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arXiv:2001.01801 · Physical review. B./Physical review. B

Longitudinal spin relaxation model applied to point-defect qubit systems

Viktor Ivády

Published Apr 17, 2020• 27 citations
arXivHTMLPDF

Abstract

Controllable, partially isolated few-level systems in semiconductors have recently gained multidisciplinary attention due to their widespread nanoscale sensing and quantum technology applications. Quantitative simulation of the dynamics and related applications of such systems is a challenging theoretical task that requires faithful description not only of the few-level systems but also their local environments. Here, we develop a method that can describe relevant relaxation processes induced by a dilute bath of nuclear and electron spins. The method utilizes an extended Lindblad equation in the framework of cluster approximation of a central spin system. We demonstrate that the proposed method can accurately describe ${\mathrm{T}}_{1}$ time of an exemplary solid-state point-defect qubit system, in particular, the nitrogen-vacancy (NV) center in diamond, at various magnetic fields and strain.

DOI
10.1103/physrevb.101.155203

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Controllable, partially isolated few-level systems in semiconductors have recently gained multidisciplinary attention due to their widespread nanoscale sensing and quantum technology applications. Quantitative simulation of the dynamics and related applications of such systems is a challenging theoretical task that requires faithful description not only of the few-level systems but also their local environments. Here, we develop a method that can describe relevant relaxation processes induced by a dilute bath of nuclear and electron spins. The method utilizes an extended Lindblad equation in the framework of cluster approximation of a central spin system. We demonstrate that the proposed method can accurately describe T1{\mathrm{T}}_{1}T1​ time of an exemplary solid-state point-defect qubit system, in particular, the nitrogen-vacancy (NV) center in diamond, at various magnetic fields and strain.
The nitrogen vacancy (NV) center in diamond, a well-studied, optically active spin defect, is the prototypical system in many state of the art quantum sensing and communication applications. In addition to the enticing properties intrinsic to the NV center, its diamond host's nuclear and electronic spin baths can be leveraged as resources for quantum information, rather than considered solely as sources of decoherence. However, current synthesis approaches result in stochastic defect spin positions, reducing the technology's potential for deterministic control and yield of NV-spin bath systems, as well as scalability and integration with other technologies. Here, we demonstrate the use of theoretical calculations of electronic central spin decoherence as an integral part of an NV-spin bath synthesis workflow, providing a path forward for the quantitative design of NV center-based quantum sensing systems. We use computationally generated coherence data to characterize the properties of single NV center qubits across relevant growth parameters to find general trends in coherence time distributions dependent on spin bath dimensionality and density. We then build a maximum likelihood estimator with our theoretical model, enabling the characterization of a test sample through NV T2* measurements. Finally, we explore the impact of dimensionality on the yield of strongly coupled electron spin systems. The methods presented herein are general and applicable to other qubit platforms that can be appropriately simulated.
Hybrid system based on nuclear spins coupled to defect electron spin in solid has been proposed as an appealing strategy to manipulate qubits for quantum information processing. While universal quantum control and the time optimal control have been arrived, the influence of environment on the system has been ignored. We studied the dynamics of the hybrid system under the surrounding environment using the quantum master equation approach. The quantum master equation and the mean-value equations of the dynamical variables have been derived. Here we focus on a special platform based on the Nitrogen-Vacancy center electronic spin in diamond and nearby carbon-13 nuclear spins.
The quantum dynamics of many-electron spin systems is investigated using a reduced-density-matrix description. Applications of interest include trapped atomic systems in optical lattices, semiconductor quantum dots, and vacancy defect centers in solids. Complimentary time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations are self-consistently developed. The general non-perturbative and non-Markovian formulations provide a fundamental framework for systematic evaluations of corrections to the standard Born (lowest-order-perturbation) and Markov (short-memory-time) approximations. Particular attention is given to decoherence and relaxation processes, together with spectral-line broadening phenomena, that are induced by interactions of many-electron spin systems with photons, phonons, nuclear spins, external electric, magnetic, and electromagnetic fields. Within the framework of a quantum-open-systems (reduced-density-operator) approach, these processes are treated either as coherent interactions or as environmental interactions. The environmental interactions are incorporated by means of the general expressions that are derived for the time-domain and frequency-domain Liouville-space self-energy operators, for which the tetradic-matrix elements are explicitly evaluated in the diagonal-resolvent, lowest-order, and Markov (short-memory time) approximations.
We study the longitudinal relaxation of a nitrogen-vacancy (NV) center surrounded by a 13^{13}13C nuclear spin bath in diamond. By means of cluster-correlation expansion (CCE), we numerically demonstrate the decay process of electronic state induced by cross relaxation at low temperature. It is shown that the CCE method is not only capable of describing pure-dephasing effect at large-detuning regime, but it can also simulate the quantum dynamics of populations in the nearly resonant regime. We present a proposal to slow down the decay of NV center via implementing quantum Zeno effect (QZE). The numerical result shows that QZE can effectively inhibit the decay of NV center.
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.
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.