# Realization of a crosstalk-free multi-ion node for long-distance quantum
networking

P.-C. Lai  These authors contributed equally to this work  Center for Quantum
Information, Institute for Interdisciplinary Information Sciences, Tsinghua
University, Beijing 100084, PR China  Y. Wang  These authors contributed
equally to this work  Center for Quantum Information, Institute for
Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084,
PR China  J.-X. Shi  These authors contributed equally to this work  Center
for Quantum Information, Institute for Interdisciplinary Information Sciences,
Tsinghua University, Beijing 100084, PR China  Z.-B. Cui  Center for Quantum
Information, Institute for Interdisciplinary Information Sciences, Tsinghua
University, Beijing 100084, PR China  Z.-Q. Wang  Center for Quantum
Information, Institute for Interdisciplinary Information Sciences, Tsinghua
University, Beijing 100084, PR China  S. Zhang  Center for Quantum
Information, Institute for Interdisciplinary Information Sciences, Tsinghua
University, Beijing 100084, PR China  P.-Y. Liu  Center for Quantum
Information, Institute for Interdisciplinary Information Sciences, Tsinghua
University, Beijing 100084, PR China  Z.-C. Tian  Center for Quantum
Information, Institute for Interdisciplinary Information Sciences, Tsinghua
University, Beijing 100084, PR China  Y.-D. Sun  Center for Quantum
Information, Institute for Interdisciplinary Information Sciences, Tsinghua
University, Beijing 100084, PR China  X.-Y. Chang  Center for Quantum
Information, Institute for Interdisciplinary Information Sciences, Tsinghua
University, Beijing 100084, PR China  B.-X. Qi  Center for Quantum
Information, Institute for Interdisciplinary Information Sciences, Tsinghua
University, Beijing 100084, PR China  Y.-Y. Huang  Center for Quantum
Information, Institute for Interdisciplinary Information Sciences, Tsinghua
University, Beijing 100084, PR China  Z.-C. Zhou  Center for Quantum
Information, Institute for Interdisciplinary Information Sciences, Tsinghua
University, Beijing 100084, PR China  Hefei National Laboratory, Hefei 230088,
PR China  Y.-K. Wu  Center for Quantum Information, Institute for
Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084,
PR China  Hefei National Laboratory, Hefei 230088, PR China  Y. Xu  Center for
Quantum Information, Institute for Interdisciplinary Information Sciences,
Tsinghua University, Beijing 100084, PR China  Hefei National Laboratory,
Hefei 230088, PR China  Y.-F. Pu<EMAIL_ADDRESS>Center for Quantum
Information, Institute for Interdisciplinary Information Sciences, Tsinghua
University, Beijing 100084, PR China  Hefei National Laboratory, Hefei 230088,
PR China  L.-M. Duan<EMAIL_ADDRESS>Center for Quantum Information,
Institute for Interdisciplinary Information Sciences, Tsinghua University,
Beijing 100084, PR China  Hefei National Laboratory, Hefei 230088, PR China

###### Abstract

Trapped atomic ions constitute one of the leading physical platforms for
building the quantum repeater nodes to realize large-scale quantum networks.
In a long-distance trapped-ion quantum network, it is essential to have
crosstalk-free dual-type qubits: one type, called the communication qubit, to
establish entangling interface with telecom photons; and the other type,
called the memory qubit, to store quantum information immune from photon
scattering under entangling attempts. Here, we report the first experimental
implementation of a telecom-compatible and crosstalk-free quantum network node
based on two trapped 40Ca+ ions. The memory qubit is encoded on a long-lived
metastable level to avoid crosstalk with the communication qubit encoded in
another subspace of the same ion species, and a quantum wavelength conversion
module is employed to generate ion-photon entanglement over a $12\,$km fiber
in a heralded style. Our work therefore constitutes an important step towards
the realization of quantum repeaters and long-distance quantum networks.

A future large-scale quantum network can link different functional nodes
together via photonic channels kimble ; weiner ; ACM ; BDCZ ; DLCZ ; rmp_gisin
; rmp_polzik , and enable numerous applications such as distributed quantum
computing distributed , networked quantum sensing oxford_clock ; ye_and_lukin
; repeater_telescope , and global quantum communication oxford_qkd ;
weifurner_qkd ; BDCZ ; DLCZ  with unprecedented performances. Recent advances
on quantum networks have been achieved on various physical systems
oxford_clock ; oxford_qkd ; weifurner_qkd ; oxford sr ; monroe_barium ;
oxford_sr_and_ca ; 230m ; lukin_siv ; hanson_distillation ; rempe ; 2021nature
; bao3nodes . Among all these different physical platforms, trapped atomic
ions constitute one of the most promising systems to build quantum repeater
nodes for scalable quantum networks, as the highest fidelities in quantum
logic operations and state detection oxford_gate ; quantiuum  have been
demonstrated on this platform, which are important for the entanglement
swapping lanyon_connection ; Eschner ; lattice , distillation lukin_siv ;
hanson_distillation , and error correction quantiuum  operations required in a
large-scale quantum network. Other advantages include the long coherence time
at the scale of a hour 1hour , and the record-high fidelity and rate in
entangling two network nodes oxford sr ; monroe_barium .

