# Remote distribution of non-classical correlations over 1250 modes between a
telecom photon and a 171Yb3+:Y2SiO5 crystal

M. Businger  Départment de Physique Appliquée, Université de Genève, 1205
Genève, Switzerland  L. Nicolas  Départment de Physique Appliquée, Université
de Genève, 1205 Genève, Switzerland  T. Sanchez Mejia  Départment de Physique
Appliquée, Université de Genève, 1205 Genève, Switzerland  A. Ferrier  Chimie
ParisTech, PSL University, CNRS, Institut de Recherche de Chimie Paris, 75005
Paris, France  Faculté des Sciences et Ingénierie, Sorbonne Université, UFR
933, 75005 Paris, France  P. Goldner  Chimie ParisTech, PSL University, CNRS,
Institut de Recherche de Chimie Paris, 75005 Paris, France  Mikael Afzelius
<EMAIL_ADDRESS>Départment de Physique Appliquée, Université de
Genève, 1205 Genève, Switzerland

###### Abstract

Quantum repeaters based on heralded entanglement require quantum nodes that
are able to generate multimode quantum correlations between memories and
telecommunication photons. The communication rate scales linearly with the
number of modes, yet highly multimode quantum storage remains challenging. In
this work, we demonstrate an atomic frequency comb quantum memory with a time-
domain mode capacity of 1250 modes and a bandwidth of 100 MHz, to our
knowledge the largest number of modes stored in the quantum regime. The memory
is based on a Y2SiO5 crystal doped with 171Yb3+ ions, with a memory wavelength
of 979 nm. The memory is interfaced with a source of non-degenerate photon
pairs at 979 and 1550 nm, bandwidth-matched to the quantum memory. We obtain
strong non-classical second-order cross correlations over all modes, for
storage times of up to $25~{}\mu$s. The telecommunication photons propagated
through 5 km of fiber before the release of the memory photons, a key
capability for quantum repeaters based on heralded entanglement and feed-
forward operations. Building on this experiment should allow distribution of
entanglement between remote quantum nodes, with enhanced rates owing to the
high multimode capacity.

Long-distance networks based on quantum repeaters Briegel  _et al._ (1998) is
a key future quantum technology that would allow long-distance quantum key
distribution Duan  _et al._ (2001) and other entanglement-based communication
tasks between remote quantum systems Kimble (2008); Wehner  _et al._ (2018).
Fiber-based quantum repeaters are based on the ability to establish
entanglement between stationary nodes (quantum memories) and flying qubits at
a telecommunication wavelength (e.g. at 1550 nm) Simon  _et al._ (2007), which
can then be extended over the entire repeater through entanglement swapping
Briegel  _et al._ (1998). Ensemble-based quantum memories are of great
interest for quantum repeaters due to their multimode (or multiplexing)
capacity, which is crucial for achieving practical rates Simon  _et al._
(2007); Sinclair  _et al._ (2014). The main systems currently under
investigation are laser-cooled alkali gases Pu  _et al._ (2017); Parniak  _et
al._ (2017); Cao  _et al._ (2020); Yu  _et al._ (2020); Pu  _et al._ (2021)
and rare-earth ion doped crystals Askarani  _et al._ (2021); Rakonjac  _et
al._ (2021); Lago-Rivera  _et al._ (2021); Liu  _et al._ (2021); Ortu  _et
al._ (2022a).

