1. INTRODUCTION

Implementing solid-state quantum storage devices with guided wave optics has several advantages, such as compactness, scalability, efficiency due to enhanced light–matter 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 quantum light storage in ${\mathrm{Tm}}^{3+}$ or ${\mathrm{Er}}^{3+}$ in ${\mathrm{LiNbO}}_3$ waveguides [7,8] and storage with optically controlled retrieval of weak coherent states in a nanophotonic crystal cavity in ${\mathrm{Nd}}^{3+}\text{:}{\mathrm{YVO}}_4$ [9]. In these remarkable realizations, the ions used do not offer the possibility of storage at the ground state, thus, the storage times are inherently limited by the lifetime of the excited state (further shortened in the case of the nanophotonic crystals by the Purcell enhancement in the cavity). Photon echoes and long spin-state lifetimes have been observed in a hybrid integrated system [10] composed by a ${\mathrm{TeO}}_2$ slab waveguide deposited onto a ${\mathrm{Pr}}^{3+}{\text{:}\mathrm{Y}}_2{\mathrm{SiO}}_5$ substrate that potentially enables efficient [11] and long-lived storage with on-demand read-out [12]. This solution, nonetheless, sacrifices the enhancement of the light–matter interaction, as the coupling between the guided wave optics, the ${\mathrm{TeO}}_2$ waveguide, and the optically active ${\mathrm{Pr}}^{3+}$ ions happens through the evanescent field.

Optical channel waveguides can be also fabricated in the bulk of crystalline substrates by femtosecond (fs) laser micromachining (FLM). This powerful technique is rapid, cost-effective, and features unique three-dimensional fabrication capabilities. Different writing regimes can be adopted [13]. One possibility consists of 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 a type II waveguide. Another possibility, substantially different from the previous one, consists of directly writing 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 [14–16]. Type II waveguides have also been recently fabricated in ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ 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, since it requires finding a very narrow processing parameter window, if any. So far, this fabrication regime has been demonstrated only in a very limited number of cases [18–20], including lithium niobate [21–23], potassium dihydrogen phosphate (KDP) [24], and polycrystalline matrices [25,26].

In the present paper, we report on the realization of type I waveguides in a ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal, and we characterize the light guiding properties at 606 nm, where ${\mathrm{Pr}}^{3+}$ features an optical transition of interest for photonic storage purposes. The small dimensions of the waveguide modes guarantee the compatibility with optical fibers and a significant enhancement of the light–matter interaction. Moreover, spectroscopic investigations reveal that the fabrication does not affect the optical properties of ${\mathrm{Pr}}^{3+}$ 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 100 times longer than in previous experiments with single photons in waveguides [7,8].

2. NEW WAVEGUIDE WRITING REGIME IN ${\mathrm{Pr}}^{3\mathbf{+}}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$

A. Fabrication of Type I Waveguides

Type I waveguides have been directly written by FLM in the volume of a ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ 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 a duration of 350 fs. The waveguides are written in a single transverse scan geometry with the laser beam propagating along the crystal ${\mathrm{D}}_1$ 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, giving a total fabrication time of $\approx 40\mathrm{s}$ for a single waveguide. These waveguides support a single optical mode at the wavelength of 606 nm, polarized along the crystal ${\mathrm{D}}_2$ 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 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. [27]) as $\mathrm{\Delta }n\approx 1.6\times {10}^{-3}$. As type I waveguides in crystals are often thermally unstable [23], it is worth mentioning that no visible degradation of our type I waveguides in ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ 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 ${\mathrm{LiNbO}}_3$ and $\mathrm{Nd}\text{:}\mathrm{Y}{\mathrm{Ca}}_4\mathrm{O}{({\mathrm{BO}}_3)}_3$ (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 [19,21]. 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 ${\mathrm{LiNbO}}_3$ [22]. Regarding type I waveguides in ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$, a fundamental explanation of the origin of the positive index change induced by ultrafast laser irradiation is still under investigation.

B. Benchmarking Type I versus Type II Waveguides

An experimental characterization was performed for comparing the guiding properties of type I and type II waveguides fabricated in ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$. 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 to 20 μm. It should be noted that the chosen irradiation parameters provide the best waveguiding properties for all values of $d$. Values of $d\ge 25\mathrm{\mu m}$ led to multimode behavior.

