Laser-written integrated platform for quantum storage of heralded single photons

Efficient and long-lived interfaces between light and matter are crucial for the development of quantum information technologies. Integrated photonics solutions for quantum storage devices offer improved performances due to light confinement and enable more complex and scalable designs. We demonstrate a novel platform for quantum light storage based on laser written waveguides. The new writing regime adopted allows us to attain waveguides with improved confining capabilities compared to previous demonstrations. We report the first demonstration of single photon storage in laser written waveguides. While we achieve storage efficiencies comparable to those observed in massive samples, the power involved for the memory preparation is strongly reduced, by a factor 100, due to an enhancement of the light-matter interaction of almost one order of magnitude. Moreover, we demonstrate excited state storage times 100 times longer than previous realizations with single photons in integrated quantum memories. Our system promises to effectively fulfill the requirements for efficient and scalable integrated quantum storage devices.


I. INTRODUCTION
Implementing solid-state quantum storage devices with guided wave optics has several advantages as compactness, scalability, efficiency due to enhanced lightmatter interaction, and improved mechanical stability [1]. The possibility of connection with other integrated quantum devices, i.e. single photon sources [2], photonic circuits [3], and detectors [4], enables the implementation of complex integrated quantum architectures. In addition, the compatibility of waveguide-based devices with fiber optics opens the way to the interconnection between quantum memories and the current fiber networks, [5] with proven extraordinary telecommunication capabilities.
Rare earth ion doped crystals, already widely known as long-lived and multiplexed optical memories with quantum storage capabilities [6], promise to be excellent systems for the development of on-chip quantum storage devices. The different approaches pursued in this respect include the quantum light storage in Tm 3+ or Er 3+ in LiNbO 3 waveguides [7,8] and the storage with optically controlled retrieval of weak coherent states in a nanophotonic crystal waveguide in Nd 3+ :YVO 4 [9]. These realizations, despite remarkable, suffer of storage times inherently limited by the coherence of the excited state and, in the case of nanophotonic crystals, of the challenging fabrication process. Photon echoes and long spin state lifetimes have been observed in a hybrid integrated system [10] composed by a TeO 2 slab waveguide deposited onto a Pr 3+ :Y 2 SiO 5 substrate, that potentially enables efficient [11] and long lived storage with on-demand read-out [12]. * These authors contributed equally to this paper † Electronic address: margherita.mazzera@icfo.es This solution, nonetheless, sacrifices the enhancement of the light matter interaction, as the coupling between the guided wave optics, the TeO 2 waveguide, and the optically active Pr 3+ ions happens through evanescent field. Optical channel waveguides can be also fabricated in the bulk of crystalline substrates by Femtosecond Laser Micromachining (FLM). This powerful technique is rapid, cost-effective and features unique threedimensional fabrication capabilities. Different writing regimes can be adopted [13]. One possibility consists in irradiating the sample at high energy fluence, for producing a pair of damaged material tracks that form the waveguide cladding, and light is guided between them due to a stress-induced positive refractive index change. This kind of structure is called type II waveguide. Another possibility is writing directly the waveguide core and fabricating a so-called type I waveguide. In this case, a much lower energy fluence is required for a positive refractive index change at the irradiated material volume. Identifying a processing window for operating in the first regime is relatively simple, in fact type II waveguides have been demonstrated in numerous different materials, including rare-earth doped crystals, mainly for integrated laser source applications [14][15][16]. Type II waveguides have also been recently fabricated in Pr 3+ :Y 2 SiO 5 and successfully employed for the coherent storage of classical pulses [17]. On the contrary, the fabrication of type I waveguides in crystalline substrates is a very challenging task, and, so far, it has been demonstrated only in a very limited number of cases [18,19], including lithium niobate [20][21][22] and polycrystalline matrices [23,24].
In the present paper we report on the realization of type I waveguides in a Pr 3+ :Y 2 SiO 5 crystal and we characterize the light guiding properties at 606 nm, where Pr 3+ features an optical transition of interest for photonic storage purposes. The small dimensions of the waveguide modes guarantee the compatibility with op-tical fibers and a significant enhancement of the lightmatter interaction. Moreover, spectroscopic investigations reveal that the fabrication doesn't affect the optical properties of Pr 3+ ions in the light guiding region. Finally, to assess the potential of our new platform as quantum memory, we implement quantum storage of heralded single photons. The achieved storage times are about 50 times longer than in previous experiments with waveguides [7,9]. II. A NEW WAVEGUIDE WRITING REGIME IN Pr 3+ :Y2SiO5 A. Fabrication of type I waveguides Type I waveguides have been directly written by FLM in the volume of a Pr 3+ :Y 2 SiO 5 crystal with a dopants concentration of 0.05%. We employed the second harmonic at 520 nm of an Yb-based commercial fs-laser source (SPIRIT-1040, Spectra-Physics) which emits a train of ultrashort laser pulses with duration of 350 fs. The waveguides are written in a single transverse scan geometry, with the laser beam propagating along the crystal D 1 axis and the sample translating along the b crystallographic direction (3.7 mm length). The laser pulses are focused 100 µm below the sample top surface by means of a 0.6 NA microscope objective. We experimentally found the optimal irradiation conditions for obtaining high quality optical waveguides as 40 nJ pulse energy, 100 µm/s translation speed, and 20 kHz repetition rate. These waveguides support a single optical mode at the wavelength of 606 nm, polarized along the crystal D 2 axis. An important parameter in the waveguide fabrication is the polarization of the writing laser, which must be linear and perpendicular to the sample translation direction, otherwise no guiding effect is observed at the irradiated lines. The measured FWHM mode diameters at 606 nm in the horizontal and vertical directions are 4.5 µm and 7.6 µm, respectively. The refractive index change of the core with respect to the substrate was estimated numerically from the guided mode profile (according to the method described in ref. [26]) as ∆n ≈ 1.6×10 −3 . As type I waveguides in crystals are often thermally unstable [22], it is worth mentioning that no visible degradation of our type I waveguides in Pr 3+ :Y 2 SiO 5 was observed, after several months of exposure to normal ambient and cryogenic conditions.
