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Europhysics Letters (EPL)

Probing non-Gaussian nuclear spin baths with entangled NV-center qutrits

Fahad Aljuaydi, Emad K. Jaradat, Hazrat Ali, A. B. A. Mohamed

Published Mar 1, 2026• 0 citations
Publisher

Abstract

Abstract Nitrogen-vacancy (NV) center decoherence is often interpreted with effective Gaussian noise models, which encode only second-order environmental correlations and can obscure intrinsically non-Gaussian nuclear-bath dynamics. Here we show that entangled NV qutrit pairs provide an operational probe of this non-Gaussianity via the time-dependent d = 3 Collins-Gisin-Linden-Massar-Popescu (CGLMP) Bell parameter , built from joint outcome probabilities using two fixed local measurement settings per party. We derive a cumulant expansion for and isolate contributions from third- and fourth-order Overhauser-field cumulants that are absent in a Gaussian model whose second cumulant is fixed by standard qubit-coherence inference under identical conditions. Exact simulations of few-spin central-spin clusters show that these higher-order bath statistics generate a structured residual at the few-percent level relative to the qubit-constrained Gaussian prediction, even when qubit coherence is accurately described by a Gaussian envelope. Our results provide an operational non-Gaussianity witness beyond qubit-constrained Gaussian inference.

DOI
10.1209/0295-5075/ae4fed

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Abstract Nitrogen-vacancy (NV) center decoherence is often interpreted with effective Gaussian noise models, which encode only second-order environmental correlations and can obscure intrinsically non-Gaussian nuclear-bath dynamics. Here we show that entangled NV qutrit pairs provide an operational probe of this non-Gaussianity via the time-dependent d = 3 Collins-Gisin-Linden-Massar-Popescu (CGLMP) Bell parameter , built from joint outcome probabilities using two fixed local measurement settings per party. We derive a cumulant expansion for and isolate contributions from third- and fourth-order Overhauser-field cumulants that are absent in a Gaussian model whose second cumulant is fixed by standard qubit-coherence inference under identical conditions. Exact simulations of few-spin central-spin clusters show that these higher-order bath statistics generate a structured residual at the few-percent level relative to the qubit-constrained Gaussian prediction, even when qubit coherence is accurately described by a Gaussian envelope. Our results provide an operational non-Gaussianity witness beyond qubit-constrained Gaussian inference.
We consider pure dephasing of Bell states of electron spin qubits interacting with a sparse bath of nuclear spins. Using the newly developed two-qubit generalization of cluster-correlation expansion method, we calculate the spin-echo decay of $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ and $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$ states for various interqubit distances. Comparing the results with calculations in which dephasing of each qubit is treated independently, we identify signatures of influence of common part of the bath on the two qubits. At large interqubit distances, this common part consists of many nuclei weakly coupled to both qubits, so that decoherence caused by it can be modeled by considering multiple uncorrelated sources of noise (clusters of nuclei), each of them weakly affecting the qubits. Consequently, the resulting genuinely two-qubit contribution to decoherence can be described as being caused by classical Gaussian noise. On the other hand, for small interqubit distances the common part of the environment contains clusters of spins that are strongly coupled to both qubits, and their contribution to two-qubit dephasing has visibly non-Gaussian character. We show that one can easily obtain information about non-Gaussianity of environmental noise affecting the qubits from the comparison of dephasing of $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ and $|\mathrm{\ensuremath{\Phi}}\ensuremath{\rangle}$ Bell states. Numerical results are obtained for two nitrogen vacancy centers interacting with a bath of 13C^{13}\mathrm{C}13C nuclei of natural concentration, for which we obtain that Gaussian description of a correlated part of environmental noise starts to hold for centers separated by about 3 nm.
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.
Abstract Nitrogen-vacancy (NV) centers in diamond have been developed into essential hardware units for a wide range of solid-state-based quantum technology applications. While such applications require the long spin coherence times of the NV centers, they are often limited due to decoherence. In this study, we theoretically investigate the decoherence of NV-spin ensembles induced by nitrogen impurities (P1 centers), which are one of the most dominant and inevitable magnetic field noise sources in diamond. We combined cluster correlation expansion and density functional theory to compute the Hahn-echo spin-coherence time of the NV centers for a broad range of P1 concentrations. Results indicate a clear linear dependence of T2 on P1 concentrations on a log scale with a slope of −1.06, which is in excellent agreement with previous experimental results. The interplay between the Jahn–Teller effect and the hyperfine interaction in the P1 center plays a critical role in determining the bath dynamics and the resulting NV decoherence. Our results provide a theoretical upper bound for the NV-spin T2 over a wide range of P1 densities, serving as a key reference for materials optimization and spin bath characterization to develop highly coherent NV-based devices for quantum information technology.
Non-Gaussian fluctuations are one of the essential properties of quantum systems. However, the direct detection of non-Gaussian fluctuations has not yet been achieved in experiments since the specific order of correlation has to be isolated from the complex dynamics of the whole system. In this Letter, we measure the second- and fourth-order correlations of ^{13}C nuclear spins around a nitrogen vacancy center in diamond, using the recently developed quantum nonlinear spectroscopy. By adjusting the detection window and the spectral resolution, we observe the Gaussian to non-Gaussian transition of the multispin system. We find that the fourth-order correlation provides a fingerprint signal that can be used to identify individual spins with the same precession frequency, suggesting that Gaussianity is a potential quantum resource for quantum sensing. Our results shed light on the study of nonequilibrium quantum many-body dynamics and quantum materials at the nanoscale.
We investigate nitrogen-vacancy center (NV) ensembles in diamond under the influence of strongly correlated electron-spin baths. We thoroughly calculate the decoherence properties of the NV central spin for bath concentrations of 0.1–1000.1\text{--}1000.1–100 ppm using the cluster-correlation expansion (CCE) method. We systematically analyze possible origins of the significant deviations in the values of the T2{T}_{2}T2​ coherence time reported in the literature. We demonstrate that significant variations can originate from the choice of averaging and fitting procedures used for the ensemble average and we point out the respective aspects that need to be considered when comparing the various theoretical studies. Our study may inspire readers to perform reliable simulations on the central spin problem. It provides an understanding and interpretation of the outcome parameters describing the dynamics of the local bath spins.
Decoherence is the biggest bottleneck in all quantum technologies. For nitrogen-vacancy (NV) centers in diamond, the loss of coherence is caused by the electron and nuclear spin bath of the diamond lattice. Here, we demonstrate that the spin bath - that typically causes decoherence - entangles the spin states of the NV electron and the host 14^{14}14N nucleus. The many-body interaction between the 14^{14}14N nucleus - electron - bath spins at an energy level anti-crossing occurring for an applied magnetic field orientation perpendicular to the NV axis is responsible for this effect. This is observed experimentally in NV ensembles via electron spin-echo measurements, where the echo envelope is modulated at the frequency of a 14^{14}14N nuclear spin transition. Using numerical simulations, we show that the spin bath coupling to the NV centers is essential for observing this modulation. Due to the zero first-order Zeeman effect at the anti-crossing, the observed oscillations have long spin-echo coherence times, 2--3 times those at the parallel magnetic field orientation. The oscillation frequency is highly stable and robust against environmental fluctuations. These findings provide new opportunities for fundamental studies of many-body physics and quantum sensing.