242 | Nature | Vol 578 | 13 February 2020
Article
nanowire single photon detectors. A successful Bell-state measurement
result projects, in a heralded way, the two atomic ensembles into a
maximally entangled state:
|⟩Ψ =1
2±TPIA(|↑⟩|↓⟩±BA|↓⟩|↑⟩B) (1)with a internal sign determined by the measurement outcome of the
Bell-state measurement.
The strong polarization dependence of DFG in the PPLN-WG makes
it difficult to perform QFC directly for a polarization encoded photon.
In this experiment, we transform the polarization encoding into time-
bin encoding^39 and let the two photonic modes pass through the QFC
module in sequence with the same polarization. As shown in Fig. 4b,
the transformation is realized through an AMZI and a fast Pockels cell
which erases the polarization distinguishability. For the time-bin encod-
ing, it is crucial that the two modes have a stable relative phase shift,
which is realized via active stabilization of the two AMZIs. Moreover, the
transformation into time-bin encoding offers an additional advantage
of robustness in long-distance transmission in fibres.
Before long-fibre experiments, we characterize the atom–atom
entanglement locally without QFC. For the measurement of the atomic
qubits, we first apply Raman rotations^40 , then we retrieve the excita-
tions into read-out photons and measure the polarization^31. Measure-
ment in an arbitrary basis is realized by configuring the Raman pulses.
Figure 5a shows the measured fidelity averaged for |Ψ±⟩ as a function
of χ. At χ ≈ 2%, we get ℱ = 0.798 ± 0.063 for |Ψ+⟩ and 0.829 ± 0.036 for
|Ψ−⟩, respectively, which are in good agreement with the theoretical
estimation. Furthermore, the fidelity is almost independent of χ, after
subtracting the accidental coincidences that are mainly due to high-
order excitations in the Raman scattering process.
The field-deployed long fibre (L = 22 km) induces 8 dB of attenuation.
Besides, the long fibre leads to random rotations of polarization. To
optimize the indistinguishability, we apply polarization filtering for
the photons after long-fibre transmission before the Bell-state meas-
urement. In addition, to get a high filtering efficiency, we perform
active polarization compensation by replacing the manual polarization
controllers in Fig. 1 with electric polarization controllers and minimiz-
ing the reflections of the filtering polarization beamsplitters. We get
an average efficiency of 98%, as shown in Fig. 4c. To reduce the back-
ground noise in the fibre channels, we carefully cover all the fusion
points and get an average background noise of about 280 Hz (including
dark counts of the detector). In the long-fibre case, to increase the
count rate, we set the excitation probability to χ = 0.038 and perform
entanglement verification in a delayed-choice fashion^41. The measured
visibility in the |↑⟩/|↓⟩ basis is V 1 = 0.684 ± 0.075 for |Ψ+⟩ and
V 1 = 0.635 ± 0.075 for |Ψ−⟩. Adjusting the Raman pulse delay δt, we could
observe a sinusoidal oscillation in the |↑⟩ ± |↓⟩ basis as shown in Fig. 5b
with a visibility of V 2 = 0.574 ± 0.064 for |Ψ+⟩ and V 2 = 0.647 ± 0.066 for
|Ψ−⟩. By assuming a similar visibility in the |↑⟩ ± i|↓⟩ basis, the entangle-
ment fidelity can be estimated as^42 F≃ 41 (1++VV 12 2)=0.7 08 ±0.0 37
for |Ψ+⟩, and 0.732 ± 0.038 for |Ψ−⟩, which greatly exceed the bound of
ℱ > 0.5 required to witness entanglement for a Bell state. The measured
heralding rate is Pher = 1.46 × 10−6, half of which is due to double-excita-
tion events from a single node. Thus the entangling probability is esti-
mated to be Pent ≈ Pher/2 = 0.73 × 10−6.Entanglement over 50 km of coiled fibres
The entangling probability in the TPI experiment^18 is low since it scales
as χ^2 and ηL^2 /2, where ηL/2 is the overall optical efficiency from one node0 50 100 150 200 250 3000.00.20.40.60102030Pump power (mW)Kconv SNR–15 –10 –5 0 5 10 150.00.51.0W (μs)(2)g
(W)abFig. 2 | Performance of the telecommunications interface. a, The conversion
efficiency ηconv and the signal-to-noise ratio (SNR) vary as a function of pump
laser power. Blue dots refer to the overall conversion efficiency of the PPLN-WG
chip, and red triangles refer to the signal-to-noise ratio at probability χ = 0.015.
b, Measurement of the second-order correlation function g(2) (results of the
Hanbury–Brown–Twiss experiment) with (red) and without (blue) QFC at
χ = 0.057. The write-out photons are only measured if the corresponding read-
out photon is detected. The error bars represent one standard deviation.
ab
Re(U) Re(U)
0.50.250.50.25Im(U)
0.10.0–0.1Fig. 3 | Tomography of the atom–photon entanglement. a, b, The
reconstructed density matrix between the write-out photon and the atomic
spin-wave in node A (a) and in node B (b). In each element of the matrix, the
height of the bar represents its real part, Re(ρ), and the colour represents its
imaginary part, Im(ρ). The transparent bars indicate the ideal density matrix of
the maximally entangled state.