The physical mechanisms that contribute to inducing a type I waveguide in crystals strongly depend on the specific material considered, encompassing the formation of lattice defects and a local change in the material polarizability. Understanding their relative weight is a difficult task. Detailed studies performed on type I waveguides written in LiNbO 3 and Nd:YCOB crystals showed that the positive refractive index change in these materials results mainly from a weak lattice distortion and partial ion migration effects taking place at the irradiated area [19,20]. Such modifications, typically observed in a regime close to the material processing threshold, essentially preserve the bulk properties of the crystal, as demonstrated for type I waveguides in LiNbO 3 [21]. Regarding type I waveguides in Pr 3+ :Y 2 SiO 5 , a fundamental explanation of the origin of the positive index change induced by ultrafast laser irradiation is still under investigation.
B. Benchmarking type I vs. type II waveguides An experimental characterization was performed for comparing the guiding properties of type I and type II waveguides fabricated in Pr 3+ :Y 2 SiO 5 . To this purpose, five different type II waveguides were inscribed in the sample employing the same setup described before, but using the laser fundamental harmonic at 1040 nm, a pulse energy of 575 nJ and a scan speed of 60 µm/s. The five waveguides differ in the separation d between the tracks forming the cladding, ranging from 10 µm to 20 µm. It should be noted that the chosen irradiation parameters provide the best waveguiding properties for all values of d. Values of d ≥ 25 µm led to multimode behavior.
We coupled all waveguides with light at 633 nm from a He-Ne source, polarized along the D 2 crystal axis, by means of a plano-convex lens (75 mm focal length, 1 inch diameter). The 1/e 2 diameter of the laser beam before the lens was 6 mm. We collected the light at the waveguide output by means of a microscope objective (40x, 0.65 numerical aperture). In this way we were able to acquire, with a CCD camera, the normalized mode intensity profile of all waveguides, reported in figure 1(a) together with a microscope picture of their transverse cross sections. In addition, we measured for every waveguide the total insertion losses (IL), defined as the ratio between the light power measured before and after the waveguide. Note that the value of IL includes the waveguide propagation losses due to scattering and absorption, the coupling losses due to mode mismatch at the waveguide input, and the Fresnel losses caused at the crystal/air interface at the waveguide output, where no anti-reflection coating was present. The results of this measurement are shown in fig. 1(b), where we plot the IL values as a function of the horizontal FWHM mode diameter for all waveguides. It is clearly visible that the reduction of d in type II waveguides (black squares) reduces the mode size, but, at the same time, leads to a dramatic increase of IL. On the other hand, the type I waveguide (blue circle) supports the smallest mode, and, simultaneously, exhibits the lowest value of IL, among all waveguides analyzed. This fact is readily explained by looking at the waveguides longitudinal profiles shown in fig. 1(c). The type I waveguide features a smooth and very uniform profile along the propagation direction. The side tracks of type II waveguides, instead, present a rough and less uniform profile, that increases light scattering, especially for small values of d. As a further comparison, we measured for the two types of waveguide the additional bending losses (BL), caused by the coupling of light to radiative modes during the propagation in a curved guided path. We thus compared the IL of a straight waveguide with that of a curved one, containing an S-band of known length and fabricated with constant radius of curvature R C . We performed this measurement for values of R C of 30 mm, 50 mm, and 90 mm, both on the type I and on type II waveguides with d = 20 µm, fabricated in a dedicated sample (S-band length = 7 mm, total sample length = 9 mm). The results obtained are shown in fig. 1(d). As expected, the values of BL increase for shorter R C for both types. However, in type I the measured BL reach particularly low values, and become almost negligible for R C >90 mm. This outcome agrees with the well known fact that BL decrease in more confining waveguides [25].
This experimental analysis allows us to conclude that type I waveguides in Pr 3+ :Y 2 SiO 5 show better guiding performances than their type II counterparts, both in terms of waveguide losses and in terms of light confinement. Fig. 2 represents the experimental setup for the spectroscopy and single photon storage measurements, presented in the next paragraphs, and the hyperfine splitting of the ground and excited crystal field levels of Pr 3+ involved in the optical transition relevant for the storage (inset).

