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arXiv:2306.00164 · PRX Quantum

Hyperfine Spectroscopy of Isotopically Engineered Group-IV Color Centers in Diamond

Isaac Harris, Cathryn P. Michaels, Kevin C. Chen, Ryan A. Parker, Michael Titze, Jesús Arjona Martínez, Madison Sutula, Ian Christen, Alexander M. Stramma, William Roth, Carola M. Purser, Martin Hayhurst Appel, Chao Li, Matthew E. Trusheim, Nicola Palmer, Matthew Markham, Edward S. Bielejec, Mete Atatüre, Dirk Englund

Published Oct 2, 2023• 24 citations

Abstract

A quantum register coupled to a spin-photon interface is a key component in quantum communication and information processing.Group-IV color centers in diamond (SiV -, GeV -, and SnV -) are promising candidates for this application, comprising an electronic spin with optical transitions coupled to a nuclear spin as the quantum register.However, the creation of a quantum register for these color centers with deterministic and strong coupling to the spin-photon interface remains challenging.Here, we make first-principles predictions of the hyperfine parameters of the group-IV color centers, which we verify experimentally with a comprehensive comparison between the spectra of spin active and spin neutral intrinsic dopant nuclei in single GeV -and SnV -emitters.In line with the theoretical predictions, detailed spectroscopy on large sample sizes reveals that hyperfine coupling causes a splitting of the optical transition of SnV -an order of magnitude larger than the optical line width and provides a magnetic field insensitive transition.This strong coupling provides access to a new regime for quantum registers in diamond color centers, opening avenues for novel spin-photon entanglement and quantum sensing schemes for these well-studied emitters.

DOI: 10.1103/prxquantum.4.040301

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A quantum register coupled to a spin-photon interface is a key component in quantum communication and information processing.Group-IV color centers in diamond (SiV -, GeV -, and SnV -) are promising candidates for this application, comprising an electronic spin with optical transitions coupled to a nuclear spin as the quantum register.However, the creation of a quantum register for these color centers with deterministic and strong coupling to the spin-photon interface remains challenging.Here, we make first-principles predictions of the hyperfine parameters of the group-IV color centers, which we verify experimentally with a comprehensive comparison between the spectra of spin active and spin neutral intrinsic dopant nuclei in single GeV -and SnV -emitters.In line with the theoretical predictions, detailed spectroscopy on large sample sizes reveals that hyperfine coupling causes a splitting of the optical transition of SnV -an order of magnitude larger than the optical line width and provides a magnetic field insensitive transition.This strong coupling provides access to a new regime for quantum registers in diamond color centers, opening avenues for novel spin-photon entanglement and quantum sensing schemes for these well-studied emitters.

Long distance quantum networking requires combining efficient spin-photon interfaces with long-lived local memories. Group-IV color centers in diamond (SiV, GeV, and SnV) are promising candidates for this application, containing an electronic spin-photon interface and dopant nuclear spin memory. Recent work has demonstrated state-of-the-art performance in spin-photon coupling and spin-spin entanglement. However, coupling between the electron and nuclear spins introduces a phase kickback during optical excitation that limits the utility of the nuclear memory. Here, we propose using the large hyperfine coupling of SnV-117 to operate the device at zero magnetic field in a regime where the memory is insensitive to optical excitation. We further demonstrate ground state spin control of a SnV-117 color center integrated in a photonic integrated circuit, showing 97.8% gate fidelity and 2.5 ms coherence time for the memory spin level. This shows the viability of the zero-field protocol for high fidelity operation, and lays the groundwork for building quantum network nodes with SnV-117 devices.

Group-IV color centers in diamond (SiV, GeV, SnV) have emerged as leading solid-state spin-photon interfaces for quantum information processing applications. However, these qubits require cryogenic temperatures to achieve high fidelity operation due to interactions with the thermal phonon bath. In this work, we: (i) derive a detailed model of the decoherence from first-order acoustic phonon processes acting on the spin-orbit fine structure of these color centers; (ii) demonstrate agreement of the model's predicted coherence times with previous measurements; (iii) identify regimes to suppress phonon-mediated decoherence by changing magnetic-field and strain bias to allow higher temperature operation. This methodology enables prediction of decoherence processes in other color centers and solid-state qubit systems coupled to a thermal bath via a parasitic two-level system. By experiment-anchored decoherence models, we facilitate optimizing qubit coherence for specific applications and devices.

