Automated Synthesis of Dynamically Corrected Quantum Gates

We address the problem of constructing dynamically corrected gates for non-Markovian open quantum systems in settings where limitations on the available control inputs and/or the presence of control noise make existing analytical approaches unfeasible. By focusing on the important case of singlet-triplet electron spin qubits, we show how ideas from optimal control theory may be used to automate the synthesis of dynamically corrected gates that simultaneously minimize the system's sensitivity against both decoherence and control errors. Explicit sequences for effecting robust single-qubit rotations subject to realistic timing and pulse-shaping constraints are provided, which can deliver substantially improved gate fidelity for state-of-the-art experimental capabilities.Comment: 5 pages; further restructure and expansio

Keplerian Squeezed States and Rydberg Wave Packets

We construct minimum-uncertainty solutions of the three-dimensional Schr\"odinger equation with a Coulomb potential. These wave packets are localized in radial and angular coordinates and are squeezed states in three dimensions. They move on elliptical keplerian trajectories and are appropriate for the description of the corresponding Rydberg wave packets, the production of which is the focus of current experimental effort. We extend our analysis to incorporate the effects of quantum defects in alkali-metal atoms, which are used in experiments.Comment: accepted for publication in Physical Review

Fluctuation Superconductivity in Mesoscopic Aluminum Rings

Fluctuations are important near phase transitions, where they can be difficult to describe quantitatively. Superconductivity in mesoscopic rings is particularly intriguing because the critical temperature is an oscillatory function of magnetic field. There is an exact theory for thermal fluctuations in one-dimensional superconducting rings, which are therefore expected to be an excellent model system. We measure the susceptibility of many rings, one ring at a time, using a scanning SQUID that can isolate magnetic signals from seven orders of magnitude larger background applied flux. We find that the fluctuation theory describes the results and that a single parameter characterizes the ways in which the fluctuations are especially important at magnetic fields where the critical temperature is suppressed.Comment: Reprinted with permission from AAA

Edge-Magnetoplasmon Wave-Packet Revivals in the Quantum Hall Effect

The quantum Hall effect is necessarily accompanied by low-energy excitations localized at the edge of a two-dimensional electron system. For the case of electrons interacting via the long-range Coulomb interaction, these excitations are edge magnetoplasmons. We address the time evolution of localized edge-magnetoplasmon wave packets. On short times the wave packets move along the edge with classical E cross B drift. We show that on longer times the wave packets can have properties similar to those of the Rydberg wave packets that are produced in atoms using short-pulsed lasers. In particular, we show that edge-magnetoplasmon wave packets can exhibit periodic revivals in which a dispersed wave packet reassembles into a localized one. We propose the study of edge-magnetoplasmon wave packets as a tool to investigate dynamical properties of integer and fractional quantum-Hall edges. Various scenarios are discussed for preparing the initial wave packet and for detecting it at a later time. We comment on the importance of magnetoplasmon-phonon coupling and on quantum and thermal fluctuations.Comment: 18 pages, RevTex, 7 figures and 2 tables included, Fig. 5 was originally 3Mbyte and had to be bitmapped for submission to archive; in the process it acquired distracting artifacts, to upload the better version, see http://physics.indiana.edu/~uli/publ/projects.htm

Elliptical Squeezed States and Rydberg Wave Packets

We present a theoretical construction for closest-to-classical wave packets localized in both angular and radial coordinates and moving on a keplerian orbit. The method produces a family of elliptical squeezed states for the planar Coulomb problem that minimize appropriate uncertainty relations in radial and angular coordinates. The time evolution of these states is studied for orbits with different semimajor axes and eccentricities. The elliptical squeezed states may be useful for a description of the motion of Rydberg wave packets excited by short-pulsed lasers in the presence of external fields, which experiments are attempting to produce. We outline an extension of the method to include certain effects of quantum defects appearing in the alkali-metal atoms used in experiments.Comment: published in Phys. Rev. A, vol. 52, p. 2234, Sept. 199

Fluxoid fluctuations in mesoscopic superconducting rings

Rings are a model system for studying phase coherence in one dimension. Superconducting rings have states with uniform phase windings that are integer multiples of 2$\pi$ called fluxoid states. When the energy difference between these fluxoid states is of order the temperature so that phase slips are energetically accessible, several states contribute to the ring's magnetic response to a flux threading the ring in thermal equilibrium and cause a suppression or downturn in the ring's magnetic susceptibility as a function of temperature. We review the theoretical framework for superconducting fluctuations in rings including a model developed by Koshnick$^1$ which includes only fluctuations in the ring's phase winding number called fluxoid fluctuations and a complete model by von Oppen and Riedel$^2$ that includes all thermal fluctuations in the Ginzburg-Landau framework. We show that for sufficiently narrow and dirty rings the two models predict a similar susceptibility response with a slightly shifted Tc indicating that fluxoid fluctuations are dominant. Finally we present magnetic susceptibility data for rings with different physical parameters which demonstrate the applicability of our models. The susceptibility data spans a region in temperature where the ring transitions from a hysteretic to a non hysteretic response to a periodic applied magnetic field. The magnetic susceptibility data, taken where transitions between fluxoid states are slow compared to the measurement time scale and the ring response was hysteretic, decreases linearly with increasing temperature resembling a mean field response with no fluctuations. At higher temperatures where fluctuations begin to play a larger role a crossover occurs and the non-hysteretic data shows a fluxoid fluctuation induced suppression of diamagnetism below the mean field response that agrees well with the models

Persistent currents in normal metal rings

The authors have measured the magnetic response of 33 individual cold mesoscopic gold rings, one ring at a time. The response of some sufficiently small rings has a component that is periodic in the flux through the ring and is attributed to a persistent current. Its period is close to h/e, and its sign and amplitude vary between rings. The amplitude distribution agrees well with predictions for the typical h/e current in diffusive rings. The temperature dependence of the amplitude, measured for four rings, is also consistent with theory. These results disagree with previous measurements of three individual metal rings that showed a much larger periodic response than expected. The use of a scanning SQUID microscope enabled in situ measurements of the sensor background. A paramagnetic linear susceptibility and a poorly understood anomaly around zero field are attributed to defect spins.Comment: Journal version. 4+ pages, 3 figures. See http://stanford.edu/group/moler/publications.html for the auxiliary document containing additional data and discussion (Ref. 29). Changes w.r.t. v1: Clarified some details in introduction and regarding experimental procedures, shortened abstract, added references and fixed some typo

Spin dynamics of wave packets evolving with the Dirac Hamiltonian in atoms with high Z

The motion of circular WP for one electron in central Coulomb field with high Z is calculated. The WP is defined in terms of solutions of the Dirac equation in order to take into account all possible relevant effects in particular the spin-orbit potential. A time scale is defined within which spin dynamics must be taken into account mainly in the atoms with high Z. Within this time scale there exists a mechanism of collapses and revivals of the spin already shown by the authors for harmonic oscillator potential and called the 'spin-orbit pendulum'. However this effect has not the exact periodicity of the simpler model, but the WP's spatial motion is nevertheless quite similar.Comment: 17 pages, 9 figures, LaTeX2e, uses IOP style files (included). Title changed, one reference adde