Solid-state ensemble quantum memories based on rare-earth (RE) ion doped
crystals can be multiplexed in time Simon  _et al._ (2007); Afzelius  _et al._
(2009), frequency Sinclair  _et al._ (2014); Yang  _et al._ (2018) and space
Heinze  _et al._ (2013); Yang  _et al._ (2018); Seri  _et al._ (2019). Time-
domain multimode storage is most efficiently achieved with the atomic
frequency comb (AFC) quantum memory Afzelius  _et al._ (2009), where the mode
capacity is proportional to the number of comb lines in the AFC Afzelius  _et
al._ (2009); Ortu  _et al._ (2022b). By consequence, a large capacity requires
both a large AFC bandwidth and a narrow homogeneous linewidth, i.e. a long
optical coherence time, to maximize the number of comb lines. AFC experiments
featuring long optical coherence times, in the range of 10 to 100 $\mu$s, have
so far only been achieved in nuclear-spin based RE-crystals (non-Kramer ions),
namely Eu3+:Y2SiO5 Jobez  _et al._ (2016); Ortu  _et al._ (2022a, b),
Pr3+:Y2SiO5 Rakonjac  _et al._ (2021); Lago-Rivera  _et al._ (2021) and
Tm3+:Y3Ga5O12 (YGG) Askarani  _et al._ (2021). However, experiments in Eu3+
and Pr3+ doped materials have shown AFC bandwidths of around 10 MHz or less,
fundamentally limited by the nuclear hyperfine splittings of the same order,
which reduces the temporal multimode capacity to the range of 10 to 100 modes
Ortu  _et al._ (2022b). Tm3+:YGG could potentially store a larger number of
modes than Pr3+ and Eu3+, owing to the enhanced nuclear Zeeman splittings
Thiel  _et al._ (2014). RE ions with electronic spin (Kramer ions), such as
Nd3+ and Er3+, on the other hand, offer higher bandwidths owing to large
hyperfine or Zeeman splits, with demonstrated AFC bandwidths ranging from 100
MHz to 6 GHz Usmani  _et al._ (2010); Tiranov  _et al._ (2015); Tang  _et al._
(2015); Askarani  _et al._ (2019); Craiciu  _et al._ (2019); Liu  _et al._
(2021). However, the measured AFC coherence times are only in the range of 10
ns to 1 $\mu$s, limited by the increased interaction with the crystal
environmenent (e.g. spectral diffusion Böttger  _et al._ (2006) and
superhyperfine coupling Usmani  _et al._ (2010); Craiciu  _et al._ (2019)). To
maximize the multimode capacity, there is thus a need to find a material where
large bandwidth and a long AFC coherence time can be achieved simultaneously.

Figure 1: Experimental setup. (a) Energy level structure of 171Yb3+:Y2SiO5 at
zero magnetic field for site II. The AFC quantum memory is created on
transition (1) and transitions (2)-(4) were used for spin polarization into
state $\ket{4_{g}}$. (b) Conceptual experimental setup showing the main
components of the SPDC source based on two periodically poled lithium niobate
(PPLN) waveguides and the 171Yb3+:Y2SiO5 (Yb:YSO) quantum memory (QM), see
main text and Methods for details. To increase absorption, the crystal is
mounted in a quadruple-pass configuration, where the backward 979 nm output
mode is separated from the input mode via an optical circulator based on a
Faraday rotator and a polarization beam splitter. The signal and idler photons
were filtered by a volaume Bragg grating (VBG) and Fabry-Pérot (FP) cavity,
and a ultra narrow fiber Bragg grating (UNFBG), respectively, and detected by
superconducting nanowire single photon detectors (SNSPDs) D1 and D2. (c) The
experimental sequence consists of a spin polarization step (200 ms) and an AFC
preparation step (50 ms), as described in the main text. Many storage trials
were made during 50 ms, where for each trial the SPDC source was pumped for a
duration of $1/\Delta$, followed by detection window of the same duration.

