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arXiv:2007.11529 · Physical Review Research

State-dependent phonon-limited spin relaxation of nitrogen-vacancy centers

Matthew Carl Cambria, Aedan Robert Gardill, Y. Li, Ariel Norambuena, Jeronimo R. Maze, Shimon Kolkowitz

Published Feb 9, 2021• 20 citations
arXivHTMLPDF

Abstract

Understanding the limits to the spin coherence of the nitrogen-vacancy (NV) center in diamond is vital to realizing the full potential of this quantum system.We show that relaxation on the |m s = -1 ↔ |m s = +1 transition occurs approximately twice as fast as relaxation on the |m s = 0 ↔ |m s = ±1 transitions under ambient conditions in native NVs in high-purity bulk diamond.The rates we observe are independent of NV concentration over four orders of magnitude, indicating they are limited by spin-phonon interactions.We find that the maximum theoretically achievable coherence time for an NV at 295 K is limited to 6.8(2) ms.Finally, we present a theoretical analysis of our results that suggests Orbach-like relaxation from quasilocalized phonons or contributions due to higher-order terms in the spin-phonon Hamiltonian are the dominant mechanism behind |m s = -1 ↔ |m s = +1 relaxation, motivating future measurements of the temperature dependence of this relaxation rate.

DOI
10.1103/physrevresearch.3.013123

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Understanding the limits to the spin coherence of the nitrogen-vacancy (NV) center in diamond is vital to realizing the full potential of this quantum system.We show that relaxation on the |m s = -1 ↔ |m s = +1 transition occurs approximately twice as fast as relaxation on the |m s = 0 ↔ |m s = ±1 transitions under ambient conditions in native NVs in high-purity bulk diamond.The rates we observe are independent of NV concentration over four orders of magnitude, indicating they are limited by spin-phonon interactions.We find that the maximum theoretically achievable coherence time for an NV at 295 K is limited to 6.8(2) ms.Finally, we present a theoretical analysis of our results that suggests Orbach-like relaxation from quasilocalized phonons or contributions due to higher-order terms in the spin-phonon Hamiltonian are the dominant mechanism behind |m s = -1 ↔ |m s = +1 relaxation, motivating future measurements of the temperature dependence of this relaxation rate.
Spin-lattice relaxation within the nitrogen-vacancy (NV) center's electronic ground-state spin triplet limits its coherence times, and thereby impacts its performance in quantum applications. We report measurements of the relaxation rates on the NV center's |m_{s}=0⟩↔|m_{s}=±1⟩ and |m_{s}=-1⟩↔|m_{s}=+1⟩ transitions as a function of temperature from 9 to 474 K in high-purity samples. We show that the temperature dependencies of the rates are reproduced by an ab initio theory of Raman scattering due to second-order spin-phonon interactions, and we discuss the applicability of the theory to other spin systems. Using a novel analytical model based on these results, we suggest that the high-temperature behavior of NV spin-lattice relaxation is dominated by interactions with two groups of quasilocalized phonons centered at 68.2(17) and 167(12) meV.
The nitrogen-vacancy (NV) center in diamond is an ideal candidate for quantum sensing because of its excellent spin coherence property as well as the possibility for optical initialization and readout. Previous studies, on the other hand, have typically been conducted at low or room temperature. The inability to fully understand the coherence properties of the NV center at high temperatures limits NV's further applications. We systematically investigate the coherence properties of NV center ensemble at temperatures ranging from 300 K to 600 K in this paper. Coherence time T2{T}_{2}T2​ decreases rapidly from $184\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\text{s}$ at 300 K to $30\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\text{s}$ at 600 K due to the interaction with paramagnetic impurities. At all experiment temperatures, both single-quantum and double-quantum transitions exhibit a T5{T}^{5}T5 relaxation rate, which is attributed to the two-phonon Raman process. Nonetheless, the inhomogeneous dephasing time T2∗{T}_{2}^{*}T2∗​ and thermal-echo decoherence time TTE{T}_{\text{TE}}TTE​ remain almost unchanged at temperature up to 600 K. A thermal-echo-based thermometer is demonstrated to have a sensitivity of 41mK/Hz41\phantom{\rule{4pt}{0ex}}\text{mK}/\sqrt{\mathrm{Hz}}41mK/Hz​ at 450 K. These findings will pave the way for NV-based high-temperature sensing and provide a more comprehensive understanding of solid-state qubit decoherence.
Thanks to their versatility, nitrogen-vacancy (N-VVV) centers in nanodiamonds have been widely adopted as nanoscale sensors. However, their sensitivities are limited by their short coherence times relative to N-VsV\mathrm{s}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-VVV spin is approximately 2 orders of magnitude shorter than would be expected if the N-VVV 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-VsV\mathrm{s}Vs in nanodiamonds should be performed at moderate axial magnetic fields (>60>60>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-VsV\mathrm{s}Vs in nanodiamonds.
Understanding the effect of vibrations on the relaxation process of individual spins is crucial for implementing nanosystems for quantum information and quantum metrology applications. In this work, we present a theoretical microscopic model to describe the spin-lattice relaxation of individual electronic spins associated to negatively charged nitrogen-vacancy centers in diamond, although our results can be extended to other spin-boson systems. Starting from a general spin-lattice interaction Hamiltonian, we provide a detailed description and solution of the quantum master equation of an electronic spin-one system coupled to a phononic bath in thermal equilibrium. Special attention is given to the dynamics of one-phonon processes below 1 K where our results agree with recent experimental findings and analytically describe the temperature and magnetic-field scaling. At higher temperatures, linear and second-order terms in the interaction Hamiltonian are considered and the temperature scaling is discussed for acoustic and quasilocalized phonons when appropriate. Our results, in addition to confirming a T5{T}^{5}T5 temperature dependence of the longitudinal relaxation rate at higher temperatures, in agreement with experimental observations, provide a theoretical background for modeling the spin-lattice relaxation at a wide range of temperatures where different temperature scalings might be expected.
Extending the coherence time of quantum systems to their physical limit is a long-standing pursuit and critical for developing quantum science and technology. By characterizing all the microscopic noise sources of the electronic spin [nitrogen-vacancy (NV) center] in diamonds using complete noise spectroscopy, we observe a previously unforeseen noise spectrum manifested as the empirical limit ( T 2 ≈ 1 2 T 1 ) that has puzzled researchers for decades in various solid-state systems. By implementing a corresponding dynamical decoupling strategy, we are able to surpass the empirical limit and approach the upper physical limit T 2 = 2 T 1 for NVs, from room temperature down to 220 kelvin. Our observations, including the independence across different spatial sites and its dependence on temperature in the same way as spin-lattice relaxation, suggest an emerging decoherence mechanism dominated by spin-lattice interaction. These results provide a unified and universal strategy for characterizing and controlling microscopic noises, thereby paving the way for achieving the physical limit in various solid-state systems.
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.