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Physical Review B

Entanglement of electron spins and geometric phases in the diamond color center coupled to the P1 center

Mohamed Hebbache

Published Nov 29, 2012• 6 citations
Publisher

Abstract

Impurity spins in semiconductors are potential quantum bits. Entanglement and topological phases are key resources in quantum computation. We prove that the coupled electron spins carried by a diamond nitrogen-vacancy color center (NV${}^{\ensuremath{-}}$) and a single substitutional nitrogen impurity (P1 center) are entangled in the immediate vicinity of the level anticrossing that appears in the Zeeman energy diagram at about 500 G. We also determine the Aharonov-Anandan, Berry, and marginal geometric phases that can be accumulated by the state vectors of this spin system when it is magnetically transported around a closed path. At the resonance where the gap between two energy levels is minimum, the geometric phases undergo discontinuities, and the entanglement of the two electron spins is maximal.

DOI
10.1103/physrevb.86.195316

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Impurity spins in semiconductors are potential quantum bits. Entanglement and topological phases are key resources in quantum computation. We prove that the coupled electron spins carried by a diamond nitrogen-vacancy color center (NV\ensuremath−{}^{\ensuremath{-}}\ensuremath−) and a single substitutional nitrogen impurity (P1 center) are entangled in the immediate vicinity of the level anticrossing that appears in the Zeeman energy diagram at about 500 G. We also determine the Aharonov-Anandan, Berry, and marginal geometric phases that can be accumulated by the state vectors of this spin system when it is magnetically transported around a closed path. At the resonance where the gap between two energy levels is minimum, the geometric phases undergo discontinuities, and the entanglement of the two electron spins is maximal.
The spin-1 carried by the nitrogen-vacancy (NV${}^{\ensuremath{-}}$) color center of a diamond is a promising candidate as a quantum bit (qubit) for the realization of a solid-state quantum computer. The interaction with the P1P1P1 center, which is a single substitutional nitrogen atom with spin-12\frac{1}{2}21​, converts the NV${}^{\ensuremath{-}}$ qubit to a multilevel system. The 18-level energy diagram of the NV${}^{\ensuremath{-}}$-P1P1P1 coupled defect pair exhibits several level anticrossings and the spin functions change sign at different values of the applied magnetic field. Beyond each resonance, the two electronic spins of the coupled triplet-doublet system flip individually or in concert, offering possibilities to implement quantum logic gates. Interlevel transitions are also possible. The transition probabilities can be predicted rigorously in the framework of the Landau-Zener theory. The spin flip occurs by quantum tunneling. It is also possible to introduce geometric phases, which can be useful for the realization of phase gates.
\n\nDiamond defect spins have emerged as potential qudits (d-dimensional quantum bit) in quantum information and quantum computing. A new scheme is proposed for realizing entangled states of GHZ (Greenberger-Horne-Zeilinger) class in a 3-qudit solid-state register. The qudits are the electron spin-1 carried by the negatively charged nitrogen-vacancy color center (NV−1) in diamond and the nuclear spin-frac12\\frac{1}{2}frac12 of two carbon-13 impurities in the first neighbour shell. Multipartite entanglements between qudits are obtained by bringing the spin system in the vicinity of a level anticrossing. The degree of entanglement between all three qudits is quantified rigorously. GHZ and GHZ-like entangled states have applications in quantum communication and computation protocols.\n
The nitrogen-vacancy center (NV center) in diamond at magnetic fields corresponding to the ground-state level anticrossing (GSLAC) region gives rise to rich photoluminescence (PL) signals due to the vanishing energy gap between the electron spin states, which enables for a broad variety of environmental couplings to have an effect on the NV center's luminescence. Previous works have addressed several aspects of the GSLAC photoluminescence, however, a comprehensive analysis of the GSLAC signature of NV ensembles in different spin environments at various external fields is missing. Here we employ a combination of experiments and recently developed numerical methods to investigate in detail the effects of transverse electric and magnetic fields, strain, P1 centers, NV centers, and the 13C^{13}\mathrm{C}13C nuclear spins on the GSLAC photoluminescence. Our comprehensive analysis provides a solid ground for advancing various microwave-free applications at the GSLAC, including but not limited to magnetometry, spectroscopy, dynamic nuclear polarization (DNP), and nuclear magnetic resonance (NMR) detection. We demonstrate that not only the most abundant 14NV^{14}\mathrm{NV}14NV center but the 15NV^{15}\mathrm{NV}15NV can also be utilized in such applications.
The nitrogen-vacancy center (NV center) in diamond at magnetic fields corresponding to the ground-state level anticrossing (GSLAC) region gives rise to rich photoluminescence (PL) signals due to the vanishing energy gap between the electron spin states, which enables for a broad variety of environmental couplings to have an effect on the NV center’s luminescence. Previous works have addressed several aspects of the GSLAC photoluminescence, however, a comprehensive analysis of the GSLAC signature of NV ensembles in different spin environments at various external fields is missing. Here we employ a combination of experiments and recently developed numerical methods to investigate in detail the effects of transverse electric and magnetic fields, strain, P1 centers, NV centers, and the 13C nuclear spins on the GSLAC photoluminescence. Our comprehensive analysis provides a solid ground for advancing various microwave-free applications at the GSLAC, including but not limited to magnetometry, spectroscopy, dynamic nuclear polarization (DNP), and nuclear magnetic resonance (NMR) detection. We demonstrate that not only the most abundant 14NV center but the 15NV can also be utilized in such applications.
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.
The physical properties of diamond crystals, such as color or electrical conductivity, can be controlled via impurities. In particular, when doped with nitrogen, optically active nitrogen-vacancy centers (NV), can be induced. The center is an outstanding quantum spin system that enables, under ambient conditions, optical initialization, readout, and coherent microwave control with applications in sensing and quantum information. Under optical and radio frequency excitation, the Zeeman splitting of the degenerate states allows the quantitative measurement of external magnetic fields with high sensitivity. This study provides a pedagogical introduction to the properties of the NV centers as well as a step-by-step process to develop and test a simple magnetic quantum sensor based on color centers with significant potential for the development of highly compact multisensor systems.