III. EXPERIMENTAL SETUP
A CW laser at 606 nm (linewidth 20 kHz) is modulated with acousto-optic modulators (AOMs) in doublepass configuration to produce the preparation pulse sequences. The preparation light is coupled into one input of a fiber beam splitter (BS, input 1 in fig. 2). In input 2 we send the input for the storage, either classical pulses or heralded single photons (see below). One output is sent to an independent optical table where the Pr 3+ :Y 2 SiO 5 crystal is maintained at 3 K, while the second output is used as reference. The light is coupled into the waveguide using a 75 mm lens, which focuses the beam to a waist < 10 µm at the input facet of the crystal. The outcoming light from the waveguide is collected with a 50 mm lens and sent to a detection stage, after a path of about 2 m. The detection is implemented with a CCD camera, for imaging and alignment, with a photo-detector, for protocols with classical light, or with a single photon detector (SPD) for experiments with single photons. For autocorrelation measurements a Hanbury Brown-Twiss setup is assembled with fiber beam splitters and additional SPDs. All the experiments are synchronized with the cycle of the cryostat (1.4 Hz). Because of vibrations, the light is efficiently coupled in the waveguide only for less than 300 ms in each cycle. Further details on the setup can be found in the Appendix.
Our heralded single photons are created with a new generation [27] of the photon pair source described in [28,29]. It is based on cavity-enhanced type I spontaneous parametric down-conversion (SPDC) in a 2 cmlong periodically-poled lithium niobate (PPLN) crystal ( fig. 2). This is placed in a bow-tie cavity (BTC) and  pumped with a 426 nm laser. The BTC is in resonance both with the signal photon at 606 nm and its heralding photon at 1436 nm (idler). The cavity lock exploits the Pound-Drever-Hall technique [29] and two mechanical choppers are used to alternate between the locking period and the single-photon measurement. The two collinearlygenerated photons are separated after the BTC using a dichroic mirror (DM, fig. 2). The signal and idler photons are distributed in 8 spectral modes. The idler photons pass through a home-made Fabry-Perot filter cavity (FC in fig. 2, linewidth 80 MHz, FSR=17 GHz), to guarantee single-spectral-mode heralding. They are then coupled into a single mode fiber to an SPD. The 606 nm photons, after passing through an etalon filter, are coupled to a single-mode polarization-maintaining (PM) fiber, and then to the input 2 of the fiber BS. The heralding efficiency of the SPDC source is η SPDC H ∼ 25% after the PM fiber and η WG H ∼ 7% in front of the waveguide. The loss is due to the BS and to mode-diameter mismatch between the PM fiber and the fiber BS, and could be readily reduced by using a fiber switch.

IV. SPECTROSCOPIC AND COHERENCE MEASUREMENTS
The inhomogeneous broadening of the transition of Pr 3+ at 606 nm in the waveguide has been estimated from the transmission of an optical pulse through the crystal while tuning the laser frequency. The full-width at half maximum (FWHM) is ∼ 9 GHz in optical depth (OD) (see inset in Fig. 2), in good agreement with bulk samples with similar ion concentrations. Moreover the central frequency did not shift with respect to the bulk. The hyperfine splitting of the levels and the oscillator strength of the transitions, measured following the spectral hole burning experiments described in ref. [30], are also consistent with those measured in the bulk. The unaltered spectroscopic properties confirm that the fabrication process does not substantially alter the crystalline structure of the modified zone.
To use the waveguide for quantum memory application the coherence of the ions in the guiding zone should be also maintained. Coherence and lifetime of the excited state are measured by means of, respectively, two-pulse [31] and three-pulse stimulated photon echo [32] experiments (TPE and SPE). A typical pulse sequence for the heterodyne detection of the TPE is shown in the inset of Fig. 3(a). The echo is detected in form of oscillations on a probe pulse 10 MHz detuned with respect to the excitation and rephasing pulses. From the exponential decay of the echo intensity (proportional to the square of the oscillation amplitude) while increasing the time τ 2 ( fig. 3(a)), we extract the coherence time of the Pr 3+ ions in the waveguide. Fig. 3(b) represents examples of heterodyne detected TPE at different storage times. In our case, probing a single-class absorption feature at the 1/2g−1/2e transition, we measure a maximum coherence time T 2 = 57 ± 10 µs. This is only slightly lower than the maximal T 2 measured in bulk samples or type II waveguides [17]. We note however that the T 2 is affected by instantaneous spectral diffusion and that higher values could in principle be achieved by decreasing the average number of atoms excited [17].
To study the lifetime of the transition and slow dephasing mechanisms, e.g. spectral diffusion, we analyze the SPE measured with direct detection. A typical output of a SPE measurement is shown in fig. 3(c) while panel d sketches the temporal sequence used. To reduce the errorbar, we perform these measurements with a higher excitation power than that used in the TPE measurement, thus we expect the absolute value of T 2 to be lower due to instantaneous spectral diffusion. We measure the decay of the SPE with τ 2 for different values of τ 1 . By fitting these decays with exponentials, we extract the expected areas of the SPE (τ 1 ) for τ 2 = 0 ( fig. 3(e)). Their decay with τ 1 directly depends on the lifetime of the excited state |e , namely T 1 = 118 ± 35 µs. This value is lower than that obtained from fluorescence measurements in a different Pr 3+ :Y 2 SiO 5 crystal (about 160 µs) but in good agreement with that measured with SPE in the same bulk sample, T 1 = 103 ± 11 µs. In presence of spectral diffusion, the ions could experience frequency shifts induced by flips of the surrounding nuclear spins. This would cause a slow broadening of the ions linewidth, Γ hom , for increasing τ 1 ([33]). As we can clearly see from fig. 3(f), Γ hom (τ 1 ) = 1/ [πT 2 (τ 1 )] remains consistent over time with the value at τ 1 = 0 (solid line) (about 10 kHz), proving the absence of spectral diffusion in the timescale and excitation power analyzed. The same trend is observed in SPE measurements in the bulk crystal.
