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arXiv:1711.10280 · Physical review. B./Physical review. B

Spin-lattice relaxation of individual solid-state spins

Ariel Norambuena, Enrique Muñoz, Hossein T. Dinani, Andrey Jarmola, Patrick Maletinsky, Dmitry Budker, Jeronimo R. Maze

Published Mar 20, 2018• 63 citations

Abstract

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 ${T}^{5}$ 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.

DOI: 10.1103/physrevb.97.094304

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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

{T}^{5}

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.

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.

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.

Abstract The electron–phonon interaction is a cornerstone of condensed matter physics, playing a pivotal role in the properties of solid-state systems. When localized electronic states are coupled to lattice vibrations, phonons can induce memory effects. This study explores the non-equilibrium dynamics of a negatively charged silicon-vacancy center in diamond, analyzing the effects of both single phonon mode and structured phonon environment. Using numerical simulations and theoretical analysis, we employ trace distance as a metric to identify and understand memory effects in the transient dynamics and non-Markovian evolution. We systematically investigate the impact of longitudinal and transverse magnetic fields, phonon coupling strengths, Fock states, localized vibrations, and temperature on memory effects in this solid-state system. Our findings provide deeper insights into the interplay between electronic states and phonon environments, offering a comprehensive understanding of the conditions that govern the backflow of information in quantum solid-state devices.

Qubit coherence is an essential figure of merit for quantum information processing applications such as quantum computing, or quantum repeaters. Understanding the coherence properties of the underlying physical qubits that facilitate such applications is therefore are often limited by coupling to lattice phonons, which in turn constrains operation temperature. Here we study phonon induced electronic spin decoherence in group-IV vacancy centers in diamond. We begin by modeling the spin-phonon interaction and then employ the widely used Born-Markov approximation, highlighting its inconsistencies in this setting and its deviations from experimental observations. To close the gap between theoretical predictions and experimental results, we relax certain approximations, investigate their contributions to the predicted coherence times, and identify the dominant sources of discrepancy. We further demonstrate that experimentally measured electronic spin coherence dynamics are consistently captured within a non-Markovian framework, and we show how the magnetic field orientation influences the qubit coherence time.

We present an experimental study of the longitudinal electron-spin relaxation of ensembles of negatively charged nitrogen-vacancy (NV−) centers in diamond. The measurements were performed with samples having different NV− concentrations and at different temperatures and magnetic fields. We found that the relaxation rate

T_{1}^{-1}

increases when transition frequencies in NV− centers with different orientations become degenerate and interpret this as cross-relaxation caused by dipole-dipole interaction.

The negatively charged boron vacancy center in hexagonal boron nitride is a premier candidate for quantum sensing, yet its performance is critically limited by longitudinal spin-lattice relaxation time (

T_1

). A microscopic understanding of spin relaxation in the high magnetic field regime remains elusive, as the relevant Zeeman transitions lie far below the optical phonon energies typically invoked to describe the relaxation process. Here, we apply an \textit{ab initio} acoustic mode spin-phonon relaxation theory to this problem and quantitatively reproduce the experimental magnetic field and temperature dependence of

T_1

without empirical fitting parameters. We demonstrate that the relaxation dynamics are driven by a direct one-phonon emission and absorption process resonant with the Zeeman splitting. Furthermore, we identify the out-of-plane flexural phonon branch which is unique to two-dimensional hosts, as the primary source of decoherence, creating a distinct low-energy spectral function that facilitates spin relaxation. Our results provide a microscopic interpretation of the experimentally observed non-monotonic field and temperature dependence in two-dimensional quantum defect centers.