We coupled all waveguides with light at 633 nm from a He–Ne source polarized along the ${\mathrm{D}}_2$ crystal axis by means of a plano-convex lens (75 mm focal length, 1 in. 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 (40 times, 0.65 NA). In this way, we were able to acquire with a CCD camera the normalized mode intensity profile of all waveguides, reported in Fig. 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 full width at half-maximum (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 ($3.1\mathrm{\mu m}\times 5.9\mathrm{\mu m}$ FWHM diameters) 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 $d$. A more detailed analysis of the different contributions to the waveguide IL can be found in Supplement 1.

 

Fig. 1. (a) Optical microscope image of the waveguide transverse cross section (top row) and guided mode intensity profile (bottom row) of all fabricated waveguides. The numbers above the figures specify the separation between the laser tracks in type II waveguides. Scale bar is 10 μm. (b) Insertion losses versus FWHM mode diameter in the horizontal direction for type I (blue circle) and type II (black squares) waveguides. (c) Microscope picture of the longitudinal profile of a type I (top) and a type II waveguide with $d=10\mathrm{\mu m}$ (bottom). Scale bar is 20 μm. (d) Bending losses as a function of the radius of curvature for type I (blue circles) and type II (black squares) waveguides. Dashed lines are best exponential fits of experimental data [28]. Error bars in plots (b) and (d) are smaller than the data markers.

Download Full Size | PDF

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 ${\mathrm{R}}_C$. We performed this measurement for values of ${\mathrm{R}}_C$ of 30, 50, and 90 mm, both on the type I and type II waveguides with $d=20\mathrm{\mu m}$, fabricated in a dedicated sample (S-band $\text{length}=7\mathrm{mm}$, total sample $\text{length}=9\mathrm{mm}$). The results obtained are shown in Fig. 1(d). As expected, the values of BL increase for shorter ${\mathrm{R}}_C$ for both types. However, in type I, the measured BL reach particularly low values and become almost negligible for ${\mathrm{R}}_C>90\mathrm{mm}$. This outcome agrees with the well known fact that BL decrease in more confining waveguides [28].

This experimental analysis allows us to conclude that type I waveguides in ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ show better guiding performances than their type II counterparts, both in terms of waveguide losses and in terms of light confinement. Interestingly, the measured values of BL for type I waveguides are compatible with the fabrication of complex integrated devices, i.e., directional couplers or waveguide arrays, as bending radii in the order of tens of millimeters (mm) allow for a flexible engineering of evanescent waveguide coupling, even in samples with a limited length.

3. EXPERIMENTAL SETUP

Figure 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 ${\mathrm{Pr}}^{3+}$ involved in the optical transition relevant for the storage (inset). Note that we address only ions in one of the two possible crystallographic sites (site 1).

 

Fig. 2. Setup: a pump laser at 426 nm (blue beam) shines a periodically poled lithium niobate (PPLN) crystal in a bow-tie cavity. Photon pairs (gray beam) are generated by spontaneous parametric down-conversion and divided with a dichroic mirror (DM). The idler photon at 1436 nm (purple beam) is sent to a filter cavity (FC). The signal photon at 606 nm (orange beam) passes through an etalon and enters input 2 of a fiber beam-splitter (BS). Two chopper wheels are used to alternate between locking and the measurement period. The signal photon and the preparation light (from input 1 of the BS) emerging from one output of the BS are coupled into the ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ waveguide. The hyperfine splitting of the first sublevels of the ground ${}^3{\mathrm{H}}_4$ and the excited ${}^1{\mathrm{D}}_2$ manifolds of Pr ions in ${\mathrm{Y}}_2{\mathrm{SiO}}_5$ is shown in the inset along with the optical absorption spectrum (the data points are experimental values and the solid curve the Gaussian fit). The orange arrows highlight the specific transition chosen for the storage protocol.