One of the advantages of optical waveguides is the enhanced light-ions interaction due to the strong light confinement. To quantify the strength of this interaction we measure the Rabi frequency Ω R of the optical transition by means of optical nutation [34]. We prepare by optical-pumping a single-class absorption feature on the 1/2g − 3/2e transition and measure the population inversion time t π induced by a long resonant probe pulse. For an optically dense and inhomogeneously broadened ensemble, the Rabi frequency Ω R is defined as Ω R t π = 5.1 [34]. We repeat the measurement for several probe powers, P . From the linear fit of Ω R vs √ P , we extract Ω R = 2π × 1.75 MHz/ √ mW, i.e. an increase of 1.6 with respect to the type II waveguide [17] and almost one order of magnitude with respect to the bulk crystal (maintaining the same optics), fully matching with the expected increase due to the stronger light confinement.

A. Characterization of the heralded single photons
Before storing the signal photons, we measure the properties of the generated heralded single photons (more details can be found in the Appendix). We build a coincidence histogram using the idler detection as start and the signal photon as stop (inset in fig. 4(a)). The correlation time of our biphoton is estimated by fitting the histogram [29] (black dashed lines) as 121 ns, which corresponds to a biphoton linewidth of Γ = 1.8 MHz. This is smaller than the hyperfine splitting of the excited state, thus narrow enough to address a single transition of Pr 3+ ions. We calculate the normalized second-order cross-correlation function as g (2) s,i (∆t) = p s,i /(p s · p i ), where p s,i is the probability to detect a coincidence in a temporal window ∆t, while p s (p i ) is the probability to detect a signal (idler) count in a temporal window of the same size. The s,i , for different pump powers, with just the source (empty light dots) and after the pit (full dark points). The inset represents the time-resolved signal-idler coincidence histogram with just the source: the darker region is the window considered for the calculation of the g (2) s,i (400 ns) and the black dashed line is the temporal fit of the biphoton correlation; (b, c) Coincidences between signal photons splitted with a fiber BS, respectively before and after passing through a pit in the waveguide, sorted by the number of heralding photons between pairs of contiguous signal counts. measured g (2) s,i values for a window ∆t = 400 ns for different pump powers are plotted in fig. 4(a) (empty orange circles). The highest value, g (2) s,i (400 ns) = 209 ± 9, is achieved at the lowest measured pump power (0.1 mW), and decreases while increasing the pump power, as expected for a two-mode squeezed state [35].
We demonstrate the quantum nature of the signal-idler correlations violating the Cauchy-Schwartz (CS) inequality by more than 20 standard deviations (see VIII for details). The classical bound is set by the parameter s,s ·g s,s and g (2) i,i are the unconditional auto-correlations of the signal and idler photons, respectively. To demonstrate the single photon nature of our source, we measure the heralded auto-correlation of the signal photons, g i:s,s (∆t). This can be extracted from the histogram of fig. 4(b), built like in ref. [29,36]. We find g (2) i:s,s (400 ns) = 0.12 ± 0.01 for a pump power of 1.7 mW. This value is considerably lower than the classical bound g (2) i:s,s ≥ 1 and compatible with the single photon behavior (g (2) i:s,s ≤ 0.5) VIII. We then send the signal photons through the waveguide, where we hole-burn a transparency window (pit) of ∼ 16 MHz in the inhomogeneously broadened absorption profile of the ions (orange line in the inset of fig. 5(a)). We measure the g (2) s,i vs pump power sending the signal photons through the pit (full brown circles in fig. 4(a)). The correlations after the pit become remarkably higher because it acts as a spectral filter selecting a single signal frequency mode. We find R = 524 ± 84 after the pit for the highest measured power, violating the CS inequality by more than 6 standard deviations (assuming g (2) s,s = 2). Furthermore, we measure the g (2) i:s,s (∆t) of the signal photons after the pit: from the histogram of fig.  4(c), we extract g (2) i:s,s (400 ns) = 0.06 ± 0.04 (pump power ∼ 1.7 mW).

