Spin-lattice relaxation of individual solid-state spins

Abstract

Understanding the effect of vibrations on the relaxation process of individual spins is crucial for implementing nano systems 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 quasi-localized 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.

Coherent quantum control of nitrogen-vacancy center spins near 1000 kelvin

“…3c ) is well fitted by T 1 −1 = AT n with A = 8 × 10 −12 s −1 K −n and n = 5.6 ± 0.5, which is close to the temperature dependence due to the two-phonon Raman processes ( ) 28 . The T 5 temperature dependence of the longitudinal relaxation rate is determined by the dimension of the NV system and symmetry of the diamond lattice 28 . This model has been previously verified in diamond at temperatures up to 475 K 22 .…”

Quantifying phonon-induced non-Markovianity in color centers in diamond

“…(2) and the relation γ c (t) = γ(t) implies that the previous discussion about the negative behavior of γ(t) in Figure 2 stands as a proof of NM for the orbital states of the SiV − center-similar conclusions are obtained for the NV − center. This result is the first evidence that the phononic contribution induces NM behavior in color centers in diamond, commonly modeled as purely Markovian [21,44,45].…”

“…Thus, the expectation values σ i will depend on the matrix elements ρ ij (t) = ρ ij (0)exp(−2 t 0 γ(τ ) dτ ), which at high temperatures leads to N C ∝ exp(−πJ 0 k B T ), as shown in Figure .3-(a). Henceforth, a comparison between these measures will contribute on the debate about how to use different criteria of NM for practical applications, such as modeling the vibrations of a diamond lattice at high temperatures [21,44,45,47,48], that can be simply considered as Markovian.…”

Sensing Electrochemical Signals Using a Nitrogen-Vacancy Center in Diamond

“…The electron spin of the NV center has a spin triplet ground state. Its ground state Hamiltonian in the presence of a magnetic and an electric field is given by ( ) [ 25 ] where GHz is the ground state zero field splitting, MHz/G is the electron gyromagnetic ratio, and are the terms due to the electric field that cause transitions between the spin states with the difference in the spin projection , Here, are the components of the electric field in the NV reference frame. The coupling parameters are experimentally found to be Hz cm/V and Hz cm/V [ 26 ].…”