To enable a long-distance trapped-ion quantum network, crosstalk-free dual-
type qubits on each node and the interface of the node with the telecom
photons are two essential requirements duan pra ; duan arxiv ; duan rmp . For
dual-type qubits on each node, it is required that the memory qubits are
employed to store quantum information for later computational tasks or
establishment of remote entanglement, while the communication qubits are
interfaced with photons to link different network nodes or used occasionally
for sympathetic cooling. The memory qubits and the communication qubits are
required to be spectrally separated so that the scattered photons during
cooling, pumping, detection, and entangling attempts on the communication
qubit have no detrimental influence on the state stored in the memory qubits.
The memory and the communication qubits can be implemented either by employing
two different ion isotopes oxford_sr_and_ca ; monroe_barium , or by the same
ion species but exploiting a dual-type encoding with two sets of spectrally
separated qubit states yanghx ; huangyy ; omg . Another requisite for a long-
distance quantum network is that the network node should be interfaced with
photons in the telecom band to minimize the transmission loss in optical
fibers. This requirement has been fulfilled either by employing atomic
transitions at the telecom band erbium ; thompson erbium ; kuzmich telecom ;
changwei , or by converting the emitted photon to the telecom wavelength on an
additional module lanyon_connection ; weifurner_qkd ; keller ; ikuta ;
2021nature . Implementation of the above two essential requirements for a
long-distance quantum network together in a single node is experimentally very
challenging and has not been achieved so far in a trapped-ion system.

In this work, we report the first experimental realization of a crosstalk-free
and telecom-compatible quantum network node based on two 40Ca+ ions in a dual-
type style. The memory qubit is encoded on a metastable level which is
unaffected by the photon-scattering operations on the communication qubit due
to the large frequency difference. The two types of qubits can be coherently
converted back and forth by a Raman and a quadrupole transition. A quantum
frequency conversion module is employed to convert the near-infrared photon
emitted from the ion to the telecom band, and the heralded ion-photon
entanglement has been demonstrated over different fiber lengths at $3\,$m,
$1\,$km, and $12\,$km. We characterize the performance of the memory qubit
with the measured coherence time about $323(19)\,$ms and confirm that quantum
information is protected in the memory qubit under repeated entangling
attempts on the neighboring communication qubits until a successful record of
remote ion-photon entanglement over the $12\,$km fiber. With all these
achievements, we implement a promising quantum node based on trapped ions
which fulfils the essential requirements for a long-distance quantum network.

Figure 1: Experimental setup and crosstalk-free qubit subspaces. (A) The two-
ion quantum network node consists of a communication qubit and a memory qubit
encoded in different subspaces of 40Ca+ ion. The emitted single photons from
the communication qubit at $866\,\text{nm}$ are collected with a high-NA
objective and are further converted to $1558\,\text{nm}$ for transmission in a
long fiber. The $729\,$nm beam is individually addressed. All other beams are
global. (B) Two spectrally-separated subspaces for the communication qubit and
the memory qubit. The communication qubit subspace is a closed three-level
cycle, and the memory qubit subspace is a metastable level which is isolated
from all the dissipative operations on the communication qubit, thus is
suitable for storing quantum information. Bridges connecting these two
subspaces include $850\,\text{nm}/854\,\text{nm}$ Raman and $729\,\text{nm}$
quadruple transitions. Ion-photon entanglement is excited by a
$397\,\text{nm}$ picosecond pulse.
Figure 2: Connecting communication and memory qubit subspaces through Raman
transitions. (A) After a photon is detected, we use three successive Raman
transitions to combine two energy levels related to $|\sigma^{\pm}\rangle$
photon emission and map the ion state from the communication qubit subspace to
memory qubit subspace for further state manipulation and detection. (B) We
measure the probability of unwanted excitation to the upper state during the
Raman process with variable detunings at $350\,$MHz, $1.5\,$GHz and $18\,$GHz.
We prepare the ion to $|\uparrow_{c}\rangle$ and perform a Raman pulse driving
the transition $|\uparrow_{c}\rangle\leftrightarrow|0\rangle$ for different
time and detuning. The chance of off-resonant excitation to the upper state is
$12(1)\%$, $2.7(3)\%$ and $0.7(2)\%$ for detunings at $350\,$MHz, $1.5\,$GHz
and $18\,$GHz every $\pi$-pulse. (C) We measure the state transfer fidelity
between the memory qubit subspace bases
$|\uparrow_{c}\rangle/|\downarrow_{c}\rangle$ and the communication qubit
subspace bases $|0\rangle/|1\rangle$, with different rounds of $\pi$ pulses.
The fitted $\pi$-pulse fidelity is $99.2(2)\%$ averaged on six mutually
unbiased states. (D) Rabi oscillation driven by a
$866\,\text{nm}/866\,\text{nm}$ Raman transition. The initial
$\frac{1}{2}|1\rangle+\frac{\sqrt{3}}{2}|2\rangle$ state can be combined to
$|1\rangle$ with a fidelity of $96(2)\%$ by a $\frac{2}{3}\pi$-pulse.

