Silicon T centre hyperfine structure and memory protection schemes

TL;DR

The paper addresses protecting memory qubits in spin-photon interfaces by characterizing the hydrogen hyperfine interaction in silicon's T centre and exploiting a dephasing-protection manifold to suppress optically-induced decoherence. The authors determine the hydrogen hyperfine tensor via ODMR across magnetic-field orientations and provide a trajectory-based model for decoherence under optical excitation, along with strategies such as Purcell enhancement and average unitary corrections. They discuss implications for brokered entanglement and long-distance quantum networks using cavity-coupled T centres, and highlight prospects for multi-qubit spin registers including 13C nuclei. The work offers a practical framework for integrating robust memory qubits in silicon photonic SPI nodes.

Abstract

Combining the long-coherence of spin qubits and the capability to transmit information and entanglement through photons, spin-photon interfaces (SPIs) are a promising platform for networked quantum computation and long-distance quantum communication. SPIs that possess local `memory' qubits in addition to the optically coupled `communication' qubit can improve remote entanglement fidelities through brokered entanglement schemes and entanglement purification. In these schemes, it is critical to protect the memory qubit from decoherence during entanglement operations on the communications qubit. Silicon, a platform with mature microelectronic and nanophotonic fabrication, is host to the T centre, an SPI with emission in the telecommunications O-band that directly integrates with silicon nanophotonics. Cavity-coupled T centres are a platform for brokered entanglement distribution in silicon photonic circuits and over long-distance optical fibre links. The T centre's electron and nuclear spin qubits are an intrinsic register of communication and memory qubits respectively, with anisotropic hyperfine coupling. In this work we determine the T centre's hydrogen hyperfine coupling tensor. We also introduce schemes to protect against dephasing or eliminate relaxation of the T centre's hydrogen memory qubit during optical excitation. These results address a key challenge for practical T centre quantum networks.

Figures (5)

• Figure 1: T centre crystal structure and broker-client model. The electron and nuclear spins of the T centre can be assigned communication and memory roles respectively. Each node in the network corresponds to an addressable T centre, and each node can be as close as neighbouring photonic devices or as far as kilometres through telecom fibre connections. Remote entanglement of communication qubits is performed by interfering emission from two connected nodes. This entanglement is then transferred to the memory qubits through the hyperfine coupling (purple arrows) between the electron and nuclear spins.
• Figure 2: (a) T centre energy level diagram showing the optically detected magnetic resonance (ODMR) schemes. The optical field (green) differentially addresses the ground states. When resonant with a transition, the RF field (red) may transfer population to the 'bright' ground state and increase luminescence. At higher fields ($>1$ mT), we simultaneously address an EPR (yellow) and NMR (purple) transition to drive luminescence. Eigenstates are labelled according to the high-field spin composition, though we depict an intermediate field ordering. The sign of $A_\mathrm{eff}$ will determine whether the nuclear spin ordering flips on the $\ket{\uparrow_e}$ or $\ket{\downarrow_e}$ branch compared to high-field. (b) Principal hyperfine axes for orientation z0 Clear2024optical shown in red relative to the defect structure and silicon crystal axes (black). The z0 defect plane $(1\Bar{1}0)$ and magnetic field angles $\theta$, $\phi$ are shown. (c) Experiment configuration for ODMR.
• Figure 3: Eigenenergy differences in the T centre ground state as a function of external magnetic field applied along the (a) $<$001$>$, (b) $<$110$>$, and (c) $<$111$>$ crystal axes. The ODMR spectra (black lines) at each field are overlaid by the fit lines (coloured) for each orientation subset, which we label with the field direction and letter a--d. The upper plots show ODMR spectra of the NMR transitions at a higher field.
• Figure 4: (a) T centre energy levels at high magnetic field. We indicate the arbitrary choice of the optically-coupled hole spin state with $\ket{\updownarrow}$. (b) $\delta_\mathrm{h}$ contours in the high-field limit, shown in the hyperfine basis. The band $\delta_\mathrm{h} = 0$ is asymptotically protected from dephasing during cyclic optical excitation. (c) Evolution of the nuclear magnetic moment $\textbf{I}$ under optical excitation, starting from a ground-state eigenstate $\textbf{I}_{\mathrm{e}, \uparrow}$ aligned along the total effective magnetic field $\textbf{B}_\mathrm{eff}$, which is the sum of the external field and the effective field generated by the the electron. Because TX$_0$ has no hyperfine coupling, the nuclear spin precesses about $\textbf{B}$ during optical excitation. (d) In the long-lifetime limit, the magnetic moment is the average over the precession trajectory. Projection back into the ground state basis returns the original state with probability $[2a-1]^2$, where $a=\braket{\Uparrow_e}{\Uparrow_h}^2$ is the overlap between the ground and excited state nuclear spin up states.
• Figure 5: (a) Simulated nuclear cyclicity for T centre orientation z0 with an enhanced lifetime of 10 ns as a function of $\vec{b}$, with $B = 1$ T. State evolution is simulated out to 100 ns. (b) Calculated difference in nuclear spin splitting between the $\ket{\uparrow_e}$ and $\ket{\uparrow_h}$ states ($\delta_\mathrm{h}$). $\theta$ is the polar angle of $\textbf{B}$ from $[001]$ and $\phi$ is the azimuthal angle from $[100]$. The dashed line in both plots represents the defect plane.