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arXiv:1307.0257

Characterization of hyperfine interaction between single electron and single nuclear spins in diamond assisted by quantum beat from the nuclear spin

Jeong Hyun Shim, Nowak, B., I. Niemeyer, Zhang, J., Frederico D. Brandão, Dieter Suter

Published Jul 1, 2013• 4 citations
arXivHTMLPDF

Abstract

Precise characterization of a hyperfine interaction is a prerequisite for high fidelity manipulations of electron and nuclear spins belonging to a hybrid qubit register in diamond. Here, we demonstrate a novel scheme for determining a hyperfine interaction, using single-quantum and zero-quantum Ramsey fringes, by applying it to the system of a Nitrogen Vacancy (NV) center and a $^{13}$C nuclear spin in the 1$^{\mathrm{st}}$ shell. The zero-quantum Ramsey fringe, analogous to the quantum beat in a $Λ$-type level structure, particularly enhances the measurement precision for non-secular hyperfine terms. Precisions less than 0.5 MHz in the estimation of all the components in the hyperfine tensor were achieved. Furthermore, for the first time we experimentally determined the principal axes of the hyperfine interaction in the system. Beyond the 1$^{\mathrm{st}}$ shell, this method can be universally applied to other $^{13}$C nuclear spins interacting with the NV center.

