Optomechanical quantum bus for donor spins in silicon

TL;DR

The paper addresses the challenge of scalable, long-range coupling and optical readout for silicon donor spin qubits by proposing an on-chip optomechanical quantum bus. It combines microwave-dressed donor spins with a silicon nanobeam optomechanical resonator to achieve telecom-wavelength readout and phonon-mediated two-qubit gates, either in dispersive or resonant regimes. The work provides a detailed Hamiltonian framework for spin–phonon coupling via strain or magnetic gradients, analyzes readout via shifts in mechanical frequency with numerical GKSL benchmarks, and demonstrates the feasibility of a $\\sqrt{iSWAP}$ gate with realistic decoherence, supported by concrete device parameters. Overall, the approach offers a scalable, CMOS-compatible path to silicon-based quantum networks by linking spins, phonons, and photons on a silicon platform, with practical readout achievable at accessible temperatures and device geometries.

Abstract

Silicon is the foundation of current information technology, and a promising platform for future quantum information technology as silicon-based qubits exhibit some of the longest coherence times in solid-state. At the same time, silicon is the underlying material for advanced photonics activity, and photonics structures in silicon can be used to define optomechanical cavities where the vibrations of nanoscale mechanical resonators can be probed down to the quantum level with laser light. Here, we propose to bring all these developments together by coupling silicon donor spins into optomechanical structures. We show theoretically and numerically that this allows telecom wavelength optical readout of the spin-qubits and implementing high-fidelity entangling two-qubit gates between donor spins that are spatially separated by tens of micrometers. We present an optimized geometry of the proposed device and discuss with the help of numerical simulations the predicted performance of the proposed quantum bus. We analyze the optomechanical spin readout fidelity and find the optimal donor species for different coupling mechanisms.

Figures (11)

• Figure 1: Schematic of the optomechanical quantum bus. The dressed qubit's state affects the resonance frequency of the mechanical resonator. The mechanical displacement modulates the resonance frequency of the optical cavity. The spin-dependent mechanical frequency shifts can then be detected by measuring the noise imprinted on the phase quadrature of the light escaping from the cavity. Bringing two spin-qubits near resonance with the resonator allows logical two-qubit operations for spatially separated donor spins. The parameters are discussed in the main text.
• Figure 2: The expected shift of the mechanical resonance frequency as a function of the detunings. These shifts are calculated from the energy levels of the qubit-oscillator Hamiltonian, and thus do not consider any finite linewidths of the qubit or the resonator. The results show an interplay between the detunings: the maximal shift follows well the qubit-mechanics resonance condition $\omega_m = \sqrt{\Omega_R^2 + \Delta \nu^2}$. The inset shows a linecut at $\nu_{MW}=\gamma_eB_0$, together with an analytical calculation for the expected shift $\Delta \omega_m = \lambda^2 \Omega_R / [ 2(\omega_m^2 - \Omega_R^2) ]$noRWAanalyticalShift. For the numerical values here, we have fixed the coupling strength as $\lambda/(2\pi) = 1$ kHz, and $\omega_m/(2\pi) = 1$ MHz.
• Figure 3: Shift of the mechanical resonance frequency as a function of the coupling strength for different detunings between the mechanical resonance and the qubit's Rabi frequency. This detuning value effectively defines the possible operation temperature. Here, $\omega_m/(2\pi) = 1$ MHz and $\Delta \nu = 0$. The horizontal black line highlights the 100 Hz shift. The solid and dashed lines correspond to the mechanical resonator initialized in the thermal state ($n_{\rm th} = 3)$ and ground state, respectively.
• Figure 4: Required coupling strength $\lambda$ to cause the 100 Hz shift of the mechanical frequency for different combinations of MW and Rabi detunings. Dashed black line shows the expected Jaynes-Cummings behaviour $\Delta \omega_m = \lambda^2 \Omega_R / [ 2(\omega_m^2 - \Omega_R^2) ]$noRWAanalyticalShift. Dotted yellow line marks roughly the dispersive limit boundary. Here $n_{\rm th} = 3$. The two lowest detuning curves lie on top of each other on this scale.
• Figure 5: The $\sqrt{iSWAP}$-gate fidelity as function of Rabi detuning and coupling strength.