Temperature-Dependent Spin-Lattice Relaxation of the Nitrogen-Vacancy Spin Triplet in Diamond
Matthew Carl Cambria, Ariel Norambuena, Hossein T. Dinani, Gergő Thiering, Aedan Robert Gardill, Ishita Kemeny, Y. Li, Vincenzo Lordi, Ádám Gali, Jeronimo R. Maze, Shimon Kolkowitz
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.
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.
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 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 relaxation rate, which is attributed to the two-phonon Raman process. Nonetheless, the inhomogeneous dephasing time T2∗ and thermal-echo decoherence time TTE remain almost unchanged at temperature up to 600 K. A thermal-echo-based thermometer is demonstrated to have a sensitivity of 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.
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 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.
The nitrogen-vacancy (NV) center in diamond has emerged as a versatile atom-like system, finding diverse applications at both ambient and cryogenic temperatures. At room temperature, the NV center's spin-triplet electronic ground state has a long coherence time and can be read out and initialized using nonresonant optical excitation, which has enabled a wide range of metrology and quantum information applications. At cryogenic temperatures, the NV center exhibits a variety of narrow, atom-like optical transitions, which has made the NV center a promising platform for quantum optics applications. We use coherent optical manipulation of the NV center at cryogenic temperatures to probe its internal dynamics and aspects of its interactions with its environment.\nFirst, we investigate the intersystem crossing (ISC) process, which is a spin-dependent nonradiative decay mechanism that enables the electronic spin state to be optically initialized and read out at room temperature. We measure the ISC rates from different excited states as well as the rate at which interactions with phonons redistribute population between these states. Based on these measurements, we develop a theoretical model that unifies the phonon-induced mixing and ISC mechanisms. We find that our model is in excellent agreement with experiment and that it can be used to predict unknown elements of the NV center's electronic structure.\nSecond, we investigate a novel method of using coherent optical manipulation of the NV center's electronic spin to control a nearby nuclear spin. Coherent interactions between the NV center and nearby nuclear spins have enabled the development of NV center-based, multi-qubit quantum registers, but these techniques have generally required the application of microwave or radio-frequency radiation. We demonstrate control of the nuclear spin using an all-optical Raman technique and theoretically evaluate the extent to which the intrinsic physics of the NV center limits the coherence of this Raman-based manipulation technique.
The spin-selective photokinetics of a single matrix-isolated impurity molecule with a triplet-triplet optical transition, T 0–T 1, is considered and the manifestations of the photokinetics in the fluorescence excitation spectra and intensity autocorrelation functions g (2)(τ) of the molecule undergoing narrow-band optical excitation is studied to resolve the fine structure of the transition. The rates of intersystem crossings (ISCs) T 1→S→T 0 to and from a nonradiating singlet state S of the molecule and the rate of population relaxation among the ground (T 0) state sublevels can be obtained from the spectra and g (2)(τ) using the analytical expressions obtained. New experiments on an individual NV defect center in nanocrystals of diamond, where, for the first time, the fine structure of its triplet-triplet 3 A-3 E zero-phonon optical transition (~637 nm) at 1.4 K was resolved, are interpreted. It is concluded that the rate of the ISC transition from the m S =0 sublevel of the excited 3 E state to the singlet 1 A state (~1 kHz) is much slower than the rates from the m S =±1 substates, while the rates of ISC transitions to different m S substates of the ground 3 A state are close to each other (~1 Hz). As a result, only the optical transition between m S =0 sublevels in the 3 A-3 E manifold contributes strongly to the fluorescence. The experimentally observed double-exponential decay of the g (2)(τ) function is explained by the two pathways available to the center for it to leave the S state: (i) the S→ T 0(m S )=0) transition and (ii) the S→T 0(m S =±1) transitions followed by the slow spin-lattice relaxation T 0(m S =±1)→T 0(m S =0) (rate ~0.1 Hz). The work is important for studies where the NV center is used as a single photon source or for quantum information processing.
Among the possible defects that can occur in diamonds, one that draws attention is the nitrogen-vacancy (NV) center.Studied since the early 90s, in recent years, they became one of the most promising platforms for field applications of quantum technology at room temperature, especially for quantum sensing.They are sensitive to electric and magnetic fields, temperature, and strain, making these nanosensors a versatile platform for many applications.The NV center's spin state is easy to read and manipulate by optical means, and, most interestingly, it works well at room temperature, which facilitates its use.The great challenge to implement quantum protocols and quantum algorithms is the coherence time of the quantum states.The NV center stands out for having relatively high coherence times at room temperature.This dissertation presents measurements to characterize the electron spin coherence of NV centers in an ultrapure sample of diamond designed for quantum sensing applications.These measurements combine optical e magnetic resonance techniques.For that, a method was implemented using a conventional CCD camera and a clever imaging protocol, making it possible to perform various pulsed microwave experiments on the electron spin, such as Rabi oscillations and Hahn spin-echo, which were used for determining the characteristic relaxation times (T 1 and T 2 ).Results show that this system provides at least two readily accessible qubits that can be used in quantum protocols even at room temperature.