The parity effect in Josephson junction arrays

We study the parity effect and transport due to quasiparticles in circuits comprised of many superconducting islands. We develop a general approach and show that it is equivalent to previous methods for describing the parity effect in their more limited regimes of validity. As an example we study transport through linear arrays of Josephson junctions in the limit of negligible Josephson energy and observe the emergence of the parity effect with decreasing number of non-equilibrium quasiparticles. Due to the exponential increase in the number of relevant charge states with increasing length, in multi-junction arrays the parity effect manifests in qualitatively different ways to the two junction case. The role of charge disorder is also studied as this hides much of the parity physics which would otherwise be observed. Nonetheless, we see that the current through a multi-junction array at low bias is limited by the formation of meta-stable even-parity states.Comment: 8 pages, 5 figure

Single Crystal Sapphire at milli-Kelvin Temperatures: Observation of Electromagnetically Induced Thermal Bistability in High Q-factor Whispering Gallery Modes

Resonance modes in single crystal sapphire ($\alpha$-Al$_2$O$_3$) exhibit extremely high electrical and mechanical Q-factors ($\approx 10^9$ at 4K), which are important characteristics for electromechanical experiments at the quantum limit. We report the first cooldown of a bulk sapphire sample below superfluid liquid helium temperature (1.6K) to as low as 25mK. The electromagnetic properties were characterised at microwave frequencies, and we report the first observation of electromagnetically induced thermal bistability in whispering gallery modes due to the material $T^3$ dependence on thermal conductivity and the ultra-low dielectric loss tangent. We identify "magic temperatures" between 80 to 2100 mK, the lowest ever measured, at which the onset of bistability is suppressed and the frequency-temperature dependence is annulled. These phenomena at low temperatures make sapphire suitable for quantum metrology and ultra-stable clock applications, including the possible realization of the first quantum limited sapphire clock.Comment: 5 pages, 4 figure

High Q-factor Sapphire Whispering Gallery Mode Microwave Resonator at Single Photon Energies and milli-Kelvin Temperatures

The microwave properties of a crystalline sapphire dielectric whispering gallery mode resonator have been measured at very low excitation strength (E/hf=1) and low temperatures (T = 30 mK). The measurements were sensitive enough to observe saturation due to a highly detuned electron spin resonance, which limited the loss tangent of the material to about 2e-8 measured at 13.868 and 13.259 GHz. Small power dependent frequency shifts were also measured which correspond to an added magnetic susceptibility of order 1e-9. This work shows that quantum limited microwave resonators with Q-factors > 1e8 are possible with the implementation of a sapphire whispering gallery mode system

Insulating Josephson-junction chains as pinned Luttinger liquids

Quantum physics in one spatial dimension is remarkably rich, yet even with strong interactions and disorder, surprisingly tractable. This is due to the fact that the low-energy physics of nearly all one-dimensional systems can be cast in terms of the Luttinger liquid, a key concept that parallels that of the Fermi liquid in higher dimensions. Although there have been many theoretical proposals to use linear chains and ladders of Josephson junctions to create novel quantum phases and devices, only modest progress has been made experimentally. One major roadblock has been understanding the role of disorder in such systems. We present experimental results that establish the insulating state of linear chains of sub-micron Josephson junctions as Luttinger liquids pinned by random offset charges, providing a one-dimensional implementation of the Bose glass, strongly validating the quantum many-body theory of one-dimensional disordered systems. The ubiquity of such an electronic glass in Josephson-junction chains has important implications for their proposed use as a fundamental current standard, which is based on synchronisation of coherent tunnelling of flux quanta (quantum phase slips)

Hybrid electron spin resonance and whispering gallery mode resonance spectroscopy of Fe3+ in sapphire