B. Storage of heralded single photons
The storage protocol that we use is called Atomic Frequency Comb (AFC) [37]: the inhomogeneously broadened absorption of the ions is shaped in a spectral comb with periodicity ∆. When a photon is absorbed by the comb, its state is mapped onto a collective excitation of atoms, described by a collective Dicke state: k e −i2πδ k t c k |g 1 · · · e k · · · g N , where the frequency detuning of the atom k is δ k = m k ∆ (being m k an integer number). After a first inhomogeneous dephasing, the atoms will collectively rephase at a pre-determined time τ = 1/∆, giving rise to a photon re-emission in the forward direction, called AFC echo.
s,i calculations. The black and brown dashed lines are the temporal decays of the correlations (inset of fig. 4(a)), renormalized for losses and efficiencies after the pit and the AFC, respectively. The shaded rectangle is the region in which the accidental counts for the AFC echo are measured. The absorption profiles of the pit (orange) and the comb (brown) are plotted in the inset, with the spectrum of the single photons (black points and line, see VIII); (b) Internal storage efficiency ηAF C , at different storage times τ , for single photons (full orange points, error bars account for Poissonian statistics) and classical light (empty black circles); (c) Cross-correlation values between idler photons and stored signal photons, g AF C,i , for different τ . The orange dashed line is the classical upper bound, g s,s · g (2) i,i = 1.58 ± 0.02 (assuming g (2) s,s = 2).
The sequence of optical pulses used to create the AFC is very similar to the one explained in refs. [38,39]: after creating a 16 MHz-wide pit to empty the 1/2g and 3/2g states, we repopulate the 1/2g level with a single class of ions (duration ∼ 80 ms). Then we send a series of pulses, resonant with the 1/2g − 3/2e transition, whose Fourier transform is the AFC that we want to create (duration ∼ 35 ms). The generated feature, for a storage time of 1.5 µs, is plotted as a brown line in the inset of fig.  5(a). Note that the spectrum of the input photons (black line in the inset of fig. 5(a)) matches perfectly with the AFC (see VIII for details on the bi-photon spectrum). Thanks to the enhanced light-ions interaction, the maximum power that we inject in the waveguide during the AFC creation is ∼ 100 µW, i.e. two orders of magnitude lower than what is usually necessary in bulk, in agreement with the Ω R increase. The measurement is performed in the remaining time (∼ 150 ms), resulting in a duty cycle for the AFC storage of ∼ 21% (accounting for the duty cycle due to the cryostat vibrations). When a herald is detected, an AOM in front of the pump laser is closed to reduce the noise coming from the source during the AFC echo retrieval VIII. The minimum response time of this gate is t off P = 1.2 µs, which limits our minimum storage time to τ = 1.5 µs. For longer storage times, t off P is delayed in order to maintain τ − t off P = 0.3 µs. The AFC echo for a storage time τ = 1.5 µs is shown in fig.  5(a) (orange trace). The exponential fit of the biphoton temporal decay, measured with only the source (black dashed line of the inset in fig. 4(a)), is plotted on top of the input (black dashed line) and the AFC echo (brown dashed line), renormalized for the different count-rates. Note that the linewidth of the photons, both after the pit and emitted by the comb, remains unchanged, confirming that there is no mismatch between the width of the comb and the spectral profile of the photons. Before and after each storage experiment, we measure the coincidences between the idler and the signal photons after the pit. To account for fluctuations in power, we consider the average of the two as our reference input (gray peak in fig.  5(a)). We evaluate the storage efficiency by integrating the counts of the histogram in a 400 ns window centered at the AFC echo (dark orange region at about 1.5 µs, fig. 5(a)) divided by the counts inside a 400 ns window centered at the input (dark gray region about 0 µs, fig.  5(a)). The resulting efficiency is the internal efficiency of the process, η AF C . The total efficiency of our device is calculated multiplying η AF C by the coupling into the waveguide (∼ 40%) and the transmission through the background optical depth, e −d0 , with d 0 = 0.08 (see inset in fig. 5(a)). We perform storage experiments with an average pump power of 1.7 mW. The internal efficiencies for different storage times are shown in fig. 5(b) (full orange points). For comparison we measure the internal efficiency of our memory with classical pulses (empty black circles in fig. 5(b)), using the same comb preparation sequences, showing a good overlap between the quantum and the classical regimes. The efficiency decrease for in-creasing τ is fitted with an exponential decay, e −4/(T * 2 ∆) [39], from which we extract the effective coherence time of our storage protocol, T * 2 = 8 µs, much smaller than the T 2 (see section IV). This suggests that our storage time is at the moment limited by technical issues (e.g. power broadening, short preparation time, etc), and not by the coherence time T 2 of the Pr 3+ in the waveguide.
The g (2) AF C,i of the AFC echo is measured similarly to the one of the input: we find p s,i integrating the counts in a window of 400 ns centered at the AFC echo (the same region considered for η AF C ); p s · p i is measured integrating the accidentals coincidences after the AFC echo up to the last stored noise count, t off P + τ (light orange rectangle in fig. 5(a)), renormalized to a 400 ns window. Fig.  5(c) shows the g (2) AF C,i values for AFC echoes measured at different τ . The cross-correlation increases after the storage up to 61 ± 12 for a storage time of 1.5µs, with respect to 36±3 after the pit. This could be explained by the presence of broadband noise from the SPDC source, which is not in resonance with the Pr 3+ ions. Such noise would not be present in the temporal mode of the AFC echo, where the pump is gated off [40]. The value of the g (2) AF C,i should remain constant for different τ , as the storage efficiency is the same for the AFC echo and for the stored noise. But for longer storage times, as η AF C decreases, our signal-to-noise ratio is limited by the background noise. Nevertheless, the g (2) AF C,i remains higher than the classical bound (orange dashed line) for all the measured storage times up to τ = 5.5 µs, for which we violate the CS inequality with R = 34 ± 18 (above the classical bound by almost 2 standard deviations), effectively demonstrating the longest quantum storage in an integrated solid-state optical memory (almost 50 times longer than the previous demonstrations with AFC in waveguides [7][8][9]). Moreover, thanks to the convenient energy level scheme, our system enables the full spinwave AFC storage, thus giving access to both longer storage times and on-demand read-out [38,41,42].

