Hybrid spin-phonon architecture for scalable solid-state quantum nodes

TL;DR

The paper introduces a scalable hybrid spin-phonon architecture in SiC optomechanical crystal cavities to overcome inhomogeneity in solid-state spins. By employing Raman-facilitated interactions, it achieves an effective spin-phonon coupling $g' \approx 0.57$ MHz, enabling a two-qubit CZ gate with fidelity $F=96.80\%$ and high-fidelity generation of Dicke states ($>99\%$). Adiabatic dark-state evolution (STIRAP) provides robustness against spectral diffusion, supporting multi-spin entanglement and rapid state preparation, with Dicke states of up to several spins demonstrated in simulations. This hybrid approach offers a path to scalable, interconnected quantum nodes with optical links and potential integration with other qubit platforms, advancing quantum networks and acoustics in solid-state systems.

Abstract

Solid-state spin systems hold great promise for quantum information processing and the construction of quantum networks. However, the considerable inhomogeneity of spins in solids poses a significant challenge to the scaling of solid-state quantum systems. A practical protocol to individually control and entangle spins remains elusive. To this end, we propose a hybrid spin-phonon architecture based on spin-embedded SiC optomechanical crystal (OMC) cavities, which integrates photonic and phononic channels allowing for interactions between multiple spins. With a Raman-facilitated process, the OMC cavities support coupling between the spin and the zero-point motion of the OMC cavity mode reaching 0.57 MHz, facilitating phonon preparation and spin Rabi swap processes. Based on this, we develop a spin-phonon interface that achieves a two-qubit controlled-Z gate with a simulated fidelity of $96.80\%$ and efficiently generates highly entangled Dicke states with over $99\%$ fidelity, by engineering the strongly coupled spin-phonon dark state which is robust against loss from excited state relaxation as well as spectral inhomogeneity of the defect centers. This provides a hybrid platform for exploring spin entanglement with potential scalability and full connectivity in addition to an optical link, and offers a pathway to investigate quantum acoustics in solid-state systems.

Figures (9)

• Figure 1: Cavity spin-optomechanics. (a) Illustration of cavity optomechanics with embedded spins. Scheme I denotes the direct spin-phonon coupling and Scheme II shows the enhanced phonon coupling through Raman facilitated process. Here, $g^{\prime}$ denotes the Raman-enhanced spin-phonon coupling strength as opposed to $g$. Two lasers with frequencies $\omega_1, \omega_2$ (not labeled) drive each transitions with Rabi frequencies $\Omega_1$ and $\Omega_2$ respectively, and both drives are offset to the excited state by $\Delta$. The phonon frequency $\omega_m$ as well as the spin transition frequency $\omega_s$ are also not labeled. (b) Finite-element simulation of the optomechanical crystal cavity. The designed SiC cavities host optical cavity resonance at 195 THz within the telecom frequency and phononic resonance at 5.6 GHz.
• Figure 2: Phonon-facilitated ODRO. (a) Coherent swap between a single spin and the phonon mode. (b) The "Chevron" interference pattern, generated by sweeping the frequency offset of two laser drives. (c) Fidelity of single-phonon preparation as a function of $\Delta$, $\Omega_{1}$ and $\Omega_{2}$, where they are scaled relative to $\widetilde{\Delta}/2\pi$=230 MHz, $\widetilde{\Omega}_{1}/2\pi$=500 MHz and $\widetilde{\Omega}_{2}/2\pi$=23 MHz, which are used for the simulations in (a) and (b).
• Figure 3: Phonon-facilitated ODRO between two spins. Prepare $\ket{A,B} = \ket{g_2,g_1}$ and measure the population in $\ket{A,B} = \ket{g_1,g_2}$ as a function of spin detuning and delay. (a) Diagram showing the two spin-phonon coupling schemes. The active spins $A$ and $B$ are highlighted in red and blue which are connected to the common phononic channel by Raman facilitated process, while other spins denoted by the black sphere are inactive and remain "dark" to the phonon. (b) "Chevron" interference pattern as we tune the two spin frequencies in the opposite direction w.r.t. the phonon mode. (c) Population swapping between the two spins as we keep them aligned but vary the common detuning to the phonon mode. Interference between distant qubits is revealed by the detuning of the qubit frequency.
• Figure 4: STIRAP process for the two-qubit Controlled-Z (CZ) gate implementation. (a) STIRAP pulse sequence, where the majority of population transfer occurs during the rising and dropping stages enclosed by the "square" pulse shape. Here we only plot the absolute values of both driving amplitudes, see Supplementary Information supplement for more details. (b) Population and phase evolution when only one spin is coupled to the STIRAP process. Phonon is pumped to its first excited state and then transferred back again, which preserves the $\ket{g_2g_3}$ and $\ket{g_3g_2}$ states. (c) Population and phase evolution when two spins are coupled to the STIRAP process simultaneously. Phonon is pumped to its second excited state and then transferred back again, yielding a $\gamma_2-2\gamma_1=\pi$ phase difference for the $\ket{g_2g_2}$ input state compared to the single spin scenario. (d) Full quantum process tomography for the CZ gate demonstrated by the real part of the $\chi$ matrix, featuring a gate fidelity of 96.80%. (e) Demonstration of the feasibility of the gate protocol with some non-ideal system parameters (e.g. the spin dephasing here), over 90% gate fidelity, is still achievable with spin coherence time down to $100~\mu s$.
• Figure 5: STIRAP process for the generation of multi-spin one-excitation Dicke states $D_{1}^{N}$, where $N$ is the number of spins. (a) Pulse sequence for the adiabatic process, similar to the first half of Fig. \ref{['fig:fig4']}(a), but without the center plateau. (b) Generation of $D_{1}^{2} = \left( \ket{g_2g_1} + \ket{g_1g_2} \right)/\sqrt{2}$ in 3927 ns, with a fidelity $\mathcal{F} = \mathrm{tr}\left( \rho_{\mathrm{ideal}}\rho \right) = 99.35\%$. (c) Generation of $D_{1}^{3} = \left( \ket{g_2g_1g_1} + \ket{g_1g_2g_1} + \ket{g_1g_1g_2} \right)/\sqrt{3}$ in 2777 ns, with a fidelity $\mathcal{F} = \mathrm{tr}\left( \rho_{\mathrm{ideal}}\rho \right) = 99.36\%$. System parameters are the same as the implementation of the CZ gate.