The development of a new era of quantum devices requires an understanding of how paramagnetic dopants or impurity spins behave in crystal hosts. Here, we describe a spectroscopic technique which uses traditional electron spin resonance (ESR) combined with the measurement of a large population of electromagnetic whispering gallery modes. This allows the characterization of the physical parameters of paramagnetic impurity ions in the crystal at low temperatures. We present measurements of two ultrahigh-purity sapphires cooled to 20 mK in temperature, and determine the concentration of Fe3 ions and their frequency sensitivity to a dc magnetic field. Our method is different from ESR in that it is possible to track the resonant frequency of the ion from zero applied magnetic field to any arbitrary value, allowing excellent measurement precision. This high precision reveals anisotropic behavior of the Zeeman splitting. In both crystals, each Zeeman component demonstrates a different g factor

Emergent magnetism at transition-metal–nanocarbon interfaces

Charge transfer at metallo–molecular interfaces may be used to design multifunctional hybrids with an emergent magnetization that may offer an eco-friendly and tunable alternative to conventional magnets and devices. Here, we investigate the origin of the magnetism arising at these interfaces by using different techniques to probe 3d and 5d metal films such as Sc, Mn, Cu, and Pt in contact with fullerenes and rf-sputtered carbon layers. These systems exhibit small anisotropy and coercivity together with a high Curie point. Low-energy muon spin spectroscopy in Cu and Sc–C60 multilayers show a quick spin depolarization and oscillations attributed to nonuniform local magnetic fields close to the metallo–carbon interface. The hybridization state of the carbon layers plays a crucial role, and we observe an increased magnetization as sp3 orbitals are annealed into sp2−π graphitic states in sputtered carbon/copper multilayers. X-ray magnetic circular dichroism (XMCD) measurements at the carbon K edge of C60 layers in contact with Sc films show spin polarization in the lowest unoccupied molecular orbital (LUMO) and higher π*-molecular levels, whereas the dichroism in the σ*-resonances is small or nonexistent. These results support the idea of an interaction mediated via charge transfer from the metal and dz–π hybridization. Thin-film carbon-based magnets may allow for the manipulation of spin ordering at metallic surfaces using electrooptical signals, with potential applications in computing, sensors, and other multifunctional magnetic devices

Antiplatelet therapy with aspirin, clopidogrel, and dipyridamole versus clopidogrel alone or aspirin and dipyridamole in patients with acute cerebral ischaemia (TARDIS): a randomised, open-label, phase 3 superiority trial

Background: Intensive antiplatelet therapy with three agents might be more effective than guideline treatment for preventing recurrent events in patients with acute cerebral ischaemia. We aimed to compare the safety and efficacy of intensive antiplatelet therapy (combined aspirin, clopidogrel, and dipyridamole) with that of guideline-based antiplatelet therapy. Methods: We did an international, prospective, randomised, open-label, blinded-endpoint trial in adult participants with ischaemic stroke or transient ischaemic attack (TIA) within 48 h of onset. Participants were assigned in a 1:1 ratio using computer randomisation to receive loading doses and then 30 days of intensive antiplatelet therapy (combined aspirin 75 mg, clopidogrel 75 mg, and dipyridamole 200 mg twice daily) or guideline-based therapy (comprising either clopidogrel alone or combined aspirin and dipyridamole). Randomisation was stratified by country and index event, and minimised with prognostic baseline factors, medication use, time to randomisation, stroke-related factors, and thrombolysis. The ordinal primary outcome was the combined incidence and severity of any recurrent stroke (ischaemic or haemorrhagic; assessed using the modified Rankin Scale) or TIA within 90 days, as assessed by central telephone follow-up with masking to treatment assignment, and analysed by intention to treat. This trial is registered with the ISRCTN registry, number ISRCTN47823388. Findings: 3096 participants (1556 in the intensive antiplatelet therapy group, 1540 in the guideline antiplatelet therapy group) were recruited from 106 hospitals in four countries between April 7, 2009, and March 18, 2016. The trial was stopped early on the recommendation of the data monitoring committee. The incidence and severity of recurrent stroke or TIA did not differ between intensive and guideline therapy (93 [6%] participants vs 105 [7%]; adjusted common odds ratio [cOR] 0·90, 95% CI 0·67–1·20, p=0·47). By contrast, intensive antiplatelet therapy was associated with more, and more severe, bleeding (adjusted cOR 2·54, 95% CI 2·05–3·16, p<0·0001). Interpretation: Among patients with recent cerebral ischaemia, intensive antiplatelet therapy did not reduce the incidence and severity of recurrent stroke or TIA, but did significantly increase the risk of major bleeding. Triple antiplatelet therapy should not be used in routine clinical practice

