The nonlocal superconducting fluctuation corrections to the conductivity tensor
σij(q,ω) are calculated within the time-dependent Ginzburg-Landau framework, and their observable consequences for quantum noise magnetometry are worked out. For a single nitrogen-vacancy (NV) sensor we obtain the relaxation rate
1/T1 as a function of temperature, sample-sensor distance, and probe frequency, identifying the scales at which the nonlocality and the dynamics of the pair fluctuations cut off the critical enhancement near
Tc. For two-sensor covariance magnetometry we show that the two-point field correlator develops additional spatial structure whose range directly measures the fluctuation correlation length
ξ(T). We further analyze two channels that accompany the paraconductivity: the Maki-Thompson correction to the spin susceptibility, and the fluctuation diamagnetism. Finally, we solve exactly, to all orders in a dc electric field and at all wave vectors, for the nonequilibrium current noise of the fluctuating film: the noise decouples from the nonlinear paraconductivity, violating the fluctuation-dissipation theorem by universal factors at criticality and acquiring a bias-induced spatial anisotropy directly measurable by covariance magnetometry. The results are connected to a recent experiment measuring current noise near a thin film of BSCCO.
A single-spin qubit placed near the surface of a conductor acquires an additional contribution to its 1/T 1 relaxation rate due to magnetic noise created by electric current fluctuations in the material.We analyze this technique as a wireless probe of superconductivity in atomically thin two-dimensional materials.At temperatures T T c , the dominant contribution to the qubit relaxation rate is due to transverse electric current fluctuations arising from quasiparticle excitations.We demonstrate that this method enables detection of metal-to-superconductor transitions, as well as investigation of the symmetry of the superconducting gap function, through the noise scaling with temperature.We show that scaling of the noise with sample-probe distance provides a window into the nonlocal quasistatic conductivity of superconductors, both clean and disordered.At low temperatures the quasiparticle fluctuations get suppressed, yet the noise can be substantial due to resonant contributions from collective longitudinal modes, such as plasmons in monolayers and Josephson plasmons in bilayers.Potential experimental implications are discussed.
Atomic scale qubits, as may be realized in nitrogen vacancy (NV) centers in diamond, offer the opportunity to study magnetic field noise with nanometer scale spatial resolution. Using these spin qubits, one can learn a great deal about the magnetic-field noise correlations, and correspondingly the collective-mode spectra, in quantum materials and devices. However, to date these tools have been essentially restricted to studying Gaussian noise processes – equivalent to linear-response. In this work we will show how to extend these techniques beyond the Gaussian regime and show how to unambiguously measure higher-order magnetic noise cumulants in a local, spatially resolved way. We unveil two protocols for doing this; the first uses a single spin-qubit and different dynamical decoupling sequences to extract non-Markovian and non-Gaussian spin-echo noise. The second protocol uses two-qubit coincidence measurements to study spatially non-local cumulants in the magnetic noise. We then demonstrate the utility of these protocols by considering a model of a bath of non-interacting two-level systems, as well as a model involving spatially correlated magnetic fluctuations near a second-order Ising phase transition. In both cases, we highlight how this technique can be used to measure in a real many-body system how fluctuation dynamics converge towards the central limit theorem as a function of effective bath size. We then conclude by discussing some promising applications and extensions of this method.
Resistive transport near a superconducting phase can arise from the motion of normal-state quasiparticles or that of vortices. The conductivity alone does not distinguish between these mechanisms. We propose an unambiguous method for telling them apart, using the recently developed experimental tool of covariance magnetometry, which uses nitrogen-vacancy centers in diamond to probe real-time spatiotemporal correlations in magnetic noise. Our key insight is that, under an applied current, the underlying charge carriers leave a directional fingerprint in the spatially correlated magnetic noise above the sample: ordinary electric carriers drift parallel to the current, whereas vortices, owing to the Magnus force, drift perpendicular to it. The noise covariance detects this anisotropy and identifies the vortex-driven nature of transport. We compute the noise correlations expected for a representative thin-film superconductor and demonstrate that the anisotropic signal is well within the reach of current experimental capabilities.
Characterizing the low-energy dynamics of quantum materials is crucial for understanding strongly correlated electronic states, yet remains experimentally challenging, particularly in two-dimensional systems. Here, we leverage nitrogen-vacancy (NV) centers in diamond as a non-invasive quantum sensor to study thin-film Bi
2Sr
2CaCu
2O
8+δ (BSCCO), revealing several distinct dynamical phenomena across the superconducting phase diagram. At zero magnetic field and low temperatures, NV depolarization (
T1) spectroscopy captures GHz-scale noise from nodal quasiparticle excitations, consistent with Bardeen--Cooper--Schrieffer (BCS) mean-field theory. Near the critical temperature
Tc≈90 K, supercurrent-fluctuation-induced noise sharply reduces
T1. By analyzing the temperature scaling of
T1, we observe clear deviations from mean-field prediction, reflecting the importance of order parameter fluctuations and enabling the determination of critical exponents. Under a small magnetic field, a broad and asymmetric reduction of
T1 unveils a liquid-like phase of mobile vortices. NV decoherence (
T2) spectroscopy further probes MHz-scale noise and reveals complex vortex-solid fluctuations well below
Tc. Our results establish quantum noise spectroscopy as a non-invasive probe of superconducting dynamics over frequency and length scales complementary to existing techniques.
Quantum geometry underlies many electronic responses, but its transport signatures have so far been established mainly for pure single-particle Bloch states. Whether collective many-body fluctuations possess a measurable quantum geometry remains largely unexplored. Here we show that superconducting fluctuation transport provides a direct probe of quantum information geometry in collective many-body matter. Starting from a multicomponent time-dependent Ginzburg-Landau theory in the Gaussian fluctuation regime, we identify the equilibrium density matrix of fluctuating Cooper pairs as the static pair propagator, which defines a positive mixed-state manifold in momentum space. The geometry of this manifold is directly measurable through paraconductivity: the longitudinal paraconductivity is governed by the quantum Fisher information of superconducting fluctuation modes, while the fluctuational anomalous Hall effect is governed by the mean Uhlmann curvature, the mixed-state counterpart of Berry curvature. This correspondence further yields geometric bounds between these two transport components, with no direct analogue in normal electronic transport. Applied to chiral superconducting fluctuations in quarter-metal systems motivated by rhombohedral multilayer graphene, a symmetry-allowed Lifshitz invariant generates finite mean Uhlmann curvature and logarithmically enhances the anomalous Hall conductivity above the critical temperature. Our results establish collective superconducting fluctuations as an experimentally accessible transport probe of mixed-state quantum information geometry.