Quantum state transfer between a frequency-encoded photonic qubit and a quantum-dot spin in a nanophotonic waveguide

We propose a deterministic yet fully passive scheme to transfer the quantum state from a frequency-encoded photon to the spin of a quantum dot mediated by a nanophotonic waveguide. We assess the quality of the state transfer by studying the effects of all relevant experimental imperfections on the state-transfer fidelity. We show that a transfer fidelity exceeding $95\%$ is achievable for experimentally realistic parameters. Our work sets the stage for deterministic solid-state quantum networks tailored to frequency-encoded photonic qubits.

Figure 1

Schematics of the photon-to-spin state transfer in a $\mathrm{\Lambda }$-level emitter coupled to a one-sided nanophotonic waveguide. (a) Left: Initial state of the spin-photon system, where the superposition state $|{\psi }_p\rangle$ is encoded in frequency bins $|{\omega }_1\rangle$ and $|{\omega }_2\rangle$ separated by the ground-state splitting $\mathrm{\Delta }$. The photonic qubit scatters off an emitter (orange dot) initialized in state $|g_1\rangle$. Right: The photonic state $|{\psi }_p\rangle$ is deterministically transferred to the spin carrier $|{\psi }_s\rangle$. With symmetric decay rates ${\mathrm{\Gamma }}_1={\mathrm{\Gamma }}_2$ the final spin state corresponds to the incoming photonic state due to the superposition of SPRINT and off-resonant scattering. (b) Left: SPRINT, where a resonant photon flips the spin state from $|g_1\rangle$ to $|g_2\rangle$ (solid green arrow). Imperfections induce a small probability to decay to the original spin state (dotted pink arrow). Right: Off-resonant scattering, where the photon is almost unaffected (solid green arrow). There is a small probability to flip the spin (dotted light blue arrow) due to finite $\mathrm{\Delta }$.

Figure 2

Energy levels of the $\mathrm{\Lambda }$ system under spin dephasing noise and spectral diffusion.

Figure 3

Pulse sequence with spin echo. The spin echo sequence assumes that the state transfer occurs at $t_0$, and the $\pi$ pulse and spin readout are applied at $t_{\pi }$ and $t_R$, respectively, such that $t_R-t_{\pi }=t_{\pi }-t_0$. $t_c$ follows the probability distribution of the scattered pulse.

Figure 4

Choi-Jamiolkowski fidelities of the photon-to-spin state transfer with and without filtering as a function of the bandwidth of the input field ${\sigma }_o$. Solid lines correspond to theoretical values from Eq. (44). Symbols are simulated results. (a) Varying spin dephasing time $T_2^{*}$. All other errors are ignored, i.e., ${\gamma }_d=0, \varepsilon =0, {\sigma }_e=0, \mathrm{\Gamma }/\mathrm{\Delta }\approx 0$, and $\gamma =0$. (b) Varying pure dephasing rate ${\gamma }_d$ with $T_2^{*}\mathrm{\Gamma }=500$. $\varepsilon =0, {\sigma }_e=0, \mathrm{\Gamma }/\mathrm{\Delta }\approx 0$, and $\gamma =0$.

Figure 5

Choi-Jamiolkowski fidelities with and without filtering as a function of the dephasing rate ${\gamma }_d$ or equivalently the HOM indistinguishability $I=\mathrm{\Gamma }/(\mathrm{\Gamma }+2{\gamma }_d)$ for various spin dephasing times $T_2^{*}$ assuming optimal bandwidth of the input field. Solid lines correspond to the analytical result in Eq. (44). Symbols are simulated results. All other errors are neglected, i.e., $\varepsilon =0, {\sigma }_e=0, \mathrm{\Gamma }/\mathrm{\Delta }\approx 0$, and $\gamma =0$.

Figure 6

Comparison of average fidelities between QD (black) and Rb-atom systems (red) as a function of the input pulse duration $T_{\text{pulse}}$. Symbols denote numerical results. The full lines show the analytical results for the QDs and a simple fit for the Rb data. Dashed lines indicate the maximum achievable fidelity for the QD system predicted by Eq. (44). The parameters of the simulation are provided in the main text.