Antiplatelet therapy with aspirin, clopidogrel, and dipyridamole versus clopidogrel alone or aspirin and dipyridamole in patients with acute cerebral ischaemia (TARDIS): a randomised, open-label, phase 3 superiority trial

Background: Intensive antiplatelet therapy with three agents might be more effective than guideline treatment for preventing recurrent events in patients with acute cerebral ischaemia. We aimed to compare the safety and efficacy of intensive antiplatelet therapy (combined aspirin, clopidogrel, and dipyridamole) with that of guideline-based antiplatelet therapy.Methods: We did an international, prospective, randomised, open-label, blinded-endpoint trial in adult participants with ischaemic stroke or transient ischaemic attack (TIA) within 48 h of onset. Participants were assigned in a 1:1 ratio using computer randomisation to receive loading doses and then 30 days of intensive antiplatelet therapy (combined aspirin 75 mg, clopidogrel 75 mg, and dipyridamole 200 mg twice daily) or guideline-based therapy (comprising either clopidogrel alone or combined aspirin and dipyridamole). Randomisation was stratified by country and index event, and minimised with prognostic baseline factors, medication use, time to randomisation, stroke-related factors, and thrombolysis. The ordinal primary outcome was the combined incidence and severity of any recurrent stroke (ischaemic or haemorrhagic; assessed using the modified Rankin Scale) or TIA within 90 days, as assessed by central telephone follow-up with masking to treatment assignment, and analysed by intention to treat. This trial is registered with the ISRCTN registry, number ISRCTN47823388.Findings: 3096 participants (1556 in the intensive antiplatelet therapy group, 1540 in the guideline antiplatelet therapy group) were recruited from 106 hospitals in four countries between April 7, 2009, and March 18, 2016. The trial was stopped early on the recommendation of the data monitoring committee. The incidence and severity of recurrent stroke or TIA did not differ between intensive and guideline therapy (93 [6%] participants vs 105 [7%]; adjusted common odds ratio [cOR] 0·90, 95% CI 0·67–1·20, p=0·47). By contrast, intensive antiplatelet therapy was associated with more, and more severe, bleeding (adjusted cOR 2·54, 95% CI 2·05–3·16,

Broken symmetry and critical phenomena in population genetics : the stepping-stone model