Here, we report on an AFC quantum memory experiment in 171Yb3+:Y2SiO5 at 979
nm, where 1250 temporal modes are stored owing to its large bandwidth and long
optical coherence time. The hyperfine levels in 171Yb3+:Y2SiO5 arise from a
highly anisotropic coupling of its electronic spin $S=1/2$ to its nuclear spin
$I=1/2$, resulting in four completely hybridized and non-degenerate hyperfine
levels in both the excited and ground states Tiranov  _et al._ (2018), see
Fig. 1(a). At zero magnetic field, these states have zero first-order Zeeman
(ZEFOZ) effect, resulting in spin and optical coherence times comparable to
those of non-Kramer ions Ortu  _et al._ (2018); Welinski  _et al._ (2020). At
the same time, hyperfine splittings range from 288 MHz to 2.623 GHz (for
171Yb3+ in site II), typical of Kramer ions, and should therefore also allow
high-bandwidth quantum memories Businger  _et al._ (2020). In this work, we
exploit these unique features to simultaneously demonstrate a large memory
bandwidth of 100 MHz and an optical storage time of up to 25 $\mu$s. The
memory is interfaced with a photon-pair source based on spontaneous parametric
down conversion (SPDC), which produces non-degenerate photons at 979 nm and
1550 nm. Non-classical second-order correlations are obtained for storage
times of up to 25 $\mu$s, for which the temporal multimode capacity is shown
to be 1250 modes. Furthermore, the telecom photon is propagated through a 5 km
fiber spool to demonstrate the ability to establish remote non-classical
correlations, a key building block for quantum repeaters.

## Results

Figure 2: Non-classical correlations. Second-order cross-correlation function
$g^{(2)}_{si}(\tau_{si})$ for different AFC storage times 1/$\Delta=$ 1
$\mu$s, 5 $\mu$s, 10 $\mu$s and 25 $\mu$s. The cross-correlation function
peaks at the expected emission time of the AFC echo, $\tau_{si}=1/\Delta$,
reaching $g_{si}^{(2)}$($\tau_{si}$)$=28(4)$, $26(4)$, $21(2),$ and $14(1)$,
respectively, well above the classical limit of $2$. All measurements have a
binning size of 2 ns. The acquisition times were between 1.15 min for the
shortest storage time and up to 8.15 min for the longest storage time.

Experimental setup and procedures. The experimental set-up consists of the
171Yb3+:Y2SiO5 AFC quantum memory and a SPDC source producing correlated
photon pairs, see Fig. 1(b). The AFC quantum memory is based on the creation
of a comb-like absorption structure in an inhomogeneous absorption profile
Afzelius  _et al._ (2009), created through spectral hole burning. If the
frequency periodicity of the comb is $\Delta$, it leads to a coherent emission
of an AFC echo after a pre-determined storage time of $1/\Delta$. In this
work, the AFC is created on the optical transition between the lowest crystal-
field states of the electronic ground 2F7/2 and excited 2F5/2 states, at a
wavelength of 978.854 nm for site II Welinski  _et al._ (2016), where each
electronic state is split into four non-degenerate hyperfine states. The AFC
is created on the strong transition connecting $\ket{4_{g}}$ to $\ket{1_{e}}$,
i.e. transition (1) in Fig. 1(a). To further increase the available optical
depth $d$, the experimental sequence starts with a spin polarization step to
optically pump ions into the $\ket{4_{g}}$ state, using transitions (2), (3)
and (4), which is then followed by the AFC creation step on transition (1),
cf. Fig. 1(c). The Y2SiO5 crystal was doped with 5 ppm of 171Yb3+ Businger
_et al._ (2020), resulting in an inhomogeneous linewidth of 1.3 GHz and an
absorption coefficient of about $\alpha=1.6~{}\textrm{cm}^{-1}$. The 12 mm
long crystal was mounted in a closed-cycle cryostat, cooled to about 3 K, and
the 979 nm mode from the SPDC source passed the crystal four times to further
increase the optical depth of the AFC (see Fig.1(b).). More spectroscopic
properties of this crystal were published in Businger  _et al._ (2020),
including population relaxation rates and transition strengths of the optical-
hyperfine transitions.