Download Full Size | PDF

A CW laser at 606 nm (linewidth 20 kHz) is modulated with acousto-optic modulators (AOMs) in double-pass 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 ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ 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 $<10\mathrm{\mu m}$ 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 auto-correlation measurements, a Hanbury Brown–Twiss setup is assembled with fiber BSs and additional SPDs. All of the experiments are synchronized with the cycle of the cryostat (1.4 Hz). Because of vibrations, the light is efficiently coupled in the waveguide for less than 300 ms in each cycle. Further details on the setup can be found in Supplement 1 [29].

Our heralded single photons are created with a new generation [30] of the photon pair source described in Refs. [31,32]. It is based on cavity-enhanced type I spontaneous parametric down-conversion (SPDC) in a 2-cm-long 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 [32], and two mechanical choppers are used to alternate between the locking period and the single-photon measurement. The two collinearly generated photons are separated after the BTC using a dichroic mirror (DM, Fig. 2). The signal and idler photons are distributed in eight spectral modes. The idler photons pass through a home-made Fabry–Perot filter cavity [FC, Fig. 2, linewidth 80 MHz, free spectral range $(\mathrm{FSR})=17\mathrm{GHz}$] 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 input 2 of the fiber BS. The heralding efficiency of the SPDC source is ${\eta }_H^{\mathrm{SPDC}}\sim 25\%$ after the PM fiber and ${\eta }_H^{\mathrm{WG}}\sim 7\%$ in front of the waveguide. The loss is due to the BS and mode–diameter mismatch between the PM fiber and the fiber BS and could be readily reduced by using a fiber switch.

4. SPECTROSCOPIC AND COHERENCE MEASUREMENTS

The inhomogeneous broadening of the transition of ${\mathrm{Pr}}^{3+}$ 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 FWHM is $\sim 9\mathrm{GHz}$ in optical depth (OD, see inset in Fig. 2), which is 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. [33], 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 also be maintained. Coherence and lifetime of the optical transition are measured by means of, respectively, two-pulse [34] and three-pulse stimulated photon echo [35] 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 the 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 ${\tau }_2$ [Fig. 3(a)], we extract the coherence time of the ${\mathrm{Pr}}^{3+}$ ions in the waveguide. Figure 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 $T_2=57\pm 10\mathrm{\mu s}$. This is only slightly lower than the maximal $T_2$ measured in bulk samples or type II waveguides [17]. We note, however, that $T_2$ is affected by instantaneous spectral diffusion and that higher values could in principle be achieved by decreasing the average number of atoms excited [17].

 

Fig. 3. (a) Decay in the echo intensity for a two-photon echo pulse measurement, from which we extract the optical transition coherence time $T_2$ in the type I waveguide. The black solid line is the fit to an exponential decay, and the dotted lines indicate the error. The inset shows the temporal sequence used. The time interval between the first and second pulses is called ${\tau }_2$ (solid arrow). (b) Examples of heterodyne detected TPE at different times ${\tau }_2$. The solid orange line is the experimental signal, and the dotted black line the sinusoidal fit. The echo intensity is proportional to the square of the oscillation amplitude. (c) Area of the stimulated photon echo (SPE) in arbitrary units, varying the times ${\tau }_1$ and ${\tau }_2$; (d) temporal trace of the SPE process. The SPE signal is highlighted by the orange area. The time interval between the second and third pulses is called ${\tau }_1$ (dotted arrow); (e) values of the SPE areas at ${\tau }_2=0$ (extracted from the exponential decays of the SPE areas over ${\tau }_2$) plotted as a function of ${\tau }_1$. From the decay of the SPE versus ${\tau }_1$ (for ${\tau }_2=0$), we extract the excited-state lifetime of the ions, $T_1$; (f) homogeneous broadening of the optical transition for increasing ${\tau }_1$. The values are extracted from the decays of the SPE versus ${\tau }_2$ for different ${\tau }_1$ values. The black solid line is the value extracted from the $T_2$ measurement for ${\tau }_1=0$ with the dashed lines indicating the error.