In this thesis, I study the behaviour of the Stepping-Stone model: a stochastic model from theoretical population genetics. It was introduced by Kimura and Weiss [1][2] as a simple model to investigate the interplay of the evolutionary processes of random genetic drift, mutation, migration and selection. In particular, they were interested in the behaviour of spatially-structured populations when these processes were mediated by local interactions. From the point of view of statistical physics, the Stepping-Stone model can be viewed as a 2-species, non-equilibrium reaction-diffusion model with spatial degrees of freedom and unique fluctuations that arise from irreversible processes at the microscale. My thesis begins with a brief overview of the theory of stochastic processes that includes both the classical treatment using master equations, the Fokker-Planck equation and the Langevin equation, and modern formalisms that map these equations to operators and functional integrals. This is followed by a discussion of the steady-state and critical phenomena in the Wright-Fisher and Moran models, the non-spatial predecessors of the Stepping-Stone model. Critical phenomena in these models is shown to be associated with the breaking of a discrete symmetry that results in a discontinuous order parameter. Next, the Stepping-Stone model is introduced and reformulated using operators and pathintegrals. Kimura and Weiss were able to solve for the steady-state of the Stepping-Stone model, under certain conditions, but the dynamics of the model remained elusive. This model is related however, to the "Voter" model, which has been well-studied and is known to have a critical spatial dimension of 2 in that only for d ≤ 2 does the system asymptotically reach one of the 2 degenerate absorbing states. I extend the results of Kimura and Weiss and obtain exact results for the dynamics of the Stepping-Stone model. Two regimes of the model are analyzed: 1) the neutral regime, where selection has vanished and mutation is viewed as the control parameter. Here a steady state exists, characterized by a correlation length that diverges as the mutation rate, μ, becomes zero; and 2) the broken symmetry or "fixed" state, where selection is small but finite, and mutations so rare that the relevant description concerns the dynamics of "avalanches" or "cascades" of new alleles induced by the initial mutation and perturbing the system from the absorbing state. A unique kind of dynamical critical phenomenon occurs when selective advantage and mutation become negligible. Like the Voter model, it is qualitatively different both above and below a critical dimension d[sub c] = 2. For spatial dimension d ≤ 2 , the critical behaviour is associated with the breaking of a discrete symmetry and corresponds to fixation of one of the two alleles (genotypes). Symmetry breaking in the Stepping-Stone model is shown to be a consequence of the asymptotic return probability of a random walk—identically one for d ≤ 2 and strictly less than one for d > 2. In addition to the correlation length, the steady-state of the neutral regime is further characterized by a measure of variance defined as the amplitude of the two-point correlation function evaluated at vanishing separation. In genetics this measure of variance is known as F[sub ST], the fixation index. Exact results are derived for both the steady-state value of FST, and its asymptotic time-dependence at the critical point, which approaches 1 in both d = 1 and d = 2. At the critical point, 1 — F[sub ST]~ t[sub -1/2] for d = 1. For d = 2, a much slower decay is found, 1 — F[sub ST] ~ 1/ln(t). The d = 3 critical behaviour of F[sub ST] is that it approaches a constant C < 1 as (C — F[sub ST]) ~ t[sub -1/2]. The constant C is non-universal and related to the return probability of a random walk. It approaches 1 for very large values of the dimensionless constant K = [Λ/(2 π² Dn[sub Tg)] where Λ⁻¹ is the spatial scale of the interaction, rg is the generation time, D is the diffusion constant and n is the population density. A related infinite-alleles model was studied by both Sawyer [3] and Nagalaki[4]. These authors found similar asymptotics for the probability that two randomly choses individuals are genetically identical under certain assumptions. Sawyer[3] also proved that fixation in the infinite alleles model occurs iff the random walk followed by the individuals is recurrent. The broken symmetry or "fixed" regime of the Stepping-Stone model has been explored from the point of view of survival of rare mutant alleles, here parameterized by a coefficient of selection s. The exponent u, governing the divergence of the relaxation time as s —> 0 is calculated and found to be v = 2 for d — 1, while for d ≥ 2 it is given by the mean field value of v = 1. Two other exponents for critical spreading processes are determined and scaling arguments are presented and used to find the decay exponents that characterize the time-dependent survival probability and its asymptotic value for very long times. These results also establish the upper critical dimension of the model, d[sub c] = 2. Finally, these results are rederived and supplemented by a dynamical renormalization group (RG) analysis. The critical behaviour in d = 1 is found in both regimes to be controlled by non-trivial fixed points. The critical behaviour of the broken symmetry regime for d ≥ 2 and its RG fixed point is that of a critical branching process. For the neutral regime, however, the renormalization group flow is qualitatively different in rf = 2 and 3, reflecting the existence of broken symmetry for rf = 2. The RG flow for the rf = 3 neutral regime contains a line of fixed points with the effective description at large scales given by a Gaussian version of the time-dependent Landau-Ginsburg model. Finally, the renormalization results are found to be valid to all orders of perturbation theory.Science, Faculty ofPhysics and Astronomy, Department ofGraduat