DOI
10.48550/arxiv.1307.0257

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Precise characterization of a hyperfine interaction is a prerequisite for high fidelity manipulations of electron and nuclear spins belonging to a hybrid qubit register in diamond. Here, we demonstrate a novel scheme for determining a hyperfine interaction, using single-quantum and zero-quantum Ramsey fringes, by applying it to the system of a Nitrogen Vacancy (NV) center and a 13^{13}13C nuclear spin in the 1st^{\mathrm{st}}st shell. The zero-quantum Ramsey fringe, analogous to the quantum beat in a ΛΛΛ-type level structure, particularly enhances the measurement precision for non-secular hyperfine terms. Precisions less than 0.5 MHz in the estimation of all the components in the hyperfine tensor were achieved. Furthermore, for the first time we experimentally determined the principal axes of the hyperfine interaction in the system. Beyond the 1st^{\mathrm{st}}st shell, this method can be universally applied to other 13^{13}13C nuclear spins interacting with the NV center.
A negatively-charged nitrogen-vacancy (NV) center in diamond is a promising system for quantum computation and quantum information. It has the diamond structure with a substitutional nitrogen atom and a neighboring vacancy. An electron spin in the NV center has an exceptionally long coherence time at room temperature. Thus the NV center has a potential to realize a room-temperature quantum computer which is more efficient than a classical computer. In this dissertation, we focus on the nitrogen nuclear spin as well as the electron spin in the NV center. Every NV center has the nitrogen nuclear spin. Because of the long coherence time of the nitrogen nuclear spin, it is a good candidate for a quantum memory. Thus it is important to prepare the nitrogen nuclear spin qubit in a given pure state for quantum computation. We provide a theoretical understanding of the popular nuclear spin initialization technique. Furthermore, we propose an optimal condition for the initialization of the nitrogen nuclear spin by including the local strain in the NV center. We expect that this optimal condition can improve the purity of the nuclear spin initialization. We also propose an efficient quantum measurement protocol for the hyperfine interaction between the electron spin and the ¹⁵N nuclear spin in the NV center. A precise knowledge of the hyperfine interaction is important to reduce an error in a coherent control of the ¹⁵N nuclear spin. In this protocol, a sequence of quantum operations with successively increasing duration is utilized to estimate the hyperfine interaction with successively higher precision approaching the quantum metrology limit. Unlike common quantum metrological methods, this protocol does not need the preparation of the nuclear spin in a pure state. In the presence of realistic operation errors and electron spin decoherence, we show the overall precision of our protocol still surpasses the standard quantum limit
The negatively charged nitrogen-vacancy (NV−) center in diamond is a model quantum system for university teaching labs due to its room-temperature compatibility and cost-effective operation. Based on the low-cost experimental setup that we have developed and described for the coherent control of the electronic spin [Sewani et al., Am. J. Phys. 88, 1156–1169 (2020)], we introduce and explain here a number of more advanced experiments that probe the electron–nuclear interaction between the NV− electronic and the 14N and 13C nuclear spins. Optically detected magnetic resonance, Rabi oscillations, Ramsey fringe experiments, and Hahn echo sequences are implemented to demonstrate how the nuclear spins interact with the electron spins. Most experiments only require 15 min of measurement time and, therefore, can be completed within one teaching lab.
Abstract The decoherence of point defect qubits is often governed by the electron spin-nuclear spin hyperfine interaction that can be parameterized by using ab inito calculations in principle. So far most of the theoretical works have focused on the hyperfine interaction of the closest nuclear spins, while the accuracy of the predictions for distinct nuclear spins is barely discussed. Here we demonstrate for the case of the NV center in diamond that the absolute relative error of the computed hyperfine parameters can exceed 100% using an industry standards first-principles code. To overcome this issue, we implement an alternative method and report on significantly improved hyperfine values with O{{{{{{{\mathcal{O}}}}}}}}O O (1%) relative mean error at all distances. The provided accurate hyperfine data for the NV center enables high-precision simulation of NV quantum nodes for quantum information processing and positioning of nuclear spins by comparing experimental and theoretical hyperfine data.
Individual nuclear spins in diamond can be optically detected through hyperfine couplings with the electron spin of a single nitrogen-vacancy (NV) center; such nuclear spins have outstandingly long coherence times. Among the hyperfine couplings in the NV center, the nearest neighbor 13C nuclear spins have the largest coupling strength. Nearest neighbor 13C nuclear spins have the potential to perform fastest gate operations, providing highest fidelity in quantum computing. Herein, we report on the control of coherences in the NV center where all three nearest neighbor carbons are of the 13C isotope. Coherence among the three and four qubits are generated and analyzed at room temperature.
Abstract We employ the electronic spin of a single nitrogen-vacancy (NV) defect in diamond to detect and control the quantum state of remote nuclear spins coupled by hyperfine interaction. More precisely, our work focuses on individual 13C^{13}\text {C}13C 13 C nuclei featuring a moderate hyperfine coupling strength ( ∼1\sim 1∼1 ∼ 1 MHz) with the NV’s electron spin. Two different methods providing an efficient room-temperature polarization of these peculiar 13C^{13}\text {C}13C 13 C nuclear spins are described. The first one is based on a polarization transfer from the NV electron spin to the 13C^{13}\text {C}13C 13 C nucleus, which is mediated by the anisotropic component of the hyperfine interaction. The second one relies on coherent population trapping (CPT) within a Λ\Lambda Λ Λ -type energy-level configuration in the microwave domain, which enables to initialize the 13C^{13}\text {C}13C 13 C nuclear spin in any quantum state superposition on the Bloch sphere. This CPT protocol is performed in an unusual regime for which relaxation from the excited level of the Λ\Lambda Λ Λ -scheme is externally triggered by optical pumping and separated in time from coherent microwave excitations. For these two polarization techniques, we investigate the impact of optical illumination on the nuclear spin polarization efficiency. This work adds new methods to the quantum toolbox used for coherent control of individual nuclear spins in diamond, which might find applications in quantum metrology. Graphical Abstract
Quantum computers have the potential to speed up certain problems that are hard for classical computers. Hybrid systems, such as the nitrogen-vacancy (NV) center in diamond, are among the most promising systems to implement quantum computing, provided the control of the different types of qubits can be efficiently implemented. In the case of the NV center, the anisotropic hyperfine interaction allows one to control the nuclear spins indirectly, through gate operations targeting the electron spin, combined with free precession. Here, we demonstrate that this approach allows one to implement a full quantum algorithm, using the example of Grover's quantum search in a single NV center, whose electron is coupled to a carbon nuclear spin.