The impact of multimode sources on DLCZ type quantum repeaters

TL;DR

This work addresses the problem of achieving high-rate long-distance entanglement with DLCZ-type quantum repeaters when SPDC sources emit multimode states. It develops a detailed multimode SPDC model, derives density-matrix recursion relations for entanglement generation and swapping under pulsed and quasi-continuous driving, and optimizes experimental parameters under peak-power and acceptance-window constraints. The key finding is that multimode structure degrades fidelity, but narrow driving pulses (or small acceptance windows) can preserve high fidelity at practical swap depths, and realistic power limits allow rates close to the single-mode ideal, especially when multiplexing is employed. The results provide actionable design guidance for implementing DLCZ repeaters with SPDC sources and multiplexing, with implications for sub-second entanglement distribution over hundreds to thousands of kilometers in near-future setups.

Abstract

Long distance entanglement generation at a high rate is a major quantum technological goal yet to be fully realized, with the promise of many interesting applications, such as secure quantum computing on remote servers and quantum cryptography. One possible implementation is using a variant of the DLCZ-scheme by combining atomic-ensemble memories and linear optics with spontaneous parametric down conversion (SPDC) sources. As we edge closer to the realization of such a technology, the complete details of the underlying components become crucial. In this paper we consider the impact of the multimode emission from the SPDC source on quantum repeaters based on the DLCZ-scheme. We consider two cases, driving the SPDC using short Gaussian pulses and continuously. For pulsed driving, we find that the use of very narrow laser pulses to drive SPDC source is crucial to obtain high fidelity end-to-end entangled states but this puts demands on the peak intensity. By introducing a maximally allowed laser intensity, we find optimal pulse widths for each swap depth. For continuous driving, we find the temporal acceptance window of clicks relative to the heralding time to be a crucial parameter, and we can similarly optimize the acceptance window for each swap depth. For both cases, we thus identify optimal parameters given experimental limitations and aims. We have thus provided helpful knowledge towards the realization of long distance entanglement generation using the DLCZ-scheme.

Figures (8)

• Figure 1: a) and b) Schematics of the entanglement generation for pulsed driving a) and continuous driving b). The idler photons (blue lines) from both SPDC sources are sent to a central BSM station, whereas the signal photons (red lines) are sent to the respective quantum memory. A detection will herald the entanglement between the light stored in the two QMs. In b) we indicate the post-processing, where a click have been registered at $t_c$, and the acceptance window $T$, indicates, how much of the light associated with that detection will be included later. c) Schematic of an entanglement swap. Two neighboring pairs of entangled QMs have been generated. The photons are read out from the central QMs and sent to a BSM based on photon number resolving (PNR) detectors. The detection of a single photon swaps the entanglement to the outer QMs. d) Schematic of the final readout and post-selection. Light from the four remaining QMs are read out. At both ends, a Pauli operator acts on the output light before being read by PNR detector.
• Figure 2: Fidelity due to the multimode nature. Full lines show the complete model, and dashed lines show the approximated version, from Eq. \ref{['eq:baseFid']}. The horizontal dashed line shows 90% fidelity, which is the target set for later. The lines go in descending order in $n$ when going up the $F$ axis.
• Figure 3: The full lines show the maximal value $P_1$ can attain, if the maximal intensity of the laser is $I_\text{max}=a I_\text{thres}$. The dashed lines show the target $P_1$ for different swap depths using a target fidelity of 90%. With a source limited by a certain value of $a$, the ideal pulse width is found by the crossing of the dashed and full lines. We have used $\eta_d=0.9$ and $\eta_m=0.8$. The full lines go in ascending order in $a$ when going up the $P_{1,\text{max}}$ axis.
• Figure 4: Un-multiplexed rates pr. quantum memory for a) fixed pulse widths $\sigma$ and b) fixed maximally allowed laser intensity, $a = I_\text{max}/I_\text{thres}$. Note that $a=\infty$ in b) corresponds to the $\kappa\sigma=0$ in a). We have used a target fidelity of $90\%$, $\eta_d=0.9$, $\eta_m=0.8$, $c=\unitfrac[2\cdot10^5]{km}{s}$ and $L_\text{att}=\unit[22]{km}$. For a) (b)) the lines go in descending (ascending) order in $\kappa \sigma$ ($a$) when going up the $\tilde{R}$ axis.
• Figure 5: Fidelity and rate for continuously driven SPDC sources. Full (dashed) lines show the fidelity a) and un-multiplexed rate pr. quantum memory b) for different swap depths at different laser intensities (quantified with $x=1$ when the laser at threshold intensity) for $\kappa T=1$ ($\kappa T=5$). The dashed black line in a) shows 90% fidelity, which is used as target fidelity. We have used $\eta_d=0.9$, $\eta_m=0.8$, $c=\unitfrac[2\cdot 10^5]{km}{s}$, $L_\text{att}=\unit[22]{km}$, $\kappa\mathcal{T}=100$ and $L=\unit[500]{km}$. For a) lines go in descending order in $n$. For b) the full (dashed) lines go in order 0, 4, 1, 3 and 2 (0, 1, 4, 2 and 3) at $x^2=10^{-5}$.