VI. CONCLUSION AND OUTLOOK
In the present work we propose a new platform for the implementation of integrated quantum storage devices. We demonstrated the generation of type I waveguides in a Pr 3+ :Y 2 SiO 5 crystal using fs-laser micromachining in a new writing regime. We showed that the fabrication of type I waveguides preserves all the spectroscopic properties of Pr 3+ . We implemented a quantum storage protocol for heralded single photons, observing high nonclassical correlations for storage times 50 times longer than in previous waveguide demonstrations. The use of type I waveguides in Pr 3+ :Y 2 SiO 5 gives several advantages with respect to type II ones. In type I waveguides, the guided mode is in general sensibly smaller than what obtainable in a type II waveguide with comparable losses. This fact yields an enhancement in the interaction of the guided light with the rare earth dopants. Moreover, the very good mode matching between type I waveguides and standard single mode optical fibers would allow us to glue directly the Pr 3+ :Y 2 SiO 5 samples to fiber patch cords with low coupling losses, simplifying sensibly the procedure of light coupling inside the cryostat and avoiding the temporal constraints on the photon storage given by the cryostat vibrations. In addition, type I waveguides in Pr 3+ :Y 2 SiO 5 could also be easily interfaced with laser written optical circuits in glass, potentially opening the way to the realization of integrated hybrid glass/crystal platforms [43] embedding quantum memories. Finally, for this kind of waveguides, the absence of lateral damage tracks (present in the type II counterpart) enables greater freedom in engineering the evanescent coupling of light between different waveguides. This, together with the tighter bend radii achievable in type I waveguides, permits to easily inscribe optical circuits in Pr 3+ :Y 2 SiO 5 crystals embedding directional couplers and other integrated optics devices, for performing complex tasks besides quantum light storage, fully on chip.

VII. ACKNOWLEDGMENT
We acknowledge financial support from the European Research Council (ERC) through the Advanced Grant project CAPABLE (grant agreement n. 742745). ICFO further acknowledges financial support by the Spanish Ministry of Economy and Competitiveness (MINECO) and Fondo Europeo de Desarrollo Regional (FEDER) (FIS2015-69535-R), by MINECO Severo Ochoa through grant SEV-2015-0522 and the PhD fellowship program (for A.S.), by Fundació Cellex, and by CERCA Programme/Generalitat de Catalunya.

VIII. APPENDIX
In this appendix we report the details about the experimental setup and the measurements performed to characterize the heralded single photon source used in the main paper.

A. Experimental setup
The experimental setup for the spectroscopic characterization of the waveguides and single photon storage measurements is sketched in fig. 2 of the main text. We hereby provide a more detailed description. Our laser source at 606 nm is a Toptica DL SHG pro, frequency stabilized using the Pound-Drever-Hall technique to a home-made Fabry-Perot cavity placed in a vacuum chamber. We estimate the final laser linewidth to be about 20 kHz. The CW laser light is modulated in amplitude and frequency with acousto-optic modulators (AOMs) in double-pass configuration, driven by an arbitrary waveform generator (Signadyne). The preparation light is coupled into one input of a fiber beam splitter (BS, input 1 in fig. 2 in the main text). In input 2 we send the input for the storage (either classical pulses or heralded single photons, see below). One output is sent to an independent optical table where the Pr 3+ :Y 2 SiO 5 crystal (Scientific Materials) with laser written waveguides is maintained at 3 K (in a He closed cycle cryocooler, Oxford Instrument), while the second output is used as reference. The light is coupled into the waveguide using a 75 mm lens, which focuses the beam to a waist < 10 µm at the input facet of the crystal. The out coming light from the waveguide is collected with a 50 mm lens and sent to a detection stage, after a path of about 2 m. It is worth noting that both lenses are placed outside of the cryostat chamber, thus making the alignment of the whole system rather challenging. The detection is implemented with a CCD camera, for imaging and alignment, with a photo-detector, for protocols with classical light, or with a single photon detector (SPD) for experiments with single photons.
All the experiments are synchronized with the cycle of the cryostat (1.4 Hz) to reduce the effect of the mechanical vibrations. Two mechanical shutters are installed in the setup during the single photon measurements: one, in front of the SPD, remains closed during the preparation period; the second, in anti-phase with the first one, is installed before the input 1 of the fiber BS, and remains closed during the single photon measurement period, blocking the leakage from the preparation AOM. The SPD is a Laser Components detector with 50% detection efficiency and 10 Hz dark-count rate. For unconditional and heralded auto-correlation measurements the waveguide output is split with a fiber BS and an Excelitas SPD with 50% detection efficiency and 50 Hz dark-count rate is connected to the second output.
