Towards a Room-Temperature Spin Quantum Bus in Diamond via Electron Photoionization, Transport, and Capture

Diamond is a proven solid-state platform for spin-based quantum technology. The nitrogen-vacancy center in diamond has been used to realize small-scale quantum information processing and quantum sensing under ambient conditions. A major barrier in the development of large-scale quantum information processing in diamond is the connection of nitrogen-vacancy spin registers by a quantum bus at room temperature. Given that diamond is expected to be an ideal spin transport material, the coherent transport of spin directly between the spin registers offers a potential solution. Yet, there has been no demonstration of spin transport in diamond due to difficulties in achieving spin injection and detection via conventional methods. Here, we exploit detailed knowledge of the paramagnetic defects in diamond to identify novel mechanisms to photoionize, transport, and capture spin-polarized electrons in diamond at room temperature. Having identified these mechanisms, we explore how they may be combined to realize an on-chip spin quantum bus.

Popular Summary

Diamond is a proven solid-state platform for spin-based quantum computing. Clusters of paramagnetic defects in diamond have been used to demonstrate small-scale quantum computing under ambient conditions given the long spin coherence times (i.e., milliseconds) of nitrogen-vacancy centers and the fact that light can initialize and read out their electronic spin states. However, the development of large-scale quantum computing in diamond is inhibited by problems realizing on-chip communication channels—known as quantum buses—that allow quantum information to be exchanged between defect clusters. Here, we propose a technique to realize quantum buses in diamond.

The coherent transport of spin directly between defect clusters offers a way forward in the field of quantum communication in diamond, an ideal spin transport material. However, there have been no demonstrations of spin transport in diamond because of difficulties in achieving spin injection and detection via conventional methods. In this study, we propose combining mechanisms to realize an on-chip spin quantum bus for large-scale diamond quantum computing by connecting two defect spin clusters with a diamond nanowire. We exploit new knowledge of the paramagnetic defects in diamond to identify novel mechanisms to achieve spin-coherent photoionization, transport, and capture of electrons in diamond at room temperature.

While our findings are not yet sufficient for fault-tolerant quantum computing, we expect that our work will pave the way for future studies exploring quantum buses in diamond. Such studies could focus on, for example, improving the electrical properties of diamond nanowires.

Figure 1

(a) Diagrams of the NV and ${\mathrm{N}}_S$ centers that depict carbon (black) and nitrogen (blue) atoms and the vacancy (transparent). (b) Electronic band structure diagram depicting the defect levels of the NV ($a_1$, $e_x$, $e_y$) and ${\mathrm{N}}_S$ centers. The diamond indirect band gap and defect photoionization energies are as indicated [42, 43]. (c) Electronic structure of the ${\mathrm{NV}}^{-}$ center depicting the electronic levels (with corresponding electronic configurations in parentheses) and fine structure states (denoted by electronic spin projection) [1]. The visiblezero-phonon line energy and the zero-field fine-structure splittings of the triplet levels are as indicated. Solid arrows represent optical or spin transitions, whereas dashed arrows represent the spin-selective nonradiative ISCs that lead to optical spin polarization and readout.

Figure 2

Techniques to (a) photoionize an electron with spin state $|\psi ⟩$ from a $\mathrm{NV}\text{−}{{}^{14}\mathrm{N}}_S$ pair and to (b) subsequently capture and optically detect its spin at another $\mathrm{NV}\text{−}{{}^{14}\mathrm{N}}_S$ pair. Each box corresponds to an optical or microwave pulse described in the text and has its indicative length denoted above. For optical pulses, the box color represents the wavelength of the pulse (red, 1.7–1.946 eV; green, typically 2.32 eV). The evolution of the charge and spin states of each defect and the transport electron are represented by solid arrows and are as annotated. The respective $1\text{−}\mu \mathrm{s}$ and 180-ns time frames for ${}^{14}{\mathrm{N}}_S$ nuclear spin and transport electron spin relaxation are indicated by dashed arrows.

Figure 3

(a) A simple transport architecture consisting of two surface electrodes (dark blue) on bulk diamond (gray). (b) Example architecture for transport via a nanowire (gray) on top of a substrate (brown) with end electrodes (dark blue). In (a) and (b), the ionizing and capture centers are depicted as red spheres and the initial and final electron probability densities are depicted above in orange. All other labels are as described in the text. (c) The shaded region defines the nanowire dimension $l$ and applied electric field $E$ where the electron probability density at the capture center is the required $\rho >50\mu {\mathrm{m}}^{-3}$ to yield a capture time $<100\mathrm{ns}$.

Figure 4

(a) Sketch of two nodes of the proposed spin quantum bus network constructed from diamond nanowires (white) on top of a substrate (brown). Spin clusters A and B (red) are located at the nodes and contain logic (either the N nuclear spin of the NV center or a ${}^{13}\mathrm{C}$ isotopic impurity), NV, and ${}^{14}{\mathrm{N}}_S$ spins. Nearby ensembles of ${\mathrm{N}}_S$ centers (green) for recharging the ${}^{14}{\mathrm{N}}_S$ centers in the clusters are located in compartments next to the nodes. Surface electrodes (blue) are used to control electron transport between clusters and the recharge process. At each node, four of the electrodes are arranged in a quadruple configuration to aid in trapping the transport electron at the node. A magnetic field ($B$ field) defines the spin quantization axis and is aligned with the (assumed identical) axes of the NV centers. For clarity, optical, microwave, and magnetic control structures have not been included in the sketch. (b) The proposed protocol to generate entanglement between the logic qubits located in clusters A and B. See text for details of the protocol.

Figure 5

The one- (a) and two-photon (b) ionization mechanisms of ${\mathrm{NV}}^{-}$. The depicted mechanisms correspond to photionization from the $m_s=+1$ spin state of the ${\mathrm{NV}}^{-}$ ground ${}^3{A}_2$ level. In (a), one photon with energy $>2.6\mathrm{eV}$ ejects an electron from the spin-up $e$ spin orbitals of ${\mathrm{NV}}^{-}$ into the conduction band. In (b), one photon with energy $>1.946\mathrm{eV}$ promotes an electron from the occupied spin-down $a_1$ spin orbital to one of the unoccupied spin-down $e$ spin orbitals (i.e., a transition from ${}^3{A}_2$ to ${}^{3}E$). A second photon with energy $>1.946\mathrm{eV}$ ejects an electron from either the spin-up $e$ spin orbitals or the occupied spin-down $e$ spin orbital into the conduction band. In (a) and (b), occupied or unoccupied spin orbitals are depicted as solid or dashed lines, filled circles represent electrons and solid arrows denote spin-up or spin-down electrons, wavelike arrows denote photons. Panel (c) depicts the estimated ultimate photoionization fidelity ${\mathcal{F}}_{\mathrm{NV}}(\lambda )$ for one-photon photoionization (solid black line, left axis) [76] as well as the one-photon photoionization [42] (dashed blue line, right axis) and optical absorption [77] (dashed red line, right axis) transition rates per unit optical power (in the confocal arrangement described in Ref. [42]).