Download Full Size | PDF

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 Fig. 3(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 ${\tau }_2$ for different values of ${\tau }_1$. By fitting these decays with exponentials, we extract the expected areas of the $\mathrm{SPE}({\tau }_1)$ for ${\tau }_2=0$ [Fig. 3(e)]. Their decay with ${\tau }_1$ directly depends on the lifetime of the excited state $|e⟩$, namely, $T_1=118\pm 35\mathrm{\mu s}$. This value is lower than that obtained from fluorescence measurements (about 160 μs) but in good agreement with that measured with SPE in the same bulk sample, $T_1=103\pm 11\mathrm{\mu s}$. In the 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 ${\mathrm{\Gamma }}_{\mathrm{hom}}$ for increasing ${\tau }_1$ [36]. As we can clearly see from Fig. 3(f), ${\mathrm{\Gamma }}_{\mathrm{hom}}({\tau }_1)=1/[\pi T_2({\tau }_1)]$ remains consistent over time with the value at ${\tau }_1=0$ (solid line, about 10 kHz), proving the absence of spectral diffusion in the analyzed timescale and excitation power. 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 ${\mathrm{\Omega }}_R$ of the optical transition by means of optical nutation [37]. We prepare by optical pumping a single-class absorption feature on the $1/2g-3/2e$ transition and measuring the population inversion time $t_{\pi }$ induced by a long resonant probe pulse. For an optically dense and inhomogeneously broadened ensemble, the Rabi frequency ${\mathrm{\Omega }}_R$ is calculated as ${\mathrm{\Omega }}_R{t}_{\pi }=5.1$ [from Eq. (1) in Ref. [37]]. We repeat the measurement for several probe powers $P$. From the linear fit of ${\mathrm{\Omega }}_R$ versus $\sqrt{P}$, we extract ${\mathrm{\Omega }}_R=2\pi \times 1.75\mathrm{MHz}/\sqrt{\mathrm{mW}}$, 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 (further details can be found in Supplement 1 [29]).

5. STORAGE OF HERALDED SINGLE PHOTONS

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 Supplement 1 [29]). We build a coincidence histogram using the idler detection as the start and the signal photon as the stop [inset in Fig. 4(a)]. The correlation time of our biphoton is estimated by fitting the histogram [32] (black dashed lines) as 121 ns, which corresponds to a biphoton linewidth of $\mathrm{\Gamma }=1.8\mathrm{MHz}$. This is smaller than the hyperfine splitting of the excited state, thus narrow enough to address a single transition of ${\mathrm{Pr}}^{3+}$ ions. We calculate the normalized second-order cross-correlation function as $g_{s,i}^{(2)}(\mathrm{\Delta }t)=p_{s,i}/(p_s·p_i)$, where $p_{s,i}$ is the probability to detect a coincidence in a temporal window $\mathrm{\Delta }t$, while $p_s$ ($p_i$) is the probability to detect a signal (idler) count in a temporal window of the same size. The measured $g_{s,i}^{(2)}$ values for a window $\mathrm{\Delta }t=400\mathrm{ns}$ for different pump powers are plotted in Fig. 4(a) (empty orange circles). The highest value $g_{s,i}^{(2)}(400\mathrm{ns})=209\pm 9$ 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 [38].

 

Fig. 4. (a) Measured $g_{s,i}^{(2)}$ 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 $g_{s,i}^{(2)}$ (400 ns), and the black dashed line is the temporal fit of the biphoton correlation; (b), (c) coincidences between signal photons split 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.

Download Full Size | PDF

We demonstrate the quantum nature of the signal–idler correlations violating the Cauchy-Schwartz (CS) inequality by more than 20 standard deviations (see Ref. [29] for details). The classical bound is set by the parameter $R=\frac{{(g_{s,i}^{(2)})}^2}{g_{s,s}^{(2)}{g}_{i,i}^{(2)}}\le 1$, where $g_{s,s}^{(2)}$ and $g_{i,i}^{(2)}$ 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 $g_{i\text{:}s,s}^{(2)}(\mathrm{\Delta }t)$. This can be extracted from the histogram of Fig. 4(b), built like in Ref. [32,39]. We find $g_{i\text{:}s,s}^{(2)}(400\mathrm{ns})=0.12\pm 0.01$ for a pump power of 1.7 mW. This value is considerably lower than the classical bound $g_{i\text{:}s,s}^{(2)}\ge 1$ and compatible with the single-photon behavior ($g_{i\text{:}s,s}^{(2)}\le 0.5$) [29].