For a finite optical depth $d$ of the AFC transition, the highest echo
efficiency is obtained with square-shaped comb teeth, for an optimal comb
finesse Bonarota  _et al._ (2010). Such combs can be efficiently generated by
using a complex phase- and amplitude-modulated adiabatic pulse, which
simultaneously burns a large number of square-shaped spectral holes at
multiple frequencies Jobez  _et al._ (2016). In Eu3+ and Pr3+, this
preparation method has been successfully implemented to maximize the AFC echo
efficiency, while also creating high-resolution AFCs allowing for storage
times in the range of 10 to 100 $\mu$s Jobez  _et al._ (2016); Rakonjac  _et
al._ (2021); Lago-Rivera  _et al._ (2021); Ortu  _et al._ (2022b). For the low
bandwidths in these materials ($<$ 10 MHz), this can be achieved using an
acousto-optic modulator Jobez  _et al._ (2016). However, applying the same
method for creating large-bandwidth, high-resolution AFCs over 100 MHz, using
a high-bandwidth electro-optic modulator (EOM) phase modulator, turned out to
be challenging. The periodic, multi-frequency pulse of Ref. Jobez  _et al._
(2016) interferes in the time-domain, resulting in low average power and
inefficient optical pumping when the number of frequency bands is increased.
For an intensity modulator with fixed maximum modulation amplitude (AOM or
EOM), the average power is inversely proportional to the number of comb lines.
Here we propose a modified pulse that significantly increases the average
pulse energy after the intensity modulator, similarly to the Schroeder method
used in telecommunications Schroeder (1970); Oswald  _et al._ (2021) (see
Supplementary Materials). The pulse allows for efficient creation of a 100 MHz
AFC, consisting of up to 2500 comb lines, with a well-defined square shape for
each AFC tooth. The same EOM was used to address the (1)-(4) transitions,
which spans about 5.6 GHz, by using a combination of arbitrary waveform
generators, fixed microwave oscillators and IQ mixers to generate the relevant
frequencies, see Methods for details. Note that the spin polarization pulses
are also chirped over 100 MHz to achieve a flat initial optical depth before
the AFC creation step.

The SPDC photons were produced by pumping a non-linear waveguide in a LiNbO3
crystal (PPLN), at a pump wavelength of 600 nm, as shown in Fig. 1(b). The
quasi-phase-matching assured that signal-idler photon pairs were produced at
979 nm (signal) and 1550 nm (idler). The pump laser was generated through sum
frequency generation (SFG) in an identical PPLN, using the same 979 nm laser
which prepares the AFC memory and a telecom 1550 nm laser. To match the
bandwidth of the 979 nm photons to the AFC bandwidth, the broad SPDC spectrum
(bandwidth of 197 GHz) was filtered down on the signal mode using a Fabry-
Pérot (FP) cavity with a full width at half maximum (FWHM) linewidth of 64
MHz. The idler photons were also filtered down to a FWHM of 500 MHz, to reduce
the probability of detecting uncorrelated photons. The filtered 979 nm photons
were interfaced with the quantum memory, while the filtered telecom photons
were detected directly. Both photons travel through 50 m of fiber before being
detected, except in the case of the measurement discussed in relation to Fig.
5 where the telecom photon went through a 5-km fiber spool. The timing of the
entire experimental sequence is shown in Fig. 1(c). More details on the
experimental setup and procedures can be found in the Methods section.

Non-classical correlations. From the singles and coincidence detections of the
idler and signal photons, one can compute the normalized second-order cross-
correlation function $g^{(2)}_{si}(\tau_{si})$ as a function of the relative
delay between the detected signal and idler photons $\tau_{si}$. Ideally, the
signal and idler modes have thermal statistics individually, in which case the
Cauchy-Schwarz inequality implies that $g^{(2)}_{si}(\tau_{si})>2$ is a proof
of non-classical correlations between the photons Chou  _et al._ (2004). In an
initial characterization, we measured the second-order auto-correlation
functions of both modes without the memory in order to reduce losses. These
were $g^{(2)}_{ss}(0)=1.8(1)$ and $g^{(2)}_{ii}(0)=1.7(2)$, slightly below 2
as expected for thermal states and added detector jitter (see Supplementary
Materials). By consequence, $g^{(2)}_{si}(\tau_{si})=2$ is a conservative
lower bound for non-classical correlations.

In Fig. 2, we show the cross-correlation function $g^{(2)}_{si}(\tau_{si})$
measured for multiple storage times between $1/\Delta=1~{}\mu\textrm{s}$ and
$25~{}\mu\textrm{s}$. The peak cross-correlation value of the emitted AFC
echoes after storage are between $g^{(2)}_{si}(\tau_{si})=28$ and 14,
demonstrating strong non-classical correlations for all storage times. The
decrease in correlation with increasing storage time is mostly due to a drop
in memory efficiency and a non-negligible contribution of dark counts on the
signal detector D1 Clausen  _et al._ (2014).