The quantum network node is based on two 40Ca+ ions in a segmented blade trap,
with trapping frequencies at
$\text{(}\omega_{x},\omega_{y},\omega_{z}\text{)}=2\pi\times\text{(}1.65,1.55,0.5\text{)}\,$MHz
in three dimensions and the separation between two ions at $9\,\mu$m. The
magnetic field is along the axial direction of the trap and set to $4.2\,$G in
the experiment (see Fig. 1A). Here the communication qubit stays in a closed
$3$-level subspace containing $|S_{1/2}\rangle$, $|D_{3/2}\rangle$, and
$|P_{1/2}\rangle$ (see Fig. 1B), so that all the dissipative operations on the
communication qubit including cooling, optical pumping, fluorescence detection
and photon excitation can be carried out by lasers at $397\,$nm and $866\,$nm
in this subspace, and the fluorescent photons scattered from the communication
qubit are also at these two wavelengths (or at $732\,$nm with a very rare
chance, see Fig. S1 for the full energy levels and transitions). On the other
hand, the metastable level $|D_{5/2}\rangle$ can only be driven by two
transitions at $854\,$nm or $729\,$nm, which are perfectly isolated in
frequency from the lasers or scattered photons for the operations on the
communication qubit. In addition, the communication qubit subspace is closed
under the driving with $397\,$nm and $866\,$nm laser beams, so there is no
need of inter-subspace repumping during the operations. Therefore we use
$|D_{5/2}\rangle$ subspace to carry the memory qubit, which can store quantum
information without being influenced by the operations on the communication
qubit.

There are two methods to connect these two qubit subspaces, as shown in Fig.
1B. The first is the standard quadrupole transition at $729\,$nm which
connects the $|S_{1/2}\rangle$ level in the communication qubit subspace and
$|D_{5/2}\rangle$ level in the memory qubit subspace. The $729\,$nm beam is
focused on each ion with a Gaussian radius of $2\,\mu$m via an addressing
system based on two crossed acoustic optical deflectors (AODs) and an
objective with NA (numerical aperture) $=0.24$. The typical fidelity of a
$729\,$nm $\pi$-pulse is about $99\%$ in this experiment.

Figure 3: The experimental protocol and heralded ion-photon entanglement at
different fiber lengths. (A) The protocol used in this experiment. (B-C)
Reconstructed density matrix for the ion-photon entangled state with fiber
lengths of $3\,\text{m}/1\,\text{km}$ and
$2\tau=40\,\text{ms}/200\,\text{ms}$. The entanglement fidelity is $93.8(3)\%$
and $91.2(7)\%$ in each case. (D) The performance of frequency conversion. We
use laser power at about $1.1\,$Watt (dashed line) for each polarization. (E)
Measure the coherence of the ion-photon entangled state over $12\,$km fiber by
projecting photons at $|H\rangle+|V\rangle$ (blue circle) or
$|H\rangle+i|V\rangle$ bases (red square) and measuring the visibility of
sinusoidal oscillations with different phases of $729\,\text{nm}$ rotations.

The second bridge is a Raman transition by two lasers at $850\,$nm and
$854\,$nm, which connects $|D_{3/2}\rangle$ level and $|D_{5/2}\rangle$ level
in different subspaces, as shown in Fig. 2A. The two beams co-propagate along
the magnetic field axis in complementary circular polarizations, which drive
Raman transitions between $|D_{3/2},m\rangle$ and $|D_{5/2},m-2\rangle$
($m=-1/2,+1/2,+3/2$). Here we set the Raman detuning $\Delta$ to $18\,$GHz
with the chance of unwanted excitation to the intermediate state
$|P_{3/2}\rangle$ at about $0.7(2)\%$ per $\pi$-pulse, as illustrated in Fig.
2B. We demonstrate the coherent state transfer between a memory qubit subspace
encoding on
$|\uparrow_{c}\rangle/|\downarrow_{c}\rangle\equiv|D_{5/2},m=-5/2\rangle/|D_{5/2},m=-3/2\rangle$
and a communication qubit subspace encoding on
$|0\rangle/|1\rangle\equiv|D_{3/2},m=-1/2\rangle/|D_{3/2},m=+1/2\rangle$, by
two successive Raman $\pi$-pulses which drive the transitions
$|\uparrow_{c}\rangle\leftrightarrow|0\rangle$ and
$|\downarrow_{c}\rangle\leftrightarrow|1\rangle$ respectively. Due to the
narrow linewidth of the $850\text{nm}/854\text{nm}$ laser, the Raman
transition has a long coherence time of $\sim 1\,$ms (see Fig. S5), so that
the optical phases of the beams remain constant over the interval of $\sim
10\,\mu$s between two successive Raman pulses. Thus the optical phases are
cancelled and the relative phase can be precisely controlled by setting the
phases of waveforms in the radio frequency band. We measure the average
transfer fidelity by initializing the qubit to six mutually unbiased states
(MUB) $|\uparrow\rangle$, $|\downarrow\rangle$, $|+\rangle$, $|-\rangle$,
$|L\rangle$, $|R\rangle$ encoded on
$|\uparrow_{c}\rangle/|\downarrow_{c}\rangle$, and applying variable numbers
of Raman $\pi$-pulses. The average transfer fidelity is measured to be
$99.2(2)\%$ per Raman $\pi$-pulse for six MUBs (see Fig. 2C).