Our heralded single photons are generated with a photon pair source ( fig. 2 of main text) inspired by the source described in [29]. It is based on cavity-enhanced spontaneous parametric down-conversion process (SPDC) in a 2 cm-long type I periodically-poled lithium niobate (PPLN). The non-linear crystal is pumped with a 426 nm laser (Toptica TA SHG) to produce signal photons at 606 nm and idler photons at 1436 nm. The crystal is placed inside a bow-tie cavity (BTC) with a free spectral range (FSR) of 261 MHz to enhance the generation of the photon pairs at the frequencies of the cavity modes. The BTC is in maintained resonant to both the signal and its heralding idler photon at 1436 nm with a double lock system. First of all, the cavity length is locked using the Pound-Drever-Hall technique to a reference beam at 606 nm derived from the main memory preparation laser [29]. Then, a classical beam at 1436 nm, generated as frequency difference (DFG) of the pump and the reference beam at 606 nm, is used to ensure the maximum transmission of the idler photons through the BTC. The lock of the DFG signal is operated by acting on the 426 nm pump frequency. Two mechanical choppers are used to alternate between the locking period and the singlephoton measurement. The BTC, besides enhancing the non-linear process at the two resonant wavelengths, is meant to generate ultra narrow-band photons [29]. A consequence of the double lock is the clustering effect given by the different FSR at the signal and idler frequencies [44]. This results in a spectral output of the SPDC source consisting of a main cluster with only 8 effective spectral modes separated by 261 MHz. The photons of the pair are generated collinearly and separated after the BTC using a dichroic mirror (DM, fig. 2 in the main text). The idler photon passes through a homemade Fabry-Perot filter cavity (FC in fig. 2 of the main text, linewidth 80 MHz, FSR=17 GHz), to guarantee a single-spectral-mode heralding. It is then coupled into a single mode fiber to an SPD (ID230, IDQuantique), with 10% efficiency and 10 Hz of dark-count rate. For the auto-correlation measurement of the idler photons, we use a second SPD (ID220, IDQuantique), with 10% efficiency and 400 Hz of dark-count rate. The 606 nm photons then pass through an etalon (linewidth 4.25 GHz, FSR=100 GHz) that suppresses the side clusters. Finally they are coupled in a single-mode polarizationmaintaining (PM) fiber and then to the input 2 of the fiber BS. The heralding efficiency of the SPDC source is η SPDC H ∼ 25% after the PM fiber and η WG H ∼ 7% in front of the waveguide.

B. Characterization of the heralded single photons
Before sending the signal photons through the fiber BS and to the memory setup, we directly connect the output of the source to the SPD, to measure the properties of the generated heralded single photons. We record the detection times of both signal and idler photons with a fast time-stamping electronics (Signadyne).
Then we build a time-resolved coincidence histogram, using the idler detections as start and the signal photons as stop ( fig. 6). The correlation time of our biphoton can be estimated by fitting the histogram with two exponential decays [29] (black dotted lines on top of the histogram). The two decay times are different due to the different losses experienced in the cavity by the signal and the idler photons, generated at widely different frequencies. From the right (left) decay we can extract the linewidth of the signal (idler) photons to be Γ s = 2.5 MHz (Γ i = 1.4 MHz). The resulting biphoton linewidth is Γ = 1.8 MHz in FWHM (equivalent to a coherence time of 121 ns), narrow enough to address a single transition of Pr 3+ ions.
To confirm the linewidth of the correlations, we use the crystal as a tunable ultranarrow spectral filter, following a measurement described in [38]: we hole-burn a transparency window (pit), centered each time at a different frequency around the signal photons, and we analyze the change in the coincidence rate after it. To prepare a pit we shine the crystal with strong pulses at the desired frequency and with a frequency chirp dependent on the width of the pit that we want to create, in this case ∼ 1.6 MHz. The coupling optics is free-space and outside the cryostat (see sect. VIII A). Inside the cryostat is only the waveguide which moves periodically with injection of compressed liquid He in the cooling device (cooling period 707 ms), thus the light is effectively coupled in the waveguide for a time < 300 ms. Having fiber coupled samples would relax the time limitation and enable better optical pumping. We reset the absorption spectrum and prepare the pit at the beginning of each cycle, limiting our measurement duty cycle to ∼ 30%. Having fibercoupled devices would allow us to increase significantly the duty cycle of the experiment. The coincidence rates for pits prepared at different frequencies are plotted in the inset of figure 5 of the main paper (black dots), which is reported here (fig. 7). The black line, a Lorentzian function with a linewidth of Γ = 1.8 MHz in FWHM, convoluted with the spectral trace of the pit, matches with the measured data. This confirms the linewidth estimated from the coincidence histogram ( fig. 6).
We quantify the non-classicality of the photon-pair correlations measuring the normalized second-order crosscorrelation function: g (2) s,i (∆t) = p s,i /(p s ·p i ), where p s,i is the probability to detect a coincidence in a temporal window ∆t, while p s (p i ) is the probability to detect a signal (idler) count in a temporal window of the same size. The g (2) s,i is extracted from the coincidence histogram of figure  6, by integrating the coincidence counts in a window ∆t around the coincidence peak (our signal of interest p s,i , dark orange region of the histogram) and dividing them by the coincidences outside of it (accidental coincidences between uncorrelated photons or detector dark counts, p s · p i , gray region of the histogram) [29], renormalized to a window ∆t. We integrate the counts over a window ∆t = 400 ns. The measured g (2) s,i values for different pump powers are plotted in figure 4a of the main paper (empty orange circles).