Memory efficiency and lifetime. In Fig. 3, we show a coincidence histogram for
the storage time of $1/\Delta=5~{}\mu\textrm{s}$, together with a reference
histogram measured through a transparency window of 200 MHz burned into the
inhomogeneous absorption line. The reference histogram allows one to calculate
the storage efficiency (see Methods), resulting in an efficiency of
$\eta=4.9(4)\%$. The efficiency was also characterized as a function of
storage time using bright laser pulses (see the Supplementary Materials),
which gave $9.8\%$ for $1/\Delta=5~{}\mu\textrm{s}$. The difference can be
mostly explained by the fact that the 100 MHz wide AFC absorbs at most 60% of
the 64 MHz wide Lorentzian spectrum of the signal photons. A better bandwidth
matching of the memory and signal photons should result in a larger
efficiency. We also note that the efficiency is lower than the $15\%$ reached
at $1/\Delta=5~{}\mu\textrm{s}$ with a 10-MHz wide AFC in the same crystal
Businger  _et al._ (2020), which can be mainly attributed to a lower peak
optical depth over 100 MHz after the spin polarization step.

Figure 3: Memory efficiency measurement. Two-photon coincidence detection
histograms for an AFC storage experiment with $1/\Delta=5$ $\mu s$ (red), and
for a reference measurement through a transparency window burned into the
memory crystal (blue). The shaded areas (see insets) were used to calculate
the efficiency, where the echo (reference) integration window was 20 ns (15
ns). Total integration times were 1.15 min (echo) and 0.6 min (reference),
respectively.

The classical efficiency measurement also gave an effective AFC coherence time
of $T_{2}^{\textrm{AFC}}=69(6)$ $\mu$s. In comparison, up to
$T_{2}^{\textrm{AFC}}=92(9)$ $\mu$s has been measured in Pr3+:Y2SiO5 Lago-
Rivera  _et al._ (2021), while the longest AFC coherence time of
$T_{2}^{\textrm{AFC}}=300(30)$ $\mu$s was reached in 151Eu3+:Y2SiO5 Ortu  _et
al._ (2022a). Ultimately, the AFC coherence time is limited by the coherence
time measured by photon echo, where in 171Yb3+:Y2SiO5 up to 800 $\mu$s was
measured Welinski  _et al._ (2020). In the current experiment, we believe the
laser linewidth to be the main limitation of the observed
$T_{2}^{\textrm{AFC}}$ value.

Figure 4: Temporal multimode capacity. (a) Concept of the temporal multimode
capacity analysis. The storage time is set to $1/\Delta=25~{}\mu$s, with each
mode having a duration of $T_{m}=20$ ns. (b) Total number of coincidence
detections and second-order cross-correlation, as a function of the number of
analyzed modes. The $g^{(2)}_{si}$ value is calculated by integrating over the
entire mode $T_{m}$, which reduces it to about half of the peak value reported
in Fig. 2 for 25 $\mu$s.

Quantification of the multimode capacity. The AFC quantum memory has an
inherently large temporal multimode capacity Afzelius  _et al._ (2009); Nunn
_et al._ (2008); Ortu  _et al._ (2022a) that is key to reaching practical
rates in quantum repeaters Simon  _et al._ (2007). To quantify the multimode
capacity, we define a single mode duration of $T_{m}=20$ ns that entirely
captures the AFC echo histogram peak, cf. Fig. 3. To show the capability of a
multimode memory, with respect to a single mode memory, we analyze the number
of coincidence counts and the second-order cross-correlation as a function of
the number of temporal modes that are used in post-processing. Similarly to
Lago-Rivera  _et al._ (2021), the time window used for post-processing is
progressively increased to change the number of modes used in the analysis. In
Fig. 4, we show the results of the analysis for the longest storage time of
$1/\Delta=25$ $\mu$s, where we see the coincidence counts increasing linearly
with the number of analyzed modes while the cross-correlation stays almost
constant at 7.5(2). In total, up to $N=1/(T_{m}\Delta)=1250$ modes were stored
while preserving the non-classical correlations, which to our knowledge is the
largest number of modes stored in a quantum memory in the non-classical
regime.

