Edge Tunneling of Vortices in Superconducting Thin Films

We investigate the phenomenon of the decay of a supercurrent due to the zero-temperature quantum tunneling of vortices from the edge in a thin superconducting film in the absence of an external magnetic field. An explicit formula is derived for the tunneling rate of vortices, which are subject to the Magnus force induced by the supercurrent, through the Coulomb-like potential barrier binding them to the film's edge. Our approach ensues from the non-relativistic version of a Schwinger-type calculation for the decay of the 2D vacuum previously employed for describing vortex-antivortex pair-nucleation in the bulk of the sample. In the dissipation-dominated limit, our explicit edge-tunneling formula yields numerical estimates which are compared with those obtained for bulk-nucleation to show that both mechanisms are possible for the decay of a supercurrent.Comment: REVTeX file, 15 pages, 1 Postscript figure; to appear in Phys.Rev.

The Sound of Sonoluminescence

We consider an air bubble in water under conditions of single bubble sonoluminescence (SBSL) and evaluate the emitted sound field nonperturbatively for subsonic gas-liquid interface motion. Sound emission being the dominant damping mechanism, we also implement the nonperturbative sound damping in the Rayleigh-Plesset equation for the interface motion. We evaluate numerically the sound pulse emitted during bubble collapse and compare the nonperturbative and perturbative results, showing that the usual perturbative description leads to an overestimate of the maximal surface velocity and maximal sound pressure. The radius vs. time relation for a full SBSL cycle remains deceptively unaffected.Comment: 25 pages; LaTex and 6 attached ps figure files. Accepted for publication in Physical Review

Optimized pulses for the control of uncertain qubits

Constructing high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for \pi/2- and \pi-pulses, and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from \pi/2- and \pi-pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter, to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, post facto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.Comment: 38 pages, 15 figures, RevTeX 4.1, minor modifications to the previous versio

Comment on "Transverse Force on a Quantized Vortex in a Superfluid"

The result of Thouless, Ao and Niu (TAN), that the mutual friction parameter $d_\perp =0$, contradicts to the experiments made in rotating 3He-B by Manchester group. The Manchester group observed that $d_\perp <0$ at low temperature and approaches 1 at high temperature. The reason of the contradiction is that TAN did not take into account the Iordanskii force on the vortex and the spectral flow force, which comes from the anomaly related to the low-energy bound states of fermions in cores of quantized vortices. The Iordanskii force is responsible for the negative $d_\perp <0$ at low temperature, while due to the spectral flow $d_\perp$ approaches 1 at high temperature. Relation of the spectral flow anomaly with the paradoxes of the linear and angular momenta in gapless superfluids is discussed.Comment: revtex, 2 pages, submitted to Physical Review Letters as "Comment" to the paper D.J. Thouless, P. Ao and Q. Niu, Phys. Rev. Lett. 76, 3758 (1996

Berry's Phase in the Presence of a Stochastically Evolving Environment: A Geometric Mechanism for Energy-Level Broadening

The generic Berry phase scenario in which a two-level system is coupled to a second system whose dynamical coordinate is slowly-varying is generalized to allow for stochastic evolution of the slow system. The stochastic behavior is produced by coupling the slow system to a heat resevoir which is modeled by a bath of harmonic oscillators initially in equilibrium at temperature T, and whose spectral density has a bandwidth which is small compared to the energy-level spacing of the fast system. The well-known energy-level shifts produced by Berry's phase in the fast system, in conjunction with the stochastic motion of the slow system, leads to a broadening of the fast system energy-levels. In the limit of strong damping and sufficiently low temperature, we determine the degree of level-broadening analytically, and show that the slow system dynamics satisfies a Langevin equation in which Lorentz-like and electric-like forces appear as a consequence of geometrical effects. We also determine the average energy-level shift produced in the fast system by this mechanism.Comment: 29 pages, RevTex, submitted to Phys. Rev.

