Experimental entanglement swapping through single-photon $χ^{(2)}$ nonlinearity

Abstract

In photonic quantum information processing, quantum operations using nonlinear photon-photon interactions are vital for implementing two-qubit gates and enabling faithful entanglement swapping. However, due to the weak interaction between single photons, the all-photonic realization of such quantum operations has remained out of reach so far. Herein, we demonstrate an entanglement swapping using sum-frequency generation between single photons in a $χ^{(2)}$-nonlinear optical waveguide. We show that a high signal-to-noise ratio~(SNR), stable sum-frequency-generation-based entanglement heralder with an ultralow-dark-count superconducting single-photon detector can satisfy the unprecedented SNR requirement indispensable for the swapping protocol. Furthermore, the system clock is enhanced by utilizing ultrafast telecom entangled photon-pair sources that operate in the GHz range. Our results confirm a lower bound 0.770(76) for the swapped state's fidelity, surpassing the classical limit of 0.5 successfully. Our findings highlight the strong potential of broadband all-single-photonic nonlinear interactions for further sophistication in long-distance quantum communication and photonic quantum computation.

Figures (11)

• Figure 1: SFG-BSA and SFG-based entanglement swapping.a, Schematic of the SFG-BSA, showing the operation for two $H$-polarized input photons in mode $a$ and $b$, which are combined into a single spatial mode by dichroic mirror 1 (DM1). They transmit through a polarization beamsplitter (PBS). Then, they flip to $V$ polarization by half waveplate 1 (HWP1). At the PPLN/W, the $V$-polarized photons in mode $a$ and $b$ are converted to a $V$-polarized single photon in mode $c$ via the SFG process. Finally, the SFG photon is extracted by DM2, and its polarization is flipped back to $H$-polarization by HWP2. b, Schematic of the SFG-based entanglement swapping. Detection of the $D$-/$A$-polarized SFG photon in mode $c$ at 780nm heralds a creation of entanglement between the photons in mode $d$ and $e$.
• Figure 2: Experimental setup for the SFG-based entanglement swapping. Pump pulses centered at 775nm with a 1.0-GHz repetition rate is prepared by second harmonic generation (SHG) of the electro-optic comb centered at 1550nm and used to pump EPS I and II. Each EPS consists of a PPLN/W in a Sagnac interferometer with a polarizing beamsplitter (PBS). The signal and idler photons at telecom wavelengths are divided into different spatial modes according to low pass filters (LPFs). The photon in mode $a$ at 1535nm and the photon in mode $b$ at 1585nm are narrowed by a volume holographic grating (VHG) and band pass filter (Filter I), respectively, and they are fed into the SFG-BSA unit. A flip mirror (not shown) just before the SFG-BSA is used to perform the quantum state tomography (QST) on the input quantum states. The output SFG photon in mode $c$ at 780nm is extracted by a dichroic mirror (DM) and passes through the band pass filter (Filter II) and is diffracted twice by a VHG. The polarization of the SFG photon is projected on the $A$-polarization by means of a quarter waveplate (QWP), half waveplate (HWP), and PBS. The photon-detection signal from the SNSPD (D1) is used as the start signal of a time-to-digital converter (not shown). The photons in mode $d$ and $e$ are diffracted by VHGs. The polarization correlation of the swapped state $\hat{\rho}_{de}$ is evaluated by QWPs, HWPs, and fiber-based PBSs (FPBSs) followed by SNSPDs (D2-D5).
• Figure 3: Experimental results for the SFG-based quantum teleportation.a, Density matrix of the $A$-polarized input state. The left (right) of each plot shows the real (imaginary) part of the density matrix, respectively. b, Density matrix of the entangled state. c, Density matrix of the teleported state. d, Raw counts of the teleported photons for the $A$-polarized input light. The measurement time was 13h for each basis state. Here, $R$ and $L$ represent right and left circular polarizations, respectively. The error bars were calculated assuming the Poisson statistics.
• Figure 4: Experimental results for the SFG-based entanglement swapping.a, b, Density matrices of the input states from EPS I and II, respectively. c, Two-fold coincidence counts between D1 and D2. We employed a 448-ps coincidence window corresponding to seven bins around the signal peak. d, Three-fold coincidence counts among D1, D2, and D4. The center bin corresponds to the signal event. The waveplates were set so that D2 and D4 detect $V$-polarized portions of photons $d$ and $e$, respectively. The measurement time was 226h. e, f, Raw detection counts of the swapped state for each basis state. The error bars were calculated assuming the Poisson statistics.
• Figure S1: Realistic model of SFG-based entanglement swapping. Each EPS consists of two photon pair sources. The polarization correlation measurements on the swapped state are performed by the beamsplitters in the polarization DOF followed by photon detections using threshold detectors.