Color centers associated with group-IV dopants in diamond with long-lived nuclear spins have emerged as major candidates for distributed quantum computing nodes and quantum repeaters. Several proof-of-principle experiments have already been demonstrated. A key operation for long-distance entanglement-distribution protocols are fast and robust gates between the electron spin and a nuclear spin. Here, we investigate numerically for an existing experimental platform of a Germanium-vacancy (GeV) center with a strongly-coupled

{}^{13}

C spin, how such gates can be implemented via quantum optimal control. In the presence of realistic noise we investigate different parameter regimes and gate operations and obtain robust two-qubit gates with fidelities exceeding

99.9 \%

. The framework provides a scalable strategy for group-IV quantum nodes and can be adapted to related architectures.

Color centers in diamond have emerged as leading solid-state ``artificial atoms'' for a range of quantum technologies, from quantum sensing to quantum networks. Concerted research activities are now underway to identify new color centers that combine stable spin and optical properties of the nitrogen vacancy (${\mathrm{NV}}^{\ensuremath{-}}$) with the spectral stability of the silicon vacancy (${\mathrm{SiV}}^{\ensuremath{-}}$) centers in diamond, with recent research identifying other group-IV color centers with superior properties. In this paper, we investigate a class of diamond quantum emitters from first principles, the group-III color centers, which we show to be thermodynamically stable in a spin-1, electric-field-insensitive structure. From ab initio electronic structure methods, we characterize the product Jahn-Teller (pJT) effect present in the excited-state manifold of these group-III color centers, where we capture symmetry-breaking distortions associated with strong electron-phonon coupling. These predictions can guide experimental identification of group-III vacancy centers and their use in applications in quantum information science and technology.

Color centers in diamond have attracted much interest as candidates for optically active, solid-state quantum bits. Of particular interest are inversion-symmetric color centers based on group-IV impurities in diamond because they emit strongly into their zero-phonon lines and are insensitive to electric field noise to first order. Early studies of the negatively charged tin-vacancy (${\mathrm{SnV}}^{\ensuremath{-}}$) center in diamond have found the ${\mathrm{SnV}}^{\ensuremath{-}}$ to be a promising candidate: it has high quantum efficiency, emits strongly into its zero-phonon lines, and is expected to have a long

{T}_{2}

spin coherence time at 4 K. To develop the ${\mathrm{SnV}}^{\ensuremath{-}}$ into a spin qubit requires further characterization, especially of the spin and optical properties of individual ${\mathrm{SnV}}^{\ensuremath{-}}$ in nanofabricated structures. In this work, we isolate single ${\mathrm{SnV}}^{\ensuremath{-}}$ centers in diamond nanopillars and characterize their emission properties and their spin response to a magnetic field. We observe narrow emission linewidths

<250

MHz, as well as a strong polarization dependence of each transition. We also find the Zeeman splitting under a magnetic field to be in good agreement with theoretical prediction. Our results pave the way toward future employment of single ${\mathrm{SnV}}^{\ensuremath{-}}$ centers as optically accessible quantum memories.

Accurately controlling entangling gates remains a major challenge for quantum technology applications with solid-state spin qubits. Here, we study a group-IV color-center with a strongly-coupled nuclear spin and approach the problem from a quantum control perspective. We show that there are three different types of entangling gates where the entanglement is mediated by the parallel hyperfine-coupling component, the orthogonal one or both. We derive the respective quantum speed limits (QSL) and show by means of dynamical decoupling, resonant driving of single- and double-quantum transitions, quantum optimal control and algebraic gate decomposition how these gates can be realized. We finally discuss the experimental applicability.