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arXiv:2412.17608 · Physical review. B./Physical review. B

Interplay between dressed and strong-axial-field states in nitrogen vacancy centers for quantum sensing and computation

Gabriele Zanelli, Ekaterina V. Moreva, Ettore Bernardi, Elena Losero, Sviatoslav Ditalia Tchernij, J. Forneris, Željko Pastuović, P. Traina, Ivo Pietro Degiovanni, Marco Genovese

Published Nov 3, 2025• 0 citations
arXivHTMLPDF

Abstract

The nitrogen vacancy (NV) center in diamond is an intriguing electronic spin system with applications in quantum radiometry, sensing, and computation. In those experiments, a bias magnetic field is commonly applied along the NV symmetry axis to eliminate the triplet ground-state manifold's degeneracy ( S = 1 ). In this configuration, the eigenvectors of the NV spin's projection along its axis are called strong-axial-field states. Conversely, in some experiments, a weak magnetic field is applied orthogonally to the NV symmetry axis, leading to eigenstates that are balanced linear superpositions of strong-axial-field states, referred to as dressed states. The latter are sensitive to environmental magnetic noise at the second order, allowing to perform magnetic field protected measurements while providing increased coherence times. However, if a small axial magnetic field is added in this regime, the linear superposition of strong-axial-field states becomes unbalanced. This paper presents a comprehensive study of free induction decay (FID) measurements performed on an NV center ensemble in the presence of strain and weak orthogonal magnetic field, as a function of a small magnetic field applied along the NV symmetry axis. The simultaneous detection of dressed states and unbalanced superpositions of strong-axial-field states in a single FID measurement is shown, gaining insight into coherence time, nuclear spin, and the interplay between temperature and magnetic field sensitivity. The discussion concludes by describing how the simultaneous presence of magnetically sensitive and insensitive states opens up appealing possibilities for both sensing and quantum computation applications.