This measurement alone does not demonstrate the quantum nature of our correlations, which can be shown by violating the Cauchy-Schwartz (CS) inequality. The classical bound is given by the parameter R = (g (2) s,i ) 2 g (2) s,s ·g s,s (g (2) i,i ) is the auto-correlation of the signal (idler) photons. We measure the unconditional autocorrelation of the signal (idler) photon by splitting its path with a fiber BS and detecting the two outputs with two different SPDs. From the resulting coincidence histogram we extract the auto-correlation value (similarly to the cross-correlation measurement). Using an integration window ∆t = 400 ns for comparison with the g (2) s,i , we find g (2) s,s (400 ns) = 1.051 ± 0.002 and g (2) i,i (400 ns) = 1.25 ± 0.03. The expected auto-correlation for an ideal state generated by a photon source with thermal statistics is g x,x (0) = 2 [45]. As the signal photons, measured without any filter cavity, are multi-mode and knowing that we have a number of frequency modes N = 8, we expect for the signal photons g (2) th s,s (0) = 1 + 1/N = 1.12 [46]. Anyway the auto-correlation values of both idler and signal photons are lower than expected because we measured them in a 400 ns window (instead of extracting their values in the 0-point) and because the noise generated by the source reduces the auto-correlation value (a detailed discussion can be found in [29]).
Using these values, we find for the lowest pump power R = (3.3 ± 0.3) × 10 4 , surpassing the classical bound by more than 10 standard deviations. Even for the highest pump power (2 mW), where the measured crosscorrelation is g (2) s,i (400 ns) = 13.8 ± 0.3, we find R = 145 ± 6, which violates the CS inequality by more than 20 standard deviations, thanks to the better statistics.
To demonstrate the single photon nature of our source, we measure the heralded auto-correlation g (2) i:s,s (∆t): the auto-correlation of the signal is measured conditioned on the detection of an heralding in the same integration window ∆t. The histogram of figure 4b of the main paper, inspired from [36], is built as follows: for each count in the idler detector we look for detection events in the two signal detectors, happening in the same temporal window (∆t = 400 ns around the heralding). If there is a count in one of the two signal lists, we look for the closest event in the other one. The triple-coincidences are then sorted depending on the number of heralding events between each two contiguous signal detections. The events in which a coincidence between the two signal detectors is heralded by the same idler count are plotted in the bin 0. The ratio between the counts in bin 0 and the average of the other bins (black dotted line in figure 4b of the main paper) gives the heralded auto-correlation, which we measure to be g (2) i:s,s (400 ns) = 0.12 ± 0.01 (pump power ∼ 1.7 mW). This value is considerably lower than the classical bound g (2) i:s,s ≥ 1 and compatible with the single photon behavior (g (2) i:s,s ≤ 0.5).

C. Characterization of the heralded single photons after the pit
We connect the signal photons fiber output to the input 2 of the fiber BS and we couple them into the waveguide, as sketched in the setup (figure 2 of the main paper).
We hole-burn a pit of ∼ 16 MHz in the inhomogeneously broadened absorption profile of the ions (the spectral trace of the pit in OD is plotted as an orange line in figure 7). We measure the g (2) s,i between the heralding photons and the signal photons passing through the pit similarly to the previous section. The results, measured for different powers in the same range of the measurement with just the source, are plotted in figure 4a of the main paper (full brown circles). The non-classicality of the correlations after the pit is remarkably higher than the one of the source alone. For example, the g (2) s,i at the highest pump power (2 mW) is found to be 36 ± 3, being almost three times higher than the g (2) s,i of the source alone. This can be explained by a spectral filtering effect of the pit. The spectral modes in the signal arm that do not have an heralding photon and are not filtered by the etalon (see section VIII A) are in fact absorbed by the atoms outside of the pit. Due to the low count-rate, caused by transmission losses as well as short measurement duty-cycle, we do not have enough statistics in the auto-correlation measurement of the signal after the pit (an exploratory trace more than 20 h long does not show any bunching). We consider the conservative value of 2 for an ideal two-mode squeezed state for the signal [45] and the measured value only for the idler photons, lead-ing to a classical bound of g (2) s,s · g (2) i,i = 1.58 ± 0.02. Even with this assumptions we find R = 524 ± 84 after the pit for the highest measured power, violating the CS inequality by more than 6 standard deviations.
Finally, we measure the heralded auto-correlation of the signal photons after the pit: the signals are sent through the crystal, then split with a fiber BS and detected with two different SPDs. From the post-processed histogram ( fig. 4c of the main paper) we extract g (2) i:s,s (400 ns) = 0.06 ± 0.04 (pump power ∼ 1.7 mW). We know that the g (2) i:s,s is inversely proportional to g (2) s,i for two-mode squeezed states and low pump powers [47]. This is verified in our measurement, in fact the heralded auto-correlation is lower after the pit, where the crosscorrelation is higher. For a pump power of 1.7 mW, using g (2) s,s = 2 and the measured value for g (2) i,i , we find g (2) th i:s,s = g (2) s,s · g (2) i,i /g (2) s,i ∼ 0.06 which matches with the measured heralded auto-correlation.