If we compare to other non-classical storage experiments with at least one
telecom photon for remote distribution, Lago-Rivera et al. Lago-Rivera  _et
al._ (2021) stored 62 temporal modes for $25\mu$s, limited by the much lower
AFC bandwidth of about 4 MHz (corresponding to $T_{m}=400$ ns) in Pr3+:Y2SiO5.
By combining frequency and time modes, Seri et al. Seri  _et al._ (2019)
stored 135 modes in a laser-written waveguide in Pr3+:Y2SiO5. The development
of multimode quantum memories has also progressed quickly in systems based on
laser-cooled alkali atoms. Spatial multimode storage using acousto-optic
deflectors (AOD) allowed non-classical storage of up to 225 modes in a DLCZ-
type quantum memory in 87Rb, with a memory lifetime of about $28~{}\mu$s Pu
_et al._ (2017). Using a single-photon resolving camera Parniak et al. Parniak
_et al._ (2017) showed non-classical storage in up to 665 spatial modes for up
to $50~{}\mu$s in 87Rb, and more recently bipartite entanglement across 500
modes Lipka  _et al._ (2021). However, none of these experiments involved a
telecom-compatible photon, which would also require interfacing the memory
with a quantum frequency converter Maring  _et al._ (2017).

Figure 5: Remote distribution through a telecom fiber. (a) A schematic of the
storage experiment with a 5-km long fiber spool on the telecom mode, and a
memory storage time of 25 $\mu s$. (b) Second-order cross-correlation
$g^{(2)}_{si}$ as a function of the relative detection time $\tau_{si}$. The
peak at $\tau_{si}=1.47~{}\mu$s (see inset) stems from coincidence detections
with stored 979 nm photons, whereas the larger peak at
$\tau_{si}=-23.5~{}\mu$s is due to 979 nm photons directly transmitted through
the memory. The binning size is 2 ns.

Remote distribution. With the idler photon in the low-loss telecom window at
1550 nm, our quantum node is ideally suited for remote distribution of non-
classical correlations. Given the longest AFC storage time of 25 $\mu s$, and
the speed of light in silica fibers, the idler photon can be sent through a
fiber spool of 5 km, see Fig. 5(a), and still be detected before the release
from the memory of the correlated 979 nm photon. This is a basic requirement
for quantum repeaters based on heralded entanglement and feed-forward Simon
_et al._ (2007); Sinclair  _et al._ (2014). In Fig. 5(b), the cross-
correlation peak of the emitted AFC echo appears at a relative time delay of
$\tau_{si}=1.47~{}\mu$s, meaning that the heralding idler detection after the
5 km fiber spool occurs before the 979 nm photon is released from the quantum
memory. The $g^{(2)}_{si}(\tau_{si})=12(3)$ value is well above the classical
limit, only slightly reduced from the short-distance value shown in Fig. 2,
showing the capability of the node to distribute non-classical correlations
over long distance while locally storing 1250 modes. Building on this
experiment should allow distributing entanglement between remote quantum
memories as in Ref. Lago-Rivera  _et al._ (2021), but with a greatly enhanced
multimode capacity and correspondingly higher rates.

## Discussion

In this work, we have demonstrated a high multimode capacity, large bandwidth
and long optical storage times in 171Yb3+:Y2SiO5, which are key parameters for
ensemble-based quantum repeaters. Yet, these could be improved on in the near
future, by exploiting the long intrinsic optical coherence time in
171Yb3+:Y2SiO5 and by extending the bandwidth beyond the current value of 100
MHz. Simulations of the optical pumping process show that at least 250-MHz
wide AFCs are possible in principle (for site II), using the same optical
transitions as in Ref. Businger  _et al._ (2020). The practical bandwidth is
currently limited by the laser power required to efficiently polarize and
create the AFC over a large bandwidth, which also limits the memory
efficiency. Beyond these technical limitations the memory efficiency can be
increased by exploiting cavity enhancement Moiseev  _et al._ (2010); Afzelius
and Simon (2010), which recently was demonstrated with a 500 MHz bandwidth
Davidson  _et al._ (2020).

