Flux–charge duality and topological quantum phase fluctuations in quasi-one-dimensional superconductors

Abstract

It has long been thought that macroscopic phase coherence breaks down in effectively lower-dimensional superconducting systems even at zero temperature due to enhanced topological quantum phase fluctuations. In quasione-dimensional wires, these fluctuations are described in terms of 'quantum phase-slip' (QPS): tunneling of the superconducting order parameter for the wire between states differing by ±2π in their relative phase between the wire's ends. Over the last several decades, many deviations from conventional bulk superconducting behavior have been observed in ultra-narrow superconducting nanowires, some of which have been identified with QPS. While at least some of the observations are consistent with existing theories for QPS, other observations in many cases point to contradictory conclusions or cannot be explained by these theories. Hence, our understanding of the nature of QPS, and its relationship to the various observations, has remained imcomplete. In this paper we present a new model for QPS which takes as its starting point an idea originally postulated by Mooij and Nazarov (2006 Nature Phys. 2 169): that flux-charge duality, a classical symmetry of Maxwell's equations, can be used to relate QPS to the well-known Josephson tunneling of Cooper pairs. Our model provides an alternative, and qualitatively different, conceptual basis for QPS and the phenomena which arise from it in experiments, and it appears to permit for the first time a unified understanding of observations across several different types of experiments and materials systems.

Coherent flux tunneling through NbN nanowires

“…Each of the two main findings of this work, i.e., (i) demonstration of coherent flux tunneling in a material different from InO x and (ii) its wire-width dependence, are of significant importance. They are crucial for developing more involved CQPS devices, [15][16][17][18] utilizing physics dual to conventional Josephson ones. Reproducing the flux superposition in the fully metallic superconducting rings shows that CQPS is a generic property of strongly disordered superconductors with large gap.…”

Quantum information processing using quasiclassical electromagnetic interactions between qubits and electrical resonators

“…We first consider a single qubit coupled to a microwave resonator, using the circuits of figures 1(a) and (b) to describe capacitive and inductive qubit/resonator coupling, respectively. These two circuits are chosen to be exactly dual [47][48][49][50][51][52] to each other, so that they are governed by equations of identical form, and the solution for one case can be mapped directly to the other using the transformation:…”

“…Electromagnetic qubit/resonator coupling without exchange of photons. (a) shows the electric circuit analyzed in detail; (b) is its exact dual [47][48][49][50][51][52], governed by equations of identical form. The resonator in both cases is indicated in the circuit schematic by a blue color; its damping, and the associated fluctuations, are modeled in (a) via R r and the Langevin noise source δV r , and in (b) by G r and δ I r .…”

“…To analyze our proposed qubit/resonator coupling in detail, we consider specifically the capacitively coupled circuit of figure 1(a) for definiteness, since the corresponding results for the inductive circuit of 1(b) can then be obtained using a duality transformation [47][48][49][50][51][52]. We write its classical potential energy in terms of the loop charges Q b , Q c , Q r shown in the figure by dashed red lines (for the moment taking the damping resistance R r and associated noise fluctuations δV r to be zero), which play the role of canonical position variables in a Lagrangian description of the circuit [53]…”

Linear response theory of Josephson junction arrays in a microwave cavity

“…Utilizing duality arguments, we will develop equivalent approaches for calculating the impedance of charge-dominated arrays with E C E J and for calculating the admittance of flux-dominated arrays with E C E J . The physics of the flux-dominated JJ arrays is dual to that of superconducting networks consisting of coherent quantum phase slip elements [30][31][32][33] instead of Josephson junctions, and as such the theory developed here will also be applicable to those devices.…”