The network protocol is illustrated in Fig. 3A. After $2.5\,$ms Doppler
cooling and $1.4\,$ms EIT cooling, we prepare the memory qubit on two basis
states $|\uparrow_{m}\rangle=|D_{5/2},m=+3/2\rangle$ and
$|\downarrow_{m}\rangle=|D_{5/2},m=+5/2\rangle$ via optical pumping and
$729\,$nm pulses. The memory qubit is stored for two periods of $\tau$ with a
spin echo in the middle, and read out at the end. Inside each period of
$\tau$, repetitive trials of ion-photon entangling attempts are performed in a
heralded style via an excitation pulse. Once a photon detection event is
recorded, the excitation trial halts immediately and state inspection is
performed via the Raman conversion, state manipulation, and fluorescence
detection. The intermediate cooling is performed every $N=100$ trials. In each
trial, the communication ion is first prepared to the initial state
$|S_{1/2},m=+1/2\rangle$ by $290\,$ns of optical pumping. A strong picosecond
pulse at $397\,$nm pumps the ion to the excited state $|P_{1/2},m=-1/2\rangle$
with nearly unity efficiency. The excited state then decays to
$|D_{3/2}\rangle$ level with a branching ratio of $6\%$ and emits a photon at
$866\,$nm (see Fig. 1B) branching ratio . Once this happens, the ion and the
photon are prepared into an entangled state, which can be expressed as

$|\Psi\rangle=\frac{1}{\sqrt{3}}|0\rangle|\pi\rangle+\frac{1}{\sqrt{6}}|1\rangle|\sigma^{-}\rangle+\frac{1}{\sqrt{2}}|2\rangle|\sigma^{+}\rangle$
(1)

where $|0\rangle\equiv|D_{3/2},m=-1/2\rangle\rangle$,
$|1\rangle\equiv|D_{3/2},m=+1/2\rangle$,
$|2\rangle\equiv|D_{3/2},m=-3/2\rangle$, and the weights are from the Clebsh-
Gordan coefficients of the corresponding transitions. The emitted photon is
collected by an objective of NA $=0.52$ with the optical axis perpendicular to
the magnetic field, and then coupled into a single-mode fiber. In this case,
the emission in the $|\pi\rangle$ polarization will be projected to
$|H\rangle$, and $|\sigma^{\pm}\rangle$ will be projected to $|V\rangle$ with
a half probability. Thus the entangled state becomes
$|\Psi\rangle=\frac{1}{\sqrt{2}}[|0\rangle|H\rangle+(\frac{1}{2}|1\rangle+\frac{\sqrt{3}}{2}|2\rangle)|V\rangle]$.
We further combine $\frac{1}{2}|1\rangle+\frac{\sqrt{3}}{2}|2\rangle$ into
$|1\rangle$ and convert the ion state to the memory qubit subspace via three
successive Raman transitions, including ($1$) a $850\text{nm}/854\text{nm}$
Raman converting $|0\rangle$ to $|\uparrow_{c}\rangle$, ($2$) a
$866\text{nm}/866\text{nm}$ Raman which converts
$\frac{1}{2}|1\rangle+\frac{\sqrt{3}}{2}|2\rangle$ to $|1\rangle$, and ($3$)
another $850\text{nm}/854\text{nm}$ Raman converting $|1\rangle$ to
$|\downarrow_{c}\rangle$ (see Fig. 2A). After these three Raman transitions,
we end up with a maximally entangled Bell state:

$|\Psi\rangle=\frac{1}{\sqrt{2}}(|\uparrow_{c}\rangle|H\rangle+|\downarrow_{c}\rangle|V\rangle)$
(2)