Other key developments would be to demonstrate on-demand and long-duration
storage with the spin-wave AFC technique. In Ref. Businger  _et al._ (2020) we
showed a 10-MHz bandwidth spin-wave memory with a storage time of 1 ms. A
spin-wave bandwidth beyond 100 MHz can realistically be reached, by using a
combination of increased laser power in the control fields and exploiting
different lambda-systems in the hyperfine manifold with higher control field
Rabi frequency (Supplementary Materials).

There is also a highly interesting prospect of interfacing a wide-band
171Yb3+:Y2SiO5 memory with an efficient single photon source based on quantum
dots, where recent work has shown that spectrally narrow and indistinguishable
single photons can be engineered through cavity-enhanced Raman scattering
Sweeney  _et al._ (2014); Béguin  _et al._ (2018); Bennett Anthony  _et al._
(2022). Such a hybrid solid-state quantum node would pave the way for quantum
repeaters with communication rates much higher than possible with current
schemes based on probabilistic photon pair sources Sangouard  _et al._ (2007,
2011).

## Methods

Photon pair source. The SPDC source consists of two periodically poled lithium
niobate (PPLN) waveguides. The first waveguide is used to generate pump
photons at 600 nm for the second waveguide that generates correlated photons
at 979 nm and 1550 nm. Both waveguides were temperature stabilized using
Peltier-elements controlled by a PID. The waveguides have a cross section of
12 $\mu$m $\times$ 10.4 $\mu$m and a length of 3.4 cm. The poling pitch for
both crystals is 10.075 $\mu$m. As a pump source for the first waveguide, we
use a 1550 nm laser that is amplified to 200 mW and a 979 nm laser at 1 mW
that is locked onto the AFC transition. We filter out the pump beam after the
first waveguide using two dichroic mirrors and one shortpass filter with a cut
off wavelength at 750 nm. After the second PPLN waveguide, a first dichroic
mirror picks off the 600 nm light which we use to measure the pump power of
the SPDC source. During most measurements, this pump power was kept constant
at 270 $\mu$W and only changed for the power study in the Supplementary
Material. A second dichroic mirror separates the 979 nm and 1550 nm photons
which are both coupled into fibers. The 1550 nm photons are filtered down
using an ultra narrow fiber Bragg grating (UNFBG) with a FWHM of 500 MHz which
is passively temperature stabilized. We measured the frequency of this filter
every 10 min to compensate for any drifts. The 979 nm photons are first
filtered by a volume Bragg grating (VBG) with a bandwidth of 20 GHz and, after
the memory, by a FP cavity with a FWHM of 64 MHz. The cavity is also
temperature stabilized using a Peltier-element controlled by a PID and the
central frequency is probed and adjusted every 10 min during the experiments.
The cavity has a free spectral range (FSR) of 150 GHz. Additionally, we use a
longpass filter at 600 nm before the detector to filter out ambient light from
the lab.

Experimental sequence. To prepare the memory, we spin polarize the system into
the $\ket{4_{g}}$ state during 200 ms by driving transitions (2), (3) and (4)
as shown in Fig.1(a), where we drive each transition for 1 ms. The AFC is
burned on the (1) transition, for 50 ms with 1 ms long complex adiabatic
pulses. The pulses are further explained in the following paragraph and in the
Supplementary Materials. In addition the preparation mode is gated using an
AOM and a fiber based switch which are both synchronized with the 250 ms
preparation window, to reduce the burning of the zero order beam and to
suppress any leakage of the preparation mode during the detection window.
After the spin polarization and AFC preparation steps follows a measurement
sequence, where the SPDC source is pumped for a duration of $1/\Delta$ (on
period) followed by an off period of the same duration, during which 979 nm
photons emitted from the memory can be detected. The total measurement period
was 50 ms, where the SPDC source was turned on with a 50% duty cycle. The SPDC
source was gated by a fiber-coupled AOM on the 1550 nm pump light. The entire
experimental sequence is being repeated with a repetition rate of 2.3 Hz
giving an overall duty cycle of the measurement window of 5.75%.

