Detection of diamond surface electric-field noise is of importance for studying the coherence properties of shallow nitrogen-vacancy (NV) centers. Using the double quantum relaxation method, we demonstrated that the noise has a power-law frequency dependence, and it increases slowly from 295 K to 420 K but reduces quickly at higher temperatures. As the Dutta-Horn model described, the noise is created by ensembles of two-level systems with activation energies ranging from 0.3 eV to 0.6 eV. For diamond surface passivation, we found that the solid covering material (PMMA) outperforms the liquid one (glycerol) in reducing the electric-field noise, which was attributed to the presence of surface-modified phononic coupling noise. We anticipate that our findings will contribute to a better understanding of the origins of surface 1/f electric-field noise, as well as identify optimal covering materials for enhancing the coherence time of near-surface NV centers.
Surfaces enable useful functionalities for quantum systems, e.g., as interfaces to sensing targets, but often result in surface-induced decoherence where unpaired electron spins are common culprits. Here we show that the coherence time of a near-surface qubit is increased by coherent radio-frequency driving of surface electron spins, where we use a diamond nitrogen-vacancy (NV) center as a model qubit. This technique is complementary to other methods of suppressing decoherence and, importantly, requires no additional materials processing or control of the qubit. Further, by combining driving with the increased magnetic susceptibility of the double-quantum basis, we realize an overall fivefold sensitivity enhancement in NV magnetometry. Informed by our results, we discuss a path toward relaxation-limited coherence times for near-surface NV centers. The surface-spin driving technique presented here is broadly applicable to a wide variety of qubit platforms afflicted by surface-induced decoherence.
Nitrogen vacancy centers (NV) in proximity to diamond surfaces are promising nanoscale quantum sensors. However, their coherence properties are negatively affected by magnetic and electric surface noise, whose origin and detailed impact have remained elusive. Using atomistic models of diamond surfaces derived with density functional theory, together with decoherence time calculations with cluster correlation expansion methods, we quantify the effects of surface crystallographic orientation and functionalization, and of the density of unpaired electrons on the NV Hahn-echo time
T2. We determine a crossover depth at which
T2 ceases to be limited by surface nuclear spins and recovers the bulk-limited value. We find that for static surface-electron baths, the ratio between the NV depth and the separation between surface electron spins determines a transition from fast-fluctuating to quasi-static noise, leading to a dependence of
T2 on orientation for specific surfaces. We also find that the modulation of
T2 by spin-phonon relaxations leads to motional-narrowing at sub-microsecond relaxation times. Importantly, our calculations show that it is only when accounting for surface-spin in-sequence hopping that measured
T2 values as a function of depth can be reproduced, thus highlighting the importance of hopping-mediated models to describe the surface spin noise affecting NV sensors. Overall, our work provides clear guidelines for engineering diamond surfaces to achieve enhanced NV coherence for quantum sensing and information processing applications.
Nanoscale quantum probes such as the nitrogen-vacancy (NV) center in diamonds have demonstrated remarkable sensing capabilities over the past decade as control over fabrication and manipulation of these systems has evolved. The biocompatibility and rich surface chemistry of diamonds has added to the utility of these probes but, as the size of these nanoscale systems is reduced, the surface chemistry of diamond begins to impact the quantum properties of the NV center. In this work, we systematically study the effect of the diamond surface chemistry on the quantum coherence of the NV center in nanodiamonds (NDs) 50 nm in size. Our results show that a borane-reduced diamond surface can on average double the spin relaxation time of individual NV centers in nanodiamonds when compared to thermally oxidized surfaces. Using a combination of infrared and X-ray absorption spectroscopy techniques, we correlate the changes in quantum relaxation rates with the conversion of sp 2 carbon to C–O and C–H bonds on the diamond surface. These findings implicate double-bonded carbon species as a dominant source of spin noise for near surface NV centers. The link between the surface chemistry and quantum coherence indicates that through tailored engineering of the surface, the quantum properties and magnetic sensitivity of these nanoscale systems may approach that observed in bulk diamond.
We study the dynamics of quantum three-level systems due to fast fluctuations of their environment (white noise). As an example, we model the decoherence and dephasing of nitrogen-vacancy (NV) centers in diamond that are positioned near a surface that gives rise to quickly fluctuating magnetic field noise, with and without the presence of a rf field that couples levels of the ground electronic state manifold. We use a simple quantum mechanical model that allows for analytical solutions. The model treats the NV three-level ground state in the presence of rapidly fluctuating magnetic fields that arise from the environment and result in decoherence, dephasing, and dissipation. We show that the magnetic field fluctuations can couple all the elements of the density matrix of the three-level system. Hence, all 9 eigenmodes may contribute to both population and coherence dynamics. We also discuss consequences for fitting experiments in which decoherence plays a role.
Thanks to their versatility, nitrogen-vacancy (N-
V) centers in nanodiamonds have been widely adopted as nanoscale sensors. However, their sensitivities are limited by their short coherence times relative to N-
Vs in bulk diamond. A more complete understanding of the origins of decoherence in nanodiamonds is critical to improving their performance. Here we present measurements of fast spin relaxation on qutrit transitions between the energy eigenstates composed of the ${m}_{s}=|\ifmmode\pm\else\textpm\fi{}1⟩$ states of the N-${V}^{\ensuremath{-}}$ electronic ground state in approximately 40-nm nanodiamonds under ambient conditions. For frequency splittings between these states of 20 MHz or less the maximum theoretically achievable coherence time of the N-
V spin is approximately 2 orders of magnitude shorter than would be expected if the N-
V spin is treated as a qubit. We attribute this fast relaxation to electric field noise. We observe a strong falloff of the qutrit relaxation rate with the splitting between the states, suggesting that, whenever possible, measurements with N-
Vs in nanodiamonds should be performed at moderate axial magnetic fields (
>60 G). We also observe that the qutrit relaxation rate changes with time. These findings indicate that surface electric field noise is a major source of decoherence for N-
Vs in nanodiamonds.