 figures; minor stylistic changes, references added. To be published in the memorial volume 'From Fields to Strings: Circumnavigating Theoretical Phyiscs', World Scientific, 2004. Dedicated to the memory of Ian Koga

A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills

We probe the long-range spin chain approach to planar N=4 gauge theory at high loop order. A recently employed hyperbolic spin chain invented by Inozemtsev is suitable for the SU(2) subsector of the state space up to three loops, but ceases to exhibit the conjectured thermodynamic scaling properties at higher orders. We indicate how this may be bypassed while nevertheless preserving integrability, and suggest the corresponding all-loop asymptotic Bethe ansatz. We also propose the local part of the all-loop gauge transfer matrix, leading to conjectures for the asymptotically exact formulae for all local commuting charges. The ansatz is finally shown to be related to a standard inhomogeneous spin chain. A comparison of our ansatz to semi-classical string theory uncovers a detailed, non-perturbative agreement between the corresponding expressions for the infinite tower of local charge densities. However, the respective Bethe equations differ slightly, and we end by refining and elaborating a previously proposed possible explanation for this disagreement.Comment: 48 pages, 1 figure. v2, further results added: discussion of the relationship to an inhomogeneous spin chain, normalization in sec 3 unified, v3: minor mistakes corrected, published versio