We report an experimental study of the longitudinal relaxation time (T1) of the electron spin associated with single nitrogen-vacancy (NV) defects hosted in nanodiamonds (ND). We first show that T1 decreases over three orders of magnitude when the ND size is reduced from 100 to 10 nm owing to the interaction of the NV electron spin with a bath of paramagnetic centers lying on the ND surface. We next tune the magnetic environment by decorating the ND surface with Gd 3+ ions and observe an efficient T1-quenching, which demonstrates magnetic noise sensing with a single electron spin. We estimate a sensitivity down to ≈ 14 electron spins detected within 10 s, using a single NV defect hosted in a 10-nm-size ND. These results pave the way towards T1-based nanoscale imaging of the spin density in biological samples. PACS numbers:The ability to detect spins is the cornerstone of magnetic resonance imaging (MRI), which is currently one of the most important tools in life science. However, the sensitivity of conventional MRI techniques is limited to large spin ensembles, which in turn restricts the spatial resolution at the micrometer scale [1, 2]. Extending MRI techniques at the nanoscale can be achieved at sub-Kelvin temperature with magnetic resonance force microscopy, through the detection of weak magnetic forces [3, 4]. Another strategy consists in directly sensing the magnetic field created by spin magnetic moments with a nanoscale magnetometer. In that context, the electron spin associated with a nitrogen-vacancy (NV) defect in diamond has been recently proposed as an ultrasensitive and atomic-sized magnetic field sensor [5]. In the last years, many schemes based on dynamical decoupling pulse sequences have been devised for sensing ac or randomly fluctuating magnetic fields with a single NV spin [6][7][8][9]. These protocols recently enabled nuclear magnetic resonance measurements on a few cubic nanometers sample volume [10,11] and the detection of a single electron spin under ambient conditions [12].An alternative approach for sensing randomly fluctuating magnetic fields -i.e. magnetic noise -is based on the measurement of the longitudinal spin relaxation time (T 1 ) of the NV defect electron spin. Using an ensemble of NV defects and a T 1 -based sensing scheme, Steinert et al. recently demonstrated magnetic noise sensing with a sensitivity down to 1000 statistically polarized electron spins, as well as imaging of spin-labeled cellular structures with a diffraction-limited spatial resolution (≈ 500 nm) [13]. Bringing the spatial resolution down to few nanometers could be achieved by using a single NV defect integrated in a scanning device, e.g. with a nanodiamond (ND) attached to the tip of an atomic force microscope (AFM) [14,15]. With this application in mind, we study here the T 1 time of single NV defects hosted in NDs, as a function of ND size and magnetic environment. We first report a decrease of T 1 over three orders of magnitude when the ND size is reduced from 100 to 10 nm. This behavior is explained by ...

We analyze the impact of electric field and magnetic field fluctuations in the decoherence of the electronic spin associated with a single nitrogen-vacancy (NV) defect in diamond by engineering spin eigenstates protected either against magnetic noise or against electric noise. The competition between these noise sources is analyzed quantitatively by changing their relative strength through modifications of the environment. This study provides significant insights into the decoherence of the NV electronic spin, which is valuable for quantum metrology and sensing applications.Improving the coherence time of solid-state spin qubits is a central challenge in quantum technologies. Decoherence is induced by fluctuations of the local environment and can be mitigated by following several strategies. On one hand, the tools of material science can be exploited to engineer host samples with quantum grade purity 1 . As an example, millisecond-long coherence times have been achieved for electron spin impurities in isotopically purified diamond samples at room temperature 1,2 , while few seconds can be obtained in purified silicon at low temperature 3 . On the other hand, the coherence time can be improved through active quantum control of the many-body environment 4-7 or by decoupling the central spin from its fluctuations, either by applying periodic spin flips 8-10 or by engineering spin eigenstates which are protected against environmental noise [11][12][13][14] . However, for these strategies to be effective, it is crucial to first identify the sources of noise and understand precisely their impact on the coherence properties of the central spin.Here we analyze how magnetic and electric field fluctuations impair the quantum coherence of the electronic spin associated with a single nitrogen-vacancy (NV) defect in diamond. This atomic-sized defect is attracting considerable interest for a broad range of applications including quantum metrology and sensing 15-17 , quantum information processing 18 and hybrid quantum systems [19][20][21] . For all these applications, optimal performances require a long spin coherence time. In this work, we analyze the contributions of magnetic and electric field fluctuations to spin decoherence by exploiting spin eigenstates protected either against magnetic noise or against electric noise 22 . The competition between these noise sources is then analyzed quantitatively by changing their relative strength through modifications of the NV defect environment.The NV defect in diamond has a spin triplet ground state S = 1 with a zero-field splitting D ≈ 2.88 GHz between the m s = 0 and m s = ±1 spin sublevels, where m s denotes the spin projection along the NV symmetry axis (z). The spin Hamiltonian describing the ground state in the presence of strain, electric field E and magnetic field B has been discussed in detail in Refs. [22,23]. The strain, which is induced by a local deformation of the diamond crystal, can be treated as a local static electric field Σ interacting with the NV defect throug...