It is noteworthy that the Raman beams will not influence the memory qubit
stored in the basis states $|\uparrow_{m}\rangle$ and
$|\downarrow_{m}\rangle$, as both energy levels will not be driven by
$854\text{nm}$ Raman light with the $\sigma^{+}$ polarization. The influence
is estimated to be less than $10^{-5}$ per Raman $\pi$-pulse, as shown in Fig.
S6. The reason for transferring the communication ion to the memory qubit
subspace is that we can use standard $729\text{nm}$ rotations for the qubit
state inspection in the next step. If needed, it is not hard to transfer the
entangled state back to communication qubit subspace
$|\Psi\rangle=\frac{1}{\sqrt{2}}(|0\rangle|H\rangle+|1\rangle|V\rangle)$ via
additional $850\text{nm}/854\text{nm}$ Raman pulses, or to
$|\Psi\rangle=\frac{1}{\sqrt{2}}(|\uparrow_{s}\rangle|H\rangle+|\downarrow_{s}\rangle|V\rangle)$
via $729\text{nm}$ pulses
($|\uparrow_{s}\rangle/|\downarrow_{s}\rangle\equiv|S_{\frac{1}{2}},m_{s}=\mp\frac{1}{2}\rangle$).

Figure 4: Crosstalk-free storage of quantum information in memory qubit. (A)
We measure the decay probability (orange triangle) and the storage fidelity to
the initial state
$\frac{|\uparrow_{m}\rangle+|\downarrow_{m}\rangle}{\sqrt{2}}$ (blue circle)
with variable storage time, in the protocol shown in Fig. 3A. (B) The
fidelities for six MUBs, average fidelities, and decay probability
with/without repetitive cooling, pumping, photon excitation, and state
detection on the communication qubit.

The emitted photon at $866\,\text{nm}$ can be further converted to
$1558\,\text{nm}$ on a PPLN (Periodically Poled Lithium Niobate) waveguide
surrounded by a Sagnac interferometer in a polarization-maintained style
weifurner_qkd ; ikuta . The external device efficiency about $38\%$ and a
signal-to-noise-ratio (SNR) of $22$ are achieved by $2.2\,$W of
$1950\,\text{nm}$ pumping laser, as shown in Fig. 3D.

We measure the ion-photon entanglement fidelity for three different fiber
lengths, i.e. $866\,\text{nm}$ photon over a $3\,$m fiber, $866\,\text{nm}$
photon over a $1\,$km fiber, and converted $1558\,\text{nm}$ photon over a
$12\,$km fiber, which represent the network scale of a laboratory, a
university campus, and a city, respectively. The inspection of the photonic
state is via waveplates and polarizers before the photon detector. The
inspection for ion states is through $729\,\text{nm}$ rotations and a
fluorescence detection after the heralding signal of photon detection returns
after a round-trip travel time of $2L/c$, where $L$ is the length of fiber and
$c$ is the light speed in fiber. Note that the state detection does not
influence the memory ion. We use quantum state tomography to characterize the
quality of the ion-photon entanglement at $3\,$m and $1\,$km. The density
matrix of the ion-photon state in these two cases are reconstructed via the
MLE (maximum-likelihood estimate) and are illustrated in Fig. 3B and 3C. The
measured fidelity to the most close maximally-entangled state is $93.8(3)\%$
over a $3\,$m fiber with a total storage time $2\tau=40\,$ms. The fidelity
decays a little bit to $92.4(4)\%$ at longer storage time $2\tau=200\,$ms,
mainly due to increased instability of $729\,\text{nm}$ laser power. At a
fiber length of $1\,$km, the fidelity is measured to be $91.2(7)\%$ with a
storage time of $200\,$ms. For the $12\,$km ion-photon entanglement with
$200\,$ms storage time, we characterize the fidelity by measuring the
visibilities for the ion-photon entangled state in three bases $\sigma_{x}$,
$\sigma_{y}$ and $\sigma_{z}$ pan50km . By adjusting the phase of the final
$729\text{nm}$ $\pi/2$ rotation, we could observe two sinusoidal oscillations
in the $|H\rangle+|V\rangle$ and $|H\rangle+i|V\rangle$ bases as shown in Fig.
3E with visibilities of $V_{x}=81.9\pm 10.7\%$ and $V_{y}=79.0\pm 10.4\%$.
Thus the entanglement fidelity can be estimated as
$F=\frac{1}{4}(1+V_{x}+V_{y}+V_{z})=87.7\pm 4.5\%$, with $V_{z}=89.8\pm
10.7\%$. The generation rate of heralded ion-photon entanglement over $3\,$m,
$1\,$km, $12\,$km fiber is $46\,\text{s}^{-1}$, $3.4\,\text{s}^{-1}$,
$0.032\,\text{s}^{-1}$, and the attempting rate is $264\,\text{kHz}$,
$49\,\text{kHz}$, $5\,\text{kHz}$, respectively.

