Passive quantum interconnects: multiplexed remote entanglement generation with cavity-assisted photon scattering

Abstract

We propose a time- and wavelength-multiplexed remote atom-atom entanglement generation protocol based on cavity-assisted photon scattering (CAPS). This is designed to achieve a high rate and high fidelity with robustness to operational imperfections, parameter fluctuations, and auxiliary time costs, such as percent-level photon impurity, timing and cavity parameter jitter, and atom shuttling time costs. We benchmark this protocol using comprehensive analytical and numerical modeling of the atom-cavity dynamics, including state-dependent pulse delay effects, photon temporal impurity, atom-cavity system parameter fluctuations, and crosstalk among atoms through a shared cavity mode. With realistic atom-cavity system performance, we predict $2\times 10^{5}\,\mathrm{s}^{-1}$ successful atom-atom Bell pair generation even without in-cavity qubit reset, substantially enhanced from two-photon interference based protocols, at a predicted Bell pair fidelity of 0.999.

Figures (9)

• Figure 1: High-fidelity CAPS gate. (a) CAPS protocol. A $\ket{1}_a \leftrightarrow \ket{e}_a$ transition of a three-level atom is resonantly coupled to a one-sided optical cavity with coupling rate $g$. The cavity interfaces with the propagating mode at rate $\kappa_\text{ex}$ with internal loss at rate $\kappa_\text{in}$, while the decay rate of the excited state of the atom $\ket{e}_a$ is $\gamma$. An incoming polarization-encoded photonic qubit (top) is split at a first polarizing beamsplitter (PBS): the initially $V$-polarized component is routed to a one-sided cavity through a quater-wave plate (QWP), reflected off from the cavity and back to the device towards the output port (dotted arrows), while the $H$-polarized component first transmits through the PBS, QWP and a mirror, before reflected from the PBS to be recombined with the other polarization mode (dashed arrows). Overall, this protocol implements a $CZ$ gate between the atomic qubit (encoded in $\ket{0}_a, \ket{1}_a$ basis) and a photonic qubit Duan2004. (b) High-fidelity CAPS gate implemented with a modified optical layout (green rectangle). A controllable photon loss is induced for the initially $H$-polarized mode by a half-wave plate (HWP); a single-photon detector (SPD) heralds gate failure without disturbing the atomic qubit (see text). The calibrated path delay $\tau_\text{m}$ is introduced to cancel the effect of pulse delay arising from the cavity dispersion. (c) Cavity reflectivity $|r_j(\Delta)|^2$ as a function of the detuning $\Delta/\gamma$ for atomic states $\ket{j}_a=\ket{0}_a$ (blue) and $\ket{1}_a$ (green) with an optimized cavity-QED system that satisfies Eqs. (\ref{['eq:kappa_ex_opt']},\ref{['eq:condition_for_kappa_in_gamma']}) with $C_\text{in} = 100$. Both reflectivities match at $\Delta = 0$ as $(r^\text{opt})^2$ (dashed line). (d) Phase shift upon cavity reflection, $\arg(r_j(\Delta))$. At $\Delta=0$, the phase difference is exactly $\pi$, and both slopes match as $\gamma\tau_\text{m}$ (dashed lines).
• Figure 2: Remote entanglement generation with CAPS gates. (a) Schematic of the CAPS-based remote entanglement generation with cavity-QED-based photon source. An atom-cavity system provides a single photon to be routed to other cavities for mediating atom-atom entanglement. The atom coupled to the source cavity has three levels, $\ket{u}_a, \ket{e}_a$ and $\ket{g}_a$, where excitation laser is used to excite to $\ket{e}_a$ from which the atom decays to $\ket{u}_a$, or $\ket{g}_a$, with branching ratio $p_\mathrm{br}$ where $p_\mathrm{br}>0$ results in reexicitation-induced impurity of the photon. (b) Autocorrelation function of the emitted photon, where the parameters for the source system are $C_\text{in} = 10$ and $p_\text{br} = 0.5$, and the Rabi frequency is set to generate the Gaussian wavepacket photon with $\sigma_t = 1/\gamma$. The dashed line is a guide to the eye to highlight the small tail at the top right region. (c) Two primary eigenmodes $v_1(t),v_2(t)$ with the corresponding eigenvalues $\lambda_1 = 0.68, \lambda_2 = 0.025~(P_\text{gen}=\sum_k \lambda_k = 0.72)$. The first mode closely matches the desired Gaussian function (dashed line), while the second exhibits a significant deviation. (d) Success probability of the remote entanglement generation based on sequential CAPS gates incorporating the source imperfection, where $(g,\gamma, \kappa_\text{ex}, \kappa_\text{in})$ characterize three cavity-QED systems with $C_\text{in} = 100$. The dotted lines represent the analytical upper bound $\bar{P}_\text{gen} P_\text{CAPS}$. (e) Infidelity of the generated Bell pairs. Larger source imperfection, characterized by $p_\text{br}$, degrades generated Bell states; increasing $\sigma_t$ suppresses the infidelity below $10^{-4}$ even for high $p_\mathrm{br}$, leading to a tradeoff between fidelity and success rate $\propto P_\mathrm{cc}/\sigma_t$.