DOI
10.1103/3mlm-jjqq

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The nitrogen vacancy (NV) center in diamond is an intriguing electronic spin system with applications in quantum radiometry, sensing, and computation. In those experiments, a bias magnetic field is commonly applied along the NV symmetry axis to eliminate the triplet ground-state manifold's degeneracy ( S = 1 ). In this configuration, the eigenvectors of the NV spin's projection along its axis are called strong-axial-field states. Conversely, in some experiments, a weak magnetic field is applied orthogonally to the NV symmetry axis, leading to eigenstates that are balanced linear superpositions of strong-axial-field states, referred to as dressed states. The latter are sensitive to environmental magnetic noise at the second order, allowing to perform magnetic field protected measurements while providing increased coherence times. However, if a small axial magnetic field is added in this regime, the linear superposition of strong-axial-field states becomes unbalanced. This paper presents a comprehensive study of free induction decay (FID) measurements performed on an NV center ensemble in the presence of strain and weak orthogonal magnetic field, as a function of a small magnetic field applied along the NV symmetry axis. The simultaneous detection of dressed states and unbalanced superpositions of strong-axial-field states in a single FID measurement is shown, gaining insight into coherence time, nuclear spin, and the interplay between temperature and magnetic field sensitivity. The discussion concludes by describing how the simultaneous presence of magnetically sensitive and insensitive states opens up appealing possibilities for both sensing and quantum computation applications.
Abstract Quantum sensing exploits the strong sensitivity of quantum systems to measure small external signals. The nitrogen-vacancy (NV) center in diamond is one of the most promising platforms for real-world quantum sensing applications, predominantly used as a magnetometer. However, its magnetic field sensitivity vanishes when a bias magnetic field acts perpendicular to the NV axis. Here, we introduce a different sensing strategy assisted by the nitrogen nuclear spin that uses the entanglement between the electron and nuclear spins to restore the magnetic field sensitivity. This, in turn, allows us to detect small changes in the magnetic field angle relative to the NV axis. Furthermore, based on the same underlying principle, we show that the NV coupling strength to magnetic noise, and hence its coherence time, exhibits a strong asymmetric angle dependence. This allows us to uncover the directional properties of the local magnetic environment and to realize maximal decoupling from anisotropic noise.
The recent decade has witnessed exciting developments in quantum science and technology. Quantum sensing is a rapidly growing branch, which exploits the fragility of quantum systems to detect small external signals. The extreme control at the single-atom level and the remarkably long coherence time of engineered quantum systems enable unprecedented sensitivity and precision, beating the performance of classical techniques. The nitrogen-vacancy (NV) center in diamond is one of the most promising quantum sensors. Its unique advantages have attracted considerable attention, including a long spin coherence time throughout a broad temperature range, nanoscale resolution limited by the sensor-sample distance, convenient optical control of its spin states and remarkably versatile sensing capabilities. Its properties are well studied under a bias magnetic field oriented along its quantization axis. However, its sensing capabilities in the presence of an off-axis magnetic field are much less explored. My research aims to unlock the full potential of NV quantum sensor by developing new sensing modalities under a magnetic field acting perpendicular to the NV axis, and furthermore, integrating them into a scanning probe microscope. In this dissertation, I will report our progress toward building a scanning NV multimodal quantum imaging platform, which will open up exciting opportunities in measuring nanoscale phenomena. The first chapter provides an introduction to the background of quantum sensing with NV centers, followed by a discussion on its basic properties and established sensing techniques. The second and third chapters are dedicated to two experiments performed under a perpendicular magnetic field where traditional NV magnetometry based on the Zeeman effect fails. In the second chapter, I will introduce a new sensing strategy that uses the entanglement between the electron and nuclear spins to restore the magnetic field sensitivity under this unfavored condition. This allows us to sense small changes in the magnetic field angle relative to the NV axis, and to detect anisotropic magnetic noise in the local environment. In the third chapter, I will present our latest development of scanning NV electrometry, where a single NV at the apex of a diamond scanning probe images external alternating (AC) and direct (DC) electric fields with sub-100 nm resolution. In the last chapter, I will discuss our efforts on four experiments that were left unfinished. I will present the results we have achieved, analyze the challenges that we faced and propose potential solutions to overcome them.
The nitrogen-vacancy (NV) center in diamond can be operated as a microwave-dressed qubit. In the ideal two-level limit, its transition frequency is first-order insensitive to static magnetic fields, providing robustness against magnetic detuning noise. In practical diamond devices, however, residual transverse crystal strain mixes the ∣ms=±1⟩\ket{m_{s}=\pm1}∣ms​=±1⟩ spin sublevels and modifies the dressed qubit. In this study, we derive an analytical effective two-level model of a strained dressed NV qubit by perturbatively eliminating the far-detuned spectator state from the full three-level dressed Hamiltonian. We obtain closed-form expressions for the dressed-state splitting, the spin-locking mixing angle, and the longitudinal magnetic-field coupling. We show that transverse strain shifts the dressed-state resonance and tilts the spin-locking axis. These two effects restore a finite DC-field response and thereby quantify the loss of magnetic robustness. We demonstrate these features in simulated pulsed electron spin resonance spectra that incorporate rate-equation-based optical readout. We further derive exact validity criteria from the eigenvalues and spectator weights of the full three-level Hamiltonian. For practical use, we reduce these criteria to two controlled guidelines: the spectator-like branch must remain above the nominal upper dressed state, and its branch-specific admixture must remain small. A validity diagram over the axial-field--transverse-strain plane summarizes these approximate conditions and provides practical guidelines for designing dressed-NV sensing experiments.
We report on detailed studies of electronic and nuclear spin states in the diamond-nitrogen-vacancy (NV) center under weak transverse magnetic fields. We numerically predict and experimentally verify a previously unobserved NV hyperfine level anticrossing (LAC) occurring at bias fields of tens of gauss—two orders of magnitude lower than previously reported LACs at ∼ 500 and ∼ 1000 G axial magnetic fields. We then discuss how the NV ground-state Hamiltonian can be manipulated in this regime to tailor the NV's sensitivity to environmental factors and to map into the nuclear spin state.
We report on detailed studies of electronic and nuclear spin states in the diamond-nitrogen-vacancy (NV) center under weak transverse magnetic fields. We numerically predict and experimentally verify a previously unobserved NV hyperfine level anticrossing (LAC) occurring at bias fields of tens of gauss---two orders of magnitude lower than previously reported LACs at $\ensuremath{\sim}500$ and $\ensuremath{\sim}1000$ G axial magnetic fields. We then discuss how the NV ground-state Hamiltonian can be manipulated in this regime to tailor the NV's sensitivity to environmental factors and to map into the nuclear spin state.
Among the possible defects that can occur in diamonds, one that draws attention is the nitrogen-vacancy (NV) center.Studied since the early 90s, in recent years, they became one of the most promising platforms for field applications of quantum technology at room temperature, especially for quantum sensing.They are sensitive to electric and magnetic fields, temperature, and strain, making these nanosensors a versatile platform for many applications.The NV center's spin state is easy to read and manipulate by optical means, and, most interestingly, it works well at room temperature, which facilitates its use.The great challenge to implement quantum protocols and quantum algorithms is the coherence time of the quantum states.The NV center stands out for having relatively high coherence times at room temperature.This dissertation presents measurements to characterize the electron spin coherence of NV centers in an ultrapure sample of diamond designed for quantum sensing applications.These measurements combine optical e magnetic resonance techniques.For that, a method was implemented using a conventional CCD camera and a clever imaging protocol, making it possible to perform various pulsed microwave experiments on the electron spin, such as Rabi oscillations and Hahn spin-echo, which were used for determining the characteristic relaxation times (T 1 and T 2 ).Results show that this system provides at least two readily accessible qubits that can be used in quantum protocols even at room temperature.