In the last step, we verify that the memory ion can protect the stored quantum
information from the dissipative operations on the communication qubit. Unlike
the ground state, the metastable $|D_{5/2}\rangle$ level has a finite lifetime
and will decay to $|S_{1/2}\rangle$ in a timescale of $T_{1}\sim 1\,$s, which
means the stored quantum information will suffer from noticeable degradation
if the storage time is comparable to $T_{1}$. The good news is that this error
can be probed via fluorescence detection, which means once happened, it can be
discarded to avoid influencing the fidelity of the network task, but at a cost
of deteriorated efficiency kauffman midcircuit ; midcircuit2 ; midcircuit3 ;
thompson erasure ; quantiuum . In the protocol of this experiment, after a
storage time of $2\tau$, the memory qubit is analyzed first by a fluorescence
detection to probe whether it has decayed to $|S_{1/2}\rangle$ (the first
state detection on the memory qubit). If the memory ion is in the bright
state, the protocol terminates and starts over. If the memory ion is in the
dark state, we rotate the ion state and execute the second state detection to
perform single-qubit state tomography on the quantum state.

We characterize the probability of the level decay by the first state
detection with variable storage time $2\tau$, and the fitted lifetime of the
memory qubit is found to be $T_{1}^{\prime}=0.79(3)\,$s (Fig. 4A). We
attribute the deviation from the precise lifetime $T_{1}=1.168(7)\,$s of
$|D_{5/2}\rangle$ lifetime  to the leakage from $854\,\text{nm}$ and
$729\,\text{nm}$ beams. We further initialize the memory ion to
$|+\rangle=\frac{|\uparrow_{m}\rangle+|\downarrow_{m}\rangle}{\sqrt{2}}$ at
the beginning of the protocol, and measure the storage fidelity with variable
time $2\tau$, conditioned on that the memory qubit is still in
$|D_{5/2}\rangle$ to exclude the influence from $T_{1}^{\prime}$. In this way,
the memory dephasing time is found to be $T_{2}=323(19)\,$ms, as shown in Fig.
4A. The fidelity oscillates with the storage time, and can be well fitted by a
double-frequency noise model at $50\,$Hz and $150\,$Hz. To confirm that the
operations performed on the communication qubit does not influence the memory
qubit, we measure the storage fidelities of six mutually unbiased bases (MUBs)
with $2\tau=120\,$ms, with or without all the dissipative operations on the
communication qubit. We find the average storage fidelity of six bases is
$0.907(2)/0.904(2)$ with/without operations on the communication ion, and the
averaged decay probability is $0.147(3)/0.142(3)$ with/without operations on
the communication ion. Since both of the storage fidelity and decay
probability cannot be distinguished considering the statistical error, we
confirm the operations on the communication ion does not influence the memory
ion.

In summary, we experimentally realize a novel two-ion quantum network node,
which can be performed in a crosstalk-free style and is suitable for
distributing quantum entanglement over metropolitan-scale fiber network. Our
scheme is useful not only for trapped-ion system, but also suitable for other
physical platforms which have long-lived metastable energy levels such as
neutral 171Yb atoms in a tweezer array kauffman midcircuit ; midcircuit2 ;
midcircuit3 ; thompson erasure . Under current crosstalk-free excitation
scheme, we can also switch to ion-photon entanglement at $397\text{nm}$ for
higher rate and fidelity on the laboratory scale oxford sr ; monroe_barium ,
by only changing the objective in the setup. The remote entangling rate can be
substantially increased if high-efficiency quantum wavelength conversion from
UV to telecom band is developed Silberhorn ; Lobino ; Quraishi . It is also
important to further improve the remote ion-photon entanglement generation
rate. We believe that the enhancements through a cavity 230m ;
lanyon_connection ; keller ; Takahashi ; rempe ; thompson erbium  or via
multiplexing 225 ; multipurpose ; 2021nature ; rmp_gisin ; enhancement ;
lanyon multiplexing ; haffner multiplexing  are promising approaches towards
this goal.

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Acknowledgements: We acknowledge helpful discussions with Lai Zhou, Chi Zhang,
Lu Feng, Panyu Hou, and Ye Wang.

Funding: This work is supported by Innovation Program for Quantum Science and
Technology (No.2021ZD0301604), the Tsinghua University Initiative Scientific
Research Program and the Ministry of Education of China through its fund to
the IIIS. Y.F.P. acknowledges support from the start-up fund and the Dushi
Program from Tsinghua University. Y.K.W. acknowledges support from the start-
up fund from Tsinghua University.

Author Contributions: P.C.L., Y. W., J.X.S. Z.B.C., Z.Q.W., S.Z., P.Y.L.,
Z.C.T., Y.D.S., X.Y.C., B.X.Q., Y.Y.H., Z.C.Z. and Y.F.P. carried out the
experiment. Y.F.P. and L.M.D. supervised the project. All the authors
contributed to the discussion and the writing.

Competing interests: X.Y.C., B.X.Q., Y.Y.H., Z.C.Z., Y.K.W., Y.X., Y.F.P. and
L.M.D. hold shares with HYQ Co. The other authors declare no competing
interests.

Data and materials availability: All data needed to evaluate the conclusions
in the paper are present in the paper and/or the Supplementary Materials.