Temporal Interferometry: A Mechanism for Controlling Qubit Transitions During Twisted Rapid Passage with Possible Application to Quantum Computing

In an adiabatic rapid passage experiment, the Bloch vector of a two-level system (qubit) is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle $\phi (t)$ at the same time that it is inverted. For polynomial twist: $\phi (t) \sim Bt^{n}$. We show that for $n \geq 3$, multiple avoided crossings can occur during the inversion of the external field, and that these crossings give rise to strong interference effects in the qubit transition probability. The transition probability is found to be a function of the twist strength $B$, which can be used to control the time-separation of the avoided crossings, and hence the character of the interference. Constructive and destructive interference are possible. The interference effects are a consequence of the temporal phase coherence of the wavefunction. The ability to vary this coherence by varying the temporal separation of the avoided crossings renders twisted rapid passage with adjustable twist strength into a temporal interferometer through which qubit transitions can be greatly enhanced or suppressed. Possible application of this interference mechanism to construction of fast fault-tolerant quantum CNOT and NOT gates is discussed.Comment: 29 pages, 16 figures, submitted to Phys. Rev.

Quantum error correction : an introductory guide

Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to gate compilation strategies at the software level. As such, familiarity with quantum coding is an essential prerequisite for the understanding of current and future quantum computing architectures. In this review, we provide an introductory guide to the theory and implementation of quantum error correction codes. Where possible, fundamental concepts are described using the simplest examples of detection and correction codes, the working of which can be verified by hand. We outline the construction and operation of the surface code, the most widely pursued error correction protocol for experiment. Finally, we discuss issues that arise in the practical implementation of the surface code and other quantum error correction codes

Selfdual Spin 2 Theory in a 2+1 Dimensional Constant Curvature Space-Time

The Lagrangian constraint analysis of the selfdual massive spin 2 theory in a 2+1 dimensional flat space-time and its extension to a curved one, are performed. Demanding consistence of degrees of freedom in the model with gravitational interaction, gives rise to physical restrictions on non minimal coupling terms and background. Finally, a constant curvature scenario is explored, showing the existence of forbidden mass values. Causality in these spaces is discussed. Aspects related with the construction of the reduced action and the one-particle exchange amplitude, are noted.Comment: 20 pages, references added, little modifications performe

PESSTO monitoring of SN 2012hn: further heterogeneity among faint type I supernovae

We present optical and infrared monitoring data of SN 2012hn collected by the Public ESO Spectroscopic Survey for Transient Objects (PESSTO). We show that SN 2012hn has a faint peak magnitude (MR ~ -15.7) and shows no hydrogen and no clear evidence for helium in its spectral evolution. Instead, we detect prominent Ca II lines at all epochs, which relates this transient to previously described 'Ca-rich' or 'gap' transients. However, the photospheric spectra (from -3 to +32 d with respect to peak) of SN 2012hn show a series of absorption lines which are unique, and a red continuum that is likely intrinsic rather than due to extinction. Lines of Ti II and Cr II are visible. This may be a temperature effect, which could also explain the red photospheric colour. A nebular spectrum at +150d shows prominent CaII, OI, CI and possibly MgI lines which appear similar in strength to those displayed by core-collapse SNe. To add to the puzzle, SN 2012hn is located at a projected distance of 6 kpc from an E/S0 host and is not close to any obvious starforming region. Overall SN 2012hn resembles a group of faint H-poor SNe that have been discovered recently and for which a convincing and consistent physical explanation is still missing. They all appear to explode preferentially in remote locations offset from a massive host galaxy with deep limits on any dwarf host galaxies, favouring old progenitor systems. SN 2012hn adds heterogeneity to this sample of objects. We discuss potential explosion channels including He-shell detonations and double detonations of white dwarfs as well as peculiar core-collapse SNe.Comment: 14 pages, 14 figures, accepted to MNRAS on 14/10/201