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arXiv:1511.09049 · Physical review. B./Physical review. B

Decoherence of three-level systems: Application to nitrogen-vacancy centers in diamond near a surface

Shigeru Ajisaka, Y. B. Band

Published Oct 19, 2016• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.94.134107

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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.
We probe the relaxation dynamics of the full three-level spin system of near-surface nitrogen-vacancy (NV) centers in diamond to define a T_{1} relaxation time that sets the T_{2}≤2T_{1} coherence limit of the NV's subset qubit superpositions. We find that double-quantum spin relaxation via electric field noise dominates T_{1} of near-surface NVs at low applied magnetic fields. Furthermore, we differentiate 1/f^{α} spectra of electric and magnetic field noise using a novel noise-spectroscopy technique, with broad applications in probing surface-induced decoherence at material interfaces.
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.
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.
The nitrogen-vacancy (NV) defect center in diamond has demonstrated great capability for nanoscale magnetic sensing and imaging for both static and periodically modulated target fields. However, it remains a challenge to detect and image randomly fluctuating magnetic fields. Recent theoretical and numerical works have outlined detection schemes that exploit changes in decoherence of the detector spin as a sensitive measure for fluctuating fields. Here we experimentally monitor the decoherence of a scanning NV center in order to image the fluctuating magnetic fields from paramagnetic impurities on an underlying diamond surface. We detect a signal corresponding to roughly 800 μB in 2 s of integration time, without any control on the target spins, and obtain magnetic-field spectral information using dynamical decoupling techniques. The extracted spatial and temporal properties of the surface paramagnetic impurities provide insight to prolonging the coherence of near-surface qubits for quantum information and metrology applications.
Nitrogen vacancy (NV-) color centers in diamond are a prime candidate for use in quantum information devices, owing to their spin-1 ground state, straightforward optical initialization and readout, and long intrinsic coherence times in a room-temperature solid. While the 13C nuclear spin is often a dominant source of magnetic noise, we observe transitions between electron-nuclear hyperfine states of NV- centers in 99% 13C diamond that are robust to decoherence. At magnetic field strengths ranging from 550 - 900 G, these transitions are observable by optically detected magnetic resonance (ODMR), and exhibit linewidths narrowed by factors as high as ~130 at room temperature over typical electron-type transitions observed from this spin system. We anticipate the use of these decoherence-protected transitions, in combination with dynamical decoupling methods, for storage of quantum information.
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 T2T_2T2​. We determine a crossover depth at which T2T_2T2​ 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 T2T_2T2​ on orientation for specific surfaces. We also find that the modulation of T2T_2T2​ 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 T2T_2T2​ 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.