Memory preparation. The 979 nm laser used for the preparation mode is
frequency stabilized on a home-made, high-finesse cavity and amplified with an
optical amplifier. We reach an optical peak power of 40 mW at the memory
crystal. The spin polarization pulses are hyperbolic secant (SECH) pulses
Rippe  _et al._ (2005) that are programmed with an arbitrary waveform
generator and sent into an EOM phase modulator. The pulses have a chirp
bandwidth of 100 MHz and a central frequency of 150 MHz. They are up-converted
using an IQ mixer with three different local oscillator frequencies, 2.497
GHz, 3.026 GHz and 3.277 GHz, to address transitions (2)-(4) in the
preparation sequence. The AFC preparation pulse is also programmed with a
bandwidth of 100 MHz and a central frequency of 150 MHz (see Supplementary
Information regarding the AFC pulse details). The constant frequency offset of
150 MHz that is applied to all pulses avoids superfluous frequency components
in the AFC preparation pulse. The EOM modulation creates high and low
frequency sidebands for each modulation frequency, but only the high frequency
sidebands are resonant with transitions (1)-(4). The effective peak power of
the AFC preparation pulse in the sideband is estimated to be about 10 mW.

Efficiency measurement. To measure the storage efficiency of SPDC photons in
our memory, we compare the number of coincidence events that are retrieved
after a fixed storage time of 1/$\Delta$ = 5 $\mu$s to the number of
coincidence events that would be present without a memory (reference). In the
echo window, we measure 173 coincidence events after subtracting accidental
coincidences. For the reference measurement we pump a 200 MHz wide
transparency window, which had a residual background optical depth of
$d_{0}=0.2$. The measured reference coincidences, after subtracting accidental
coincidences, was divided by the transmission coefficient $\exp(-d_{0})$,
yielding 3491 reference coincidences. The estimated efficiency is then
$173/3491\approx 4.9\%$. Fig. 3 shows the reference coincidence histogram
after subtracting accidentals and compensating for the background optical
depth.

Data acquisition. All single photon events shown here were detected with
superconducting nanowire single photon detectors (SNSPDs) with efficiencies of
20(5)% at 979 nm and 80% at 1550 nm. Background count rates due to dark counts
and ambient background light were 30 Hz for the 979 nm detector and 100 Hz for
the 1550 detector. All events were recorded using a time to digital converter
(TDC) and analyzed in a post processing step. To calculate the coincidences,
we used the idler photon as the starting event and the signal photon as the
stop event, except for the multimode analysis depicted in Fig. 4, where we
used the pulse that gates the SPDC source to define the start of the
coincidence window such that we were able to distinguish the arrival times of
idler photons.

Crystal. The memory is a 171Yb3+:Y2SiO5 crystal with a 5 ppm 171Yb doping
concentration (95% isotopic purity) that was grown using the Czochralski
method. The crystal was cut along orthogonal polarization axes denoted as D1,
D2 and b. The dimensions along D1 $\times$ D2 $\times$ b were 3.5 $\times$ 4.5
$\times$ 12 mm, where the light was propagated along the b axis and polarized
along D2 to maximize absorption.

## ACKNOWLEDGEMENTS

We thank S. Welinski and Z. Zhang for interesting discussions and initial work
on the crystal growth and characterization, and J. Hänni for initial work on
the photon pair source. We further acknowledge funding from the Swiss National
Science Foundation (SNSF) through project 197168, the European Union Horizon
2020 research and innovation program within the Flagship on Quantum
Technologies through GA 820445 (QIA) and GA 820391 (SQUARE), and the French
Agence Nationale de la Recherche through project MIRESPIN (Grant No.
ANR-19-CE47- 0011).

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