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T. Barker

Publications and source records attributed to T. Barker.

10 recordsLinked to original sources
arXiv2026

Coulomb blockade in microscopic material defects as a source of decoherence and noise in solid-state quantum circuits

A critical limitation of solid-state quantum devices arises from the materials from which they are fabricated: uncontrolled surfaces, interfaces, and structural imperfections introduce numerous sources of loss and decoherence. Despite extensive efforts, linking these decoherence mechanisms to their microscopic material origins -- essential for developing effective mitigation strategies -- remains an outstanding challenge that has slowed coherence improvements. Here, using scanning gate microscopy on live superconducting circuits we identify a previously unrecognised decoherence mechanism originating from Coulomb blockade and microwave-driven charge tunnelling in metallic grains. Such grains are ubiquitous in thin-film devices fabricated by standard lithography processes. By characterising multiple defects across different devices, we find such defects to be as common and as debilitating to device performance as two-level system (TLS) defects, while originating from a fundamentally different physical mechanism. Importantly, conventional characterisation techniques would misattribute this loss to other, microwave power-independent processes. Our observations thus reveal a widespread source of decoherence in superconducting circuits, challenging the prevailing paradigm that coherence lifetimes are primarily limited by TLS defects. Eliminating metallic grains during fabrication provides a clear and practical route to suppress this mechanism, offering a pathway towards improved coherence and reduced noise in microwave-based solid-state quantum devices.

quant-ph↗
arXiv2024

In-situ scanning gate imaging of individual two-level material defects in live superconducting quantum circuits

The low temperature physics of structurally amorphous materials is governed by two-level system defects (TLS), the exact origin and nature of which remain elusive despite decades of study. Recent advances towards realising stable high-coherence platforms for quantum computing has increased the importance of studying TLS in solid-state quantum circuits, as they are a persistent source of decoherence and instability. Here we perform scanning gate microscopy on a live superconducting quantum circuit at millikelvin temperatures to locate individual TLS. Our method directly reveals the microscopic nature of TLS and is also capable of deducing the three dimensional orientation of individual TLS electric dipole moments. Such insights, when combined with structural information of the underlying materials, can help unravel the detailed microscopic nature and chemical origin of TLS, directing strategies for their eventual mitigation.

cond-mat.mtrl-sci↗
arXiv2017

Existence and Weak* Stability for the Navier-Stokes System with Initial Values in Critical Besov Spaces

In 2016, Seregin and uSverák, conceived a notion of global in time solution (as well as proving existence of them) to the three dimensional Navier-Stokes equation with $L_3$ solenoidal initial data called 'global $L_3$ solutions'. A key feature of global $L_3$ solutions is continuity with respect to weak convergence of a sequence of solenoidal $L_3$ initial data. The first aim of this paper is to show that a similar notion of ' global $\dot{B}^{-\frac{1}{4}}_{4,\infty}$ solutions' exists for solenoidal initial data in the wider critical space $\dot{B}^{-\frac{1}{4}}_{4,\infty}$ and satisfies certain continuity properties with respect to weak* convergence of a sequence of solenoidal $\dot{B}^{-\frac{1}{4}}_{4,\infty}$ initial data. This is the widest such critical space if one requires the solution to the Navier-Stokes equations minus the caloric extension of the initial data to be in the global energy class. For the case of initial values in the wider class of $\dot{B}^{-1+\frac{3}{p}}_{p,\infty}$ initial data ($p>4)$, we prove that for any $0<T<\infty$ there exists a solution to the Navier-Stokes system on $\mathbb{R}^3 \times ]0,T[$ with this initial data. We discuss how properties of these solutions imply a new regularity criteria for 3D weak Leray-Hopf solutions in terms of the norm $\|v(\cdot,t)\|_{\dot{B}^{-1+\frac{3}{p}}_{p,\infty}}$ (as well as certain additional assumptions). The main new observation of this paper, that enables these results, regards the decomposition of homogeneous Besov spaces $\dot{B}^{-1+\frac 3 p}_{p,\infty}$. This does not appear to obviously follow from the known real interpolation theory.

math.AP↗
arXiv2016

Uniqueness Results for Weak Leray-Hopf Solutions of the Navier-Stokes System with Initial Values in Critical Spaces

The main subject of this paper concerns the establishment of certain classes of initial data, which grant short time uniqueness of the associated weak Leray-Hopf solutions of the three dimensional Navier-Stokes equations. In particular, our main theorem that this holds for any solenodial initial data, with finite $L_2(\mathbb{R}^3)$ norm, that also belongs to to certain subsets of $VMO^{-1}(\mathbb{R}^3)$. As a corollary of this, we obtain the same conclusion for any solenodial $u_{0}$ belonging to $L_{2}(\mathbb{R}^3)\cap \mathbb{\dot{B}}^{-1+\frac{3}{p}}_{p,\infty}(\mathbb{R}^3)$, for any $3<p<\infty$. Here, $\mathbb{\dot{B}}^{-1+\frac{3}{p}}_{p,\infty}(\mathbb{R}^3)$ denotes the closure of test functions in the critical Besov space ${\dot{B}}^{-1+\frac{3}{p}}_{p,\infty}(\mathbb{R}^3)$. Our results rely on the establishment of certain continuity properties near the initial time, for weak Leray-Hopf solutions of the Navier-Stokes equations, with these classes of initial data. Such properties seem to be of independent interest. Consequently, we are also able to show if a weak Leray-Hopf solution $u$ satisfies certain extensions of the Prodi-Serrin condition on $\mathbb{R}^3 \times ]0,T[$, then it is unique on $\mathbb{R}^3 \times ]0,T[$ amongst all other weak Leray-Hopf solutions with the same initial value. In particular, we show this is the case if $u\in L^{q,s}(0,T; L^{p,s}(\mathbb{R}^3))$ or if it's $L^{q,\infty}(0,T; L^{p,\infty}(\mathbb{R}^3))$ norm is sufficiently small, where $3<p< \infty$, $1\leq s<\infty$ and $3/p+2/q=1$.

math.AP↗
arXiv2016

Well-posed continuum equations for granular flow with compressibility and $μ(I)$-rheology

Continuum modelling of granular flow has been plagued with the issue of ill-posed equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent $μ(I)$-rheology is ill-posed when the non-dimensional strain-rate $I$ is too high or too low. Here, incorporating ideas from Critical-State Soil Mechanics, we derive conditions for well-posedness of PDEs that combine compressibility with $I$-dependent rheology. When the $I$-dependence comes from a specific friction coefficient $μ(I)$, our results show that, with compressibility, the equations are well-posed for all deformation rates provided that $μ(I)$ satisfies certain minimal, physically natural, inequalities.

cond-mat.soft↗
arXiv2016

On global solutions to the Navier-Stokes system with large $L^{3,\infty}$ initial data

This paper addresses a question concerning the behaviour of a sequence of global solutions to the Navier-Stokes equations, with the corresponding sequence of smooth initial data being bounded in the (non-energy class) weak Lebesgue space $L^{3,\infty}$. It is closely related to the question of what would be a reasonable definition of global weak solutions with a non-energy class of initial data, including the aforementioned Lorentz space. This paper can be regarded as an extension of a similar problem regarding the Lebesgue space $L_3$ to the weak Lebesgue space $L^{3,\infty}$, whose norms are both scale invariant with the respect to the Navier-Stokes scaling.

math.AP↗