Nature - USA (2020-02-13)

244 | Nature | Vol 578 | 13 February 2020

Article

Even though the fibre distance of the SPI experiment is much longer
than in the TPI experiment, the SPI scheme offers a much higher prob-
ability of entanglement creation, because only a single photon passing
through half of the whole link is detected. In contrast, the TPI scheme
requires the detection of two photons passing through the whole link.
For the extension to physically separated nodes over long distances, the
TPI scheme is straightforward, merely requiring that photons be indis-
tinguishable. However, the extension of the SPI experiment requires
more effort because the scheme is phase-sensitive. According to our
analysis in the Supplementary Information, the main difficulty is to
achieve phase correlation of remote independent control lasers. We
have performed a preliminary test with two lasers locked indepen-
dently to two ultrastable cavities, which shows that phase correlation
can be built and stable for a duration that is long enough to generate
remote entanglement (see Supplementary Information for details).
Thus it is also feasible to extend our SPI experiment to long-distance
separated nodes.
The quantum link efficiency^12 ηlink, defined as the ratio of memory
lifetime over entanglement generation time, is also an important figure
of merit for two-node experiments. In our current work, decoherence

due to atom motions results in a memory lifetime of about 70 μs, which

is much smaller than the entanglement generation time. According

to our previous work on a very similar setup^44 , applying a three-

dimensional optical lattice can improve the lifetime to the sub-second

0 2 4 6 8 10

0.00

0.25

0.50

0.75

1.00

F (%)

Fidelity

0 2 4 6

0.00

0.25

0.50

0.75

1.00

Gt(μs)

Normalized coincidences

a

b

| Ψ+〉

| Ψ–〉

Fig. 5 | Characterization of the remote entanglement via TPI. a, Average
fidelity of the remote entanglement |Ψ±⟩ generated locally as a function of χ. Blue
squares refer to the measurement result. Red triangles show the corrected
results through deduction of accidental coincidences (see Supplementary
Information). The error bars represent one standard deviation. Pink shading
indicates where fidelity is not sufficient to claim entanglement. b, Coincidences
measured in the |±⟩ = |↑⟩ ± |↓⟩ basis for the two atomic qubits, normalized by the
total coincidence of all combinations. The Raman pulse in node A is applied
slightly later than in node B with an offset of δt, which induces a linearly changing
phase in Ψ± and results in the observed oscillations. Parallel correlations (|+⟩|+⟩ or
|−⟩|−⟩) of |Ψ+⟩ (blue squares) and |Ψ−⟩ (red triangles) are shown. Solid red and
dashed blue lines correspond to the fitting results. The 5.4-s oscillation period
agrees with Zeeman splitting between |↑⟩ and |↓⟩. This plot is based on 2.9 × 10^4
heralding events during a total measurement time of 487 hours over a period of
30 days. The error bars represent one standard deviation.

0 π 2 π 3 π 4 π

0.0

0.2

0.4

0.6

0.8

1.0

Relative T

Normalized count

0 π 2 π 3 π 4 π

0.0

0.2

0.4

0.6

0.8

1.0

Relative T

Normalized count

a

b

Da

Db

Fig. 6 | Characterization of the remote entanglement via SPI. When the

atomic modes are retrieved as optical modes for interference, the photon count

in one output mode of the fibre beamsplitter oscillates as a function of the

relative phase θ between the two optical modes, normalized by the total count

of two output modes. Detector Da heralded events are shown in a; detector Db

heralded events are shown in b. Blue squares, red triangles and green dots refer

to L = 10 m, 10 km and 50 km separately. Sinusoids with corresponding colour

(solid, dashed and dotted) show the fitting results. The 50-km result is based on

1 .7 × 10^5 heralding events during a total measurement time of 6 hours over a

period of 2 days. The error bars represent one standard deviation.

Table 1 | Comparison of two-node experiments

Experiment TPI

(this work)

SPI

(this work)

NV

(2015; ref.^10 )

Physical separation 0.6 m 0.6 m 1.3 km

Overall fibre length, L 22 km 50 km 1.7 km

Entanglement probability, Pent 0.73 × 10−6 3.85 × 10−4 6.4 × 10−9

Entanglement quality ℱ = 0.720 ± 0.027 C=0.378±0.007ℱ= 0.92 ± 0.03

Entanglement creation

time, Tent

150 s 0.65 s 1.3 × 10^3 s

Quantum link efficiency, ηlink

(ref.^12 )

1.45 × 10−3 0.34 4.6 × 10−4

Assumed memory lifetime, τm0.22 s (ref.^44 ) 0.22 s (ref.^44 ) 0.6 s (refs.^12 ,^51 )

In the long-fibre case, the propagation delay results in a maximal repetition rate of Rrep = C/L,

where C ≈ 2 × 10^8  m s−1 is the speed of light in the fibre. Thus the heralded entanglement

creation time is estimated as Tent = (RrepPent)−1. For the estimation of ηlink = τm/Tent, we make use of

state-of-the-art lifetime results, as listed in the last row. We chose the 1.3-km nitrogen vacancy

(NV) experiment^10 for comparison, because it is the only previous two-node experiment that

has a fibre length in the kilometre regime.