Taming Recoil Effect in Cavity-Assisted Quantum Interconnects

TL;DR

The paper addresses recoil-induced motion–qubit coupling that limits high-fidelity remote entanglement generation in cavity-assisted HEG with trapped atoms. It introduces a kick-operator formalism to efficiently quantify motion-induced infidelity for polarization and time-bin photonic encodings, applicable to arbitrary initial motional states and both cavity and free-space emissions. Key insights show that operating in the bad-cavity regime (κ > g) with near-ground-state cooling (n̄ < 1) can suppress infidelity below 1%, and that time-bin synchronization along with detection-time filtering enables high-rate, high-fidelity operation; a driven time-multiplexed scheme demonstrates favorable rate–fidelity tradeoffs. Collectively, the framework provides a practical toolkit for designing fault-tolerant, scalable quantum networks based on trapped-atom qubits, with broad applicability across encoding schemes and network architectures.

Abstract

Photon recoil is one of the fundamental limitations for high-fidelity control of trapped-atom qubits such as neutral atoms and trapped ions. In this work, we derive an analytical model for efficiently evaluating the motion-induced infidelity in remote entanglement generation protocols. Our model is applicable for various photonic qubit encodings such as polarization, time bin, and frequency, and with arbitrary initial motional states, thus providing a crucial theoretical tool for realizing high-fidelity quantum networking. For the case of tweezer-trapped neutral atoms, our results indicate that operating in the bad-cavity regime with cavity decay rate exceeding atom-photon coupling rate, and near-ground-state cooling with motional quanta below 1, are desired to suppress the motion-induced infidelity sufficiently below the 1% level required for efficient quantum networking. Finite temperature effects can be mitigated efficiently by detection time filtering at the moderate cost of success probability and network speed. These results extend the understanding of infidelity sources in remote entanglement generation protocols, establishing a concrete path towards fault-tolerant quantum networking with scalable trapped-atom qubit systems.

Figures (10)

• Figure 1: Motion-photon entanglement in the photon-emission process. We consider a trapped three-level atom, such as one in a harmonic potential, at the antinode of the cavity modes whose wavenumbers are $k_c$. (a) Following the preparation of the atom in $\ket{e}_s$, the atom transitions to the qubit state $\ket{0}_s(\ket{1}_s)$ while generating a $\sigma^{+(-)}$ photon inside the cavity, which leaks through a coupling mirror and passes through the quarter-wave plate. Through this process, the internal, motional, and photonic states become entangled. (b) Stochastic detection times lead to different motional states from time-dependent recoil kicks, resulting in infidelity of the generated entanglement that we model and analyze in detail in this work.
• Figure 2: HEG process with polarization encoding. Alice and Bob generate the spin-photon entanglement, and the photons are sent to the Bell-state measurement (BSM) apparatus consisting of a balanced beam splitter (BS), polarizing beam splitters (PBS), and photon detectors.
• Figure 3: Motion-induced infidelity in the polarization-encoding HEG protocol. (a) Infidelity and (b) success probability of the HEG protocol as a function of detection times $(\tau_H,\tau_V)$, using parameters $(g, \kappa_\mathrm{ex}^\mathrm{opt}, \kappa_{\text{in}},\omega_x) = (5.0, 5.1, 1.0, 0.10)\gamma$, and $(\eta_x, \bar{n}_x) = (0.20, 1.0)$. Here, $p_s(\tau_H, \tau_V) = 4P_D(\tau_H, \tau_V)\Delta \tau^2$ with the time step $\Delta\tau = 0.005/\gamma$. (c) Dependence of the average infidelity on the ratio $\kappa/g$, using $(\kappa_\mathrm{in},\omega_x) = (1, 0.1)\gamma$, and $(\eta_x, \bar{n}_x)=(0.2, 1)$. The infidelity is observed to scale as $(\kappa/g)^{-1}$, as shown by a black dashed line, indicating that $\kappa \gg g$ is required to achieve sub-percent level infidelity. (d) Dependence on the ratio of $\kappa/\omega_x$ at $\kappa/g=10$. The infidelities exhibit different characteristics depending on the values of $g$, transitioning between the motional sideband-resolved regime ($\kappa/\omega_x < 1$), which yields lower infidelity, and the unresolved regime ($\kappa/\omega_x > 1$) with higher errors; see text.
• Figure 4: Mitigating the recoil-induced infidelity. (a) Dependence of the infidelity on the mean phonon number $\bar{n}_x$. Cooling to the near-ground state $\bar{n}_x < 1$ allows suppression of $\epsilon$. The dotted lines represent the averaged infidelity at $\bar{n}_x = 0$. (b) Efficient error suppression by the detection time filtering for finite-temperature atoms. Infidelity $\epsilon$ (black, left axis) and the HEG success probability (blue, right axis) change significantly by detection-time filtering, where the window is centered at the peak of temporal photon pulse (Fig. \ref{['fig:pol_infid_prob_results']}(b)). The parameters are $(g, \kappa_\text{ex}, \kappa_\text{in}, \omega) = (10, 11, 1, 0.1)\gamma$ and $\bar{n}_x = 1$.
• Figure 5: State-dependent emission of time-bin encoded photons. (a) Sequence for generating the entanglement between the spin state and the time-bin photon. (b) State-dependent excitation and free oscillation in the harmonic trap result in detrimental entanglement between the motional state and the time-bin photon, if the time-bin separation $T$ is not exactly at an integer multiple of $2\pi/\omega$, as illustrated with simplified representations of Wigner functions in the laboratory frame.