• Figure 3: Performance of the hybrid emission-CAPS networking. (a) Schematic of the configuration consisting of the atom-photon entanglement generation and the memory loading. (b, c) Success probability and infidelity of the hybrid networking incorporating the imperfection of the initial atom-photon entanglement generation process. The system parameters are the same as Figs. \ref{['fig2']}(d, e), leading to the upper bound $\bar{P}_\text{gen}^{\prime}$ of the atom-photon entanglement generation probability obtained from \ref{['eq:P_gen^mux']} by replacing $(g,\kappa,\kappa_\text{ex})$ with $(2g,2\kappa,2\kappa_\text{ex})$, respectively. The dashed lines show the performance of photon-interference-based networking for reference, obtained using the same atom-cavity systems to generate the atom-photon entanglement. In panel (b), the dotted lines show the upper bound of the success probability $P_\mathrm{gen}^\prime P_\mathrm{CAPS}$.
• Figure 4: Multiplexed CAPS operation. (a) Schematic of the time-multiplexed operation. For an efficient use of the channel, a large number of atoms (atom number $N_a$) are shuttled to the cavity in parallel, followed by the application of hiding beams to all but one atom that performs a CAPS gate with an incoming photon with temporal width $\sigma_t$. After the time window $5\sigma_t$ for the first photon arrival, the hiding beam pattern is switched such that another atom can then interact with the next incoming photon. Once all atoms interact with their respective photon, the atom array is transported out while the new array is brought into the cavity mode for the next batch of operation. This operation is highly efficient for larger $N_a$, while the network rate saturates for $\tau_s \ll 5\sigma_t N_a$ [see panel (c)]. (b) Crosstalk-induced infidelity of CAPS gates, evaluated by using \ref{['app_eq:def_of_conditional_infid_of_N_a_atoms']} for $N_a=200$ (solid lines), which agrees well with the approximate expression given by \ref{['eq:infidelity_vs_detuning']} (dashed lines). For high internal cooperativity $C_\mathrm{in} = 100$, choosing $\Delta_a/(N_a\gamma) > 2\times10^2$ keeps the crosstalk error below $10^{-3}$. (c) Remote entanglement generation rate \ref{['eq:overall_mux_rate']} with time-multiplexed hybrid emission-CAPS networking (Fig. \ref{['fig3']}) for varying $N_a$. We safely set $\sigma_t = 1/\gamma = \qty{660}{\ns}$ with $\gamma/2\pi = \qty{0.24}{\MHz}$, which, as an example, corresponds to the $^{3}\mathrm{D}_1$ state of $^{171}\mathrm{Yb}$ atoms with remote Bell pair infidelity below $10^{-3}$. The dashed lines represent the upper bound $\bar{R}_\mathrm{mux}$.
• Figure 5: Wavelength-multiplexed CAPS operations. (a) Schematic of wavelength-multiplexed cavity-QED systems where each atom in $\ket{1}_a$ couples to the different cavity modes by tuning the resonant frequency of the atoms via ac Stark shift. (b) Cavity reflection spectra evaluated by the transfer matrix method. $N_a = 10$ atoms are assigned to $N_\text{ch} = 10$ channels respectively, and we plot the reflectance for the cases with all the atoms prepared in $\ket{0}_a$ (blue line) and $\ket{1}_a$ (green line). The plot on top provides a magnified view of one representative mode. (c) Crosstalk effect for the wavelength-multiplexed CAPS gates. Considering the position dependence of the coupling strength: $g(x) = g \sin[(n_0+n)\pi x/L_\text{cav}]~(0 \leq x \leq L_\text{cav})$, the atoms are randomly placed at one of the antinodes within the region $0.45L_\text{cav} \leq x \leq 0.55L_\text{cav}$. We evaluate 50 trials with different random configurations, where the external coupling rate $\kappa_\text{ex}$ is optimized for the unshifted target atom, and the plotted infidelity is averaged over atoms coupled to $N_\text{ch}$ distinct modes. Here, we use $^{171}\mathrm{Yb}$ atoms being coupled to the high-finesse nanofiber cavity with the intrinsic finesse $\mathcal{F}_\text{int} = 2000$, on the $^3\mathrm{P}_0$--$^3\mathrm{D}_1$ transition Horikawa2025. The parameters are $\omega_\text{FSR}/2\pi = \qty{2.7}{\GHz}$, $\omega_a/2\pi = \qty{220}{\THz}$, $\gamma/2\pi = \qty{0.24}{\MHz}$, $\sigma_0/A_\text{eff} = 0.10$, and $C_\text{in} = 89$, leading to $L_\text{cav}^\text{opt} = \qty{11}{\cm}$. (d) Time-multiplexed entanglement generation rates with multiple wavelength channels. The $N_a$ atoms are partitioned into $N_\mathrm{ch}$ channels for parallel execution of time-multiplexed entanglement generation for each channel. We assume the same pulse widths and the success probability as the estimation in Fig. \ref{['fig4']}(c) for the hybrid protocol.