Cavity-assisted single-shot T center spin readout

TL;DR

This work tackles the challenge of high-fidelity, single-shot readout of a single T center electronic spin in silicon, a key ingredient for telecom-band quantum networks. It develops two cavity QED protocols—fluorescence-based readout via a spin-conserving transition and cavity-reflection readout exploiting spin-dependent reflectivity—within a four-level model coupled to a single-mode cavity. With realistic parameters (Q ≈ 2×10^5, Γ/2π ≈ 100 MHz) and a Lindblad dynamics framework, both schemes deliver single-shot fidelities above 99% in tens of microseconds, and remain robust against moderate spectral diffusion. The results establish practical routes to fast, reliable spin readout for T centers, advancing silicon-based quantum networking options and enabling cavity-mediated spin-photon interfaces.

Abstract

High-fidelity spin readout is a crucial component for quantum information processing with optically interfaced solid-state spins. Here, we propose and investigate two theoretical protocols for fast single-shot readout of cavity-coupled single T center electronic spins. For fluorescence-based readout, we selectively couple one of the T center spin-conserving transitions to a single-mode photonic cavity, exploiting the enhancement of the fluorescence emission and cyclicity. For reflection-based readout, we leverage the spin-dependent cavity reflection contrast to generate the qubit readout signal. We show that the cavity reflection approach enables high-fidelity spin readout even when the T center only has a modest cyclicity. With realistic system parameters, such as cavity quality factor $Q = 2\times10^5$ and T center optical linewidth $Γ/2π= 100$ MHz, we calculate a single-shot readout fidelity exceeding 99% within 8.7 $μ$s for both spin readout protocols.

Figures (6)

• Figure 1: Proposed cQED scheme for the T center electronic spin readout. (a) Illustration of a single T center coupled to a one-sided cavity, where the input and output laser fields ($\mathbf{a}_\text{in}$, $\mathbf{a}_\text{out}$) couple to the cavity mode at a rate of $\kappa_\text{wg}$. The cavity scattering loss rate $\kappa_\text{sc}$ is also included. The coupling rate between the single T center and the cavity mode is given by $g$ at zero field. (b) A simplified energy diagram is shown on the right. Four transitions emerge after an external magnetic field $B$ is applied. The Zeeman splittings for ground and excited states are $2\Delta_e$ and $2\Delta_g$, respectively.
• Figure 2: Spin-dependent fluorescence readout.(a) Excited state population dynamics with different initialized states. The gray shaded region represents the square laser pulse with the readout sequence shown in the top panel. The inset shows the cavity (black line) alignment with the transition A. (b) Poissonian distribution $P(N_\text{ph},k)$ of detected fluorescence photon counts under different spin initializations. The inset shows the average photon counts per pulse decay due to the optical pumping. The number of excitation pulses $N_\text{cyc}$ for readout is chosen to be $1/e$ decay point (black dashed line). Simulation parameters for panel a and b: $Q=1\times10^5$, $\Gamma/2\pi=1$ GHz, $t_\text{pulse}$$=10$ ns, $P_\text{in} = 100$ pW, and $r_g=10$. Both the cavity and the laser are tuned resonant with the transition A. (c) and (d)$r_g$ dependence of readout fidelity with cavity $Q = 1\times10^5$ (c) and $Q=2\times10^5$ (d). In both panels, solid and dashed lines represent $\Gamma/2\pi=0.1$ GHz and $\Gamma/2\pi=1$ GHz, respectively. Other system parameters can be found in Table.\ref{['tab:commonParametersFluorescentReadout']}.
• Figure 3: Spin-dependent cavity reflection readout.(a) Spin readout infidelity calculations under different laser input powers and pulse widths with optimized $\Delta_a$ and $\Delta_c$ maximizing the reflection contrast. Lower laser powers necessitate longer pulses for reaching the maximal fidelity. System parameters used are listed in Table. \ref{['tab:standardParameters']}. (b) Extracted minimum readout infidelity in panel (a) with different $r_g$ while keeping other system parameters the same. Saturation behavior happens for $r_g \geq 5$. (c) The maximum readout fidelity under different system parameters ($Q$, $\Gamma$) with $t_\text{pulse} \leq$ 50 $\mu$s and $0.1\leq P_\text{in} \leq 100$ pW.
• Figure 4: Effect of spectral diffusion on spin readout.(a) Readout infidelity at different optical transition detunings ($\delta\omega$) in two protocols. For each spectral detuning $\delta\omega$, all other system and readout parameters are kept the same as the case when $\delta\omega =0$ in the calculation. The reflection-based readout shows an asymmetric infidelity profile, which results from the larger reflection contrast decrease and optical pumping with positive detunings. (b) Readout infidelity for the two protocols under the spectral diffusion manifested as a random spectral wandering, which is modeled as a Gaussian distribution with a FWHM of 2$\Gamma_\text{sd}$. Gaussian-weighted average of the detected photon distributions at different $\delta\omega$ are used to calculate the spin readout fidelity. For both panel (a) and (b), the results are derived with cQED parameters listed in Table. \ref{['tab:standardParameters']}. Fluorescence-based readout utilizes $t_\text{pulse} = 10$ ns and $P_\text{in} = 100$ pW while the reflection-based readout uses $t_\text{pulse} = 47$$\mu$s and $P_\text{in} = 3.8$ pW. Both $\delta\omega$ and $2\Gamma_\text{sd}$ are presented in units of the fast depahsing broadend linewidth $\Gamma/2\pi = 0.1$ GHz.
• Figure 5: Contrast with different cavity efficiency $\eta_\text{cav}$.(a) The blue curve is derived from global optimization process of $\Delta_a$ and $\Delta_c$; the red curve is obtained by aligning the cavity with one of the spin-conserving transitions. (b) Optimized spin-dependent cavity reflection curves with different $\eta_\text{cav}$. All blue (orange) curves represent initialized spin state to be $\ket{\uparrow_\text{g}}$ ($\ket{\downarrow_\text{g}}$). For $\eta_\text{cav} = 0.5$ (middle panel), the black line in the inset marks the location of the optical transition A, while the red line shows the maximal contrast point. The separation between the two is due to the dispersive shift.