Supplementary Materials for
Realization of a crosstalk-free multi-ion node for long-distance quantum
networking

##  I Level structure and laser beam diagram

Fig. S1 shows the level structure of ${}^{40}\mathrm{Ca}^{+}$. In our
experiment, ion is initialized in $|S_{1/2},m=+1/2\rangle$ by optical pumping
with $\sigma^{+}$-polarized $397\,\text{nm}$ continuous laser beam and
$866\,\text{nm}$ beam. Doppler cooling, electromagnetically induced
transparency (EIT) cooling and fluorescence detection are also performed by
$397\,\text{nm}$ laser beam and $866\,\text{nm}$ beam. Fig. S2 shows the
diagram of laser beams. The addressed $729\,\text{nm}$ beam is perpendicular
to the plane and not shown.

Figure S1: ${}^{40}\mathrm{Ca}^{+}$ ion energy level structure stute thesis .
We list all the energy levels and transitions of ${}^{40}\mathrm{Ca}^{+}$ ion
in this figure. Figure S2: Laser beam diagram. The laser scheme in our
experiment.

##  II Control system

For specific purpose of heralded entanglement experiments, a home-made device
“QNetWorker” handling the entanglement attempts with high speed and precision
of decision making process has to be developed, in cooperation with the other
programmable logic unit “Sequencer”, which controls usual sequences and offers
the flexibility of managing the overall branch of decision for all qubits to
enable swift scheduling of entanglements generation and subsequent operation.

The QNetWorker functions in entanglement establishment alongside encoding
transfer for network qubits with logic controls as the following content
encapsulates:

  * •

TTL outputs for controlling $397\,$nm and $866\,$nm laser beam’s RF switches,
for driving corresponding AOM for state preparation and providing the pulse
picker with EOM trigger, which composes the trial sequence up to
$1\,\text{MHz}$ repetition rate, mainly limited by AOM latency.

  * •

Four input channels with separately adjustable time window for acquiring
signal of SNSPD. Facilitating timestamps readout of heralded events with
superior precision of $417\,$ps ($2\,$ns adopted in this work).

  * •

Decisions of consecutive sequences to manipulate communication qubits based on
heralding patterns encoded in a $4$-bit word of input events without latency.
Moreover, the subsequent sequences are synchronized with the timestamps, for
minimized $866\mathrm{nm}$ Raman transition phase error for merging gate.

  * •

Redundant interfaces of modules facilitates the potential to programmable
modulations by adequate digital output channels such as feedforward phase
correction of $866\mathrm{nm}$ Raman merging gate (not in this work) and
controlling sequences of arbitrary waveform generator based on heralding
patterns and experiment design.

Furthermore, Sequencer serves as the master controller of experiment sequences
which regulates QNetWorker for entangling trials. It enables immediate
detection right after heralding events or in-sequence manipulations and
detection of communication qubits during arbitrary gate sequences such as spin
echo of memory qubits. In principle, any sophisticated gates implementation
could be accomplished in current system.

Figure S3: Calibration of pulse laser. We verify a single $397\,$nm pulse can
drive a $\pi$-pulse by measuring the proportion of state pumped to
$|\uparrow_{s}\rangle\equiv|S_{1/2},m=-1/2\rangle$ and $|D_{3/2}\rangle$ after
excitation, with variable pulse energy.

##  III Pulse excitation

In the experiment, we use $397\,$nm pulse laser with $\sigma^{-}$ polarization
to excite ion from $|S_{1/2},m=+1/2\rangle$ to $|P_{1/2},m=-1/2\rangle$. After
pulse excitation and spontaneous decay of ion, population in
$|S_{1/2},m=-1/2\rangle$ and $|D_{3/2}\rangle$ is measured. The outcome of the
calibration process is shown in Fig. S3, with which we get the corresponding
AOM amplitude to achieve pulse area of $\pi$. The dashed line shows the
theoretical population in $|S_{1/2},m=-1/2\rangle$ and $|D_{3/2}\rangle$ for
$\pi$-pulse. State preparation and shelving error account for the fraction
exceeding theoretical value. After determination of $\pi$-pulse AOM amplitude,
we verify that the $397\,$nm pulse laser will not off-resonantly drive the ion
to $|P_{3/2}\rangle$, and induce the ion to fall out of the $3$-level
communication subspace, which results in $|3D_{5/2}\rangle$ population. We
excite ion from $|S_{1/2},m=+1/2\rangle$ to $|P_{1/2},m=-1/2\rangle$
repeatedly and measure the state of ion. Pulse excitations for over $10^{6}$
times gives no $3D_{5/2}$ population, which verifies pulse laser in our
experiment will not give rise to excitation from $|4S_{1/2}\rangle$ to
$|4P_{3/2}\rangle$.

We plot the histogram for the arrival time of $866\,$nm photon relative to
pulse excitation trigger. Fig. S4 shows the time distribution of photon
collected. Latency, jitters and exponential decay of ion give rise to the
shape of the histogram. We fit the histogram with convolution of Gaussian
distribution and exponential decay, and the fitted $1/e$ decay time is
$6.936\pm 0.147\,$ns. In the experiment, we record timestamps of photon
detected by single photon detector and optimize the detection window
accordingly to achieve a high signal to noise ratio.

Figure S4: Photon distribution. The histogram of photon arrival time relative
to the excitation trigger. The $15$-ns acceptance window of photons is between
the two dashed lines.

##  IV 850 & 854 Raman

Fig. S5A shows $850\,$nm and $854\,$nm laser locking scheme. They are locked
to the same reference cavity in the experiment. $850$ & $854$ Raman Ramsey
fringe between $|D_{3/2},m=-1/2\rangle$ and $|D_{5/2},m=-5/2\rangle$ is
measured, fitting to a Gaussian decay gives a Raman coherence time of $1019\pm
34\,\mu$s.

Figure S5: $850\,$nm & $854\,$nm laser locking scheme and Raman Ramsey. (A)
Locking schemes for two lasers. (B) Raman Ramsey fringe measurement.

In the experiment, $850$ & $854$ Raman transitions transfer qubits between two
subspaces. The Raman pulse should not influence the memory qubit due to
polarization and frequency mismatch. We prepare memory qubit to
$|+\rangle=\frac{|\uparrow_{m}\rangle+|\downarrow_{m}\rangle}{\sqrt{2}}$ and
measure population of $|S_{1/2}\rangle$ to detect the unwanted scattering,
with $850$ & $854$ Raman laser on or off. As shown in Fig. S6, we cannot
observe any notable difference between two cases in a duration of
approximately $1000$ $\pi$-pulses. The population decay happens with a chance
$<10^{-5}$ for each $\pi$-pulse.

Figure S6: Influence of 850 $\&$ 854 Raman transition to memory qubit
population. We measure the unwanted scattering probability of Raman
transitions with variable Raman interaction time.

##  V Polarization preserving QFC and spectrum filtering

Our frequency conversion device to telecom C-band is realized via difference
frequency generation (DFG) process in a periodically poled lithium niobate
(PPLN) waveguide. The $1.5\,$cm waveguide is placed at the center of a Sagnac
type interferometer to achieve polarization preserving. Temperature of the
waveguide is set to $71.5^{\circ}C$ to meet the best quasi-phase-matching
condition.

Figure S7: The PPQFC and spectrum filtering setup. The setup diagram for the
quantum frequency conversion module.

As illustrated in Fig. S7, the $866\,$nm signal photons are mixed with a
strong $1950\,$nm CW pump field by a dichroic mirror and then sent into the
Sagnac interferometer. Here the beam is divided into two arms in accordance
with its polarization on the PBS (customized for three wavelengths). One arm
with H polarizing is then flip to V polarizing on an achromatic half wave
plate to meet the phase matching polarization of the PPLN-waveguide. We place
two aspheric lenses symmetrically to couple $866\,$nm photons and $1950\,$nm
pump field together into PPLN-waveguide on dual ends with about $80\%$
coupling efficiency. Both the aspheric lenses and our waveguide have
customized anti-reflective coatings for all three wavelengths. After the
$866\,$nm signal photons are converted to $1558\,$nm in the waveguide, they
travel along the rest parts of the interferometer and coherently combined to
$1558\,$nm polarization qubits on the PBS. Finally converted photons are
picked out by a dichroic mirror and collected into a $12\,$km G652D telecom-
fiber with $80\%$ coupling efficiency.

Figure S8: Narrow spectrum transmission window. The transmission spectrum for
different filters and the photon linewidth.

To suppress the background noise and reach a high signal-background ratio,
several types of spectrum filters are utilized, as shown in Fig. S8. The
$1950\,$nm pump laser is filtered by a long pass filter to eliminate its
amplified spontaneous emission (ASE) at $1558\,$nm. In our wavelength
selection, the prominent background noise in the QFC process comes from anti-
Stokes Raman scattering of strong $1950\,$nm pump field. The measured Raman
scattering background at $1558\,$nm is about $5\,$kHz/nm with $1.1\,$W
$1950\,$nm pumping, which makes a narrow-band spectral filtering system for
converted photons necessary. Here in our setup, two band pass filters (FWHM
$5\,$nm, Center $1558\,$nm) first remove the major part of the residual
$1950\,$nm pump laser and other stray light from $1558\,$nm converted photons.
Then the photons subsequently pass a highly stable filtering etalon (FSR
$8\,$GHz, FWHM $200\,$ MHz, $90\%$ transmission) and a volume Bragg grating
(VBG, FWHM $25\,$GHz, $98\%$ reflection efficiency). This combination
determines a $200\,$MHz narrow spectrum transmission window which suppresses
the Raman background to $8\,$Hz under $1.1\,$W $1950\,$nm CW pumping. Taking
the dark count rate of SNSPD into consideration, the total background noise is
$18\,$Hz and the signal background ratio is up to $22$.