We then send the signal photons through the waveguide, where we hole-burn a transparency window (pit) of $\sim 16\mathrm{MHz}$ in the inhomogeneously broadened absorption profile of the ions [orange line in the inset of Fig. 5(a)]. We measure the $g_{s,i}^{(2)}$ versus 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 the crystal acts as a spectral filter: the pit selects a single frequency mode, while all of the others are absorbed by the ${\mathrm{Pr}}^{3+}$ ions spread over the whole inhomogeneously broadened absorption line [40–42]. We find $R=524\pm 84$ after the pit for the highest measured power, violating the CS inequality by more than 6 standard deviations (assuming $g_{s,s}^{(2)}=2$). Furthermore, we measure the $g_{i\text{:}s,s}^{(2)}(\mathrm{\Delta }t)$ of the signal photons after the pit: from the histogram of Fig. 4(c), we extract $g_{i\text{:}s,s}^{(2)}(400\mathrm{ns})=0.06\pm 0.04$ (pump power $\sim 1.7\mathrm{mW}$).

 

Fig. 5. (a) Time-resolved histogram of the idler–signal coincidences for signal photons passing through the pit (gray histogram) or the AFC for $\tau =1.5\mathrm{\mu s}$ (orange histogram). The counts in the AFC are multiplied by three. The darker regions of the peaks show the windows considered for ${\eta }_{\mathrm{AFC}}$ and $g_{s,i}^{(2)}$ 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 Ref. [29]); (b) internal storage efficiency ${\eta }_{\mathrm{AFC}}$ at different storage times $\tau$ 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 $g_{\mathrm{AFC},i}^{(2)}$ for different $\tau$. The orange dashed line is the classical upper bound $\sqrt{g_{s,s}^{(2)}·g_{i,i}^{(2)}}=1.58\pm 0.02$ (assuming $g_{s,s}^{(2)}=2$).

Download Full Size | PDF

B. Storage of Heralded Single Photons

The storage protocol that we use is called atomic frequency comb (AFC) [43]: the inhomogeneously broadened absorption of the ions is shaped in a spectral comb with periodicity $\mathrm{\Delta }$. When a photon is absorbed by the comb, its state is mapped onto a collective excitation of atoms, described by a collective Dicke state: $\sum _k{e}^{-i2\pi {\delta }_{k}t}{c}_k|g_1\cdots e_k\cdots g_N⟩$, where the frequency detuning of the atom $k$ is ${\delta }_k=m_k\mathrm{\Delta }$ (being an integer number $m_k$). After a first inhomogeneous dephasing, the atoms will collectively rephase at a predetermined time $\tau =1/\mathrm{\Delta }$, giving rise to a photon re-emission in the forward direction, called AFC echo.

The sequence of optical pulses used to create the AFC is very similar to the one explained in Refs. [44,45]: 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 $\sim 80\mathrm{ms}$). 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 $\sim 35\mathrm{ms}$). 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 Ref. [29] for details on the biphoton spectrum). Thanks to the enhanced light–ions interaction, the maximum power that we inject in the waveguide during the AFC creation is $\sim 100\mathrm{\mu W}$, i.e., two orders of magnitude lower than what is usually necessary in bulk, in agreement with the ${\mathrm{\Omega }}_R$ increase. The measurement is performed in the remaining time ($\sim 150\mathrm{ms}$), resulting in a duty cycle for the AFC storage of $\sim 21\%$ (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 [29]. The minimum response time of this gate is $t_{\mathrm{P}}^{\mathrm{off}}=1.2\mathrm{\mu s}$, which limits our minimum storage time to $\tau =1.5\mathrm{\mu s}$. For longer storage times, $t_{\mathrm{P}}^{\mathrm{off}}$ is delayed in order to maintain $\tau -t_{\mathrm{P}}^{\mathrm{off}}=0.3\mathrm{\mu s}$. The AFC echo for a storage time $\tau =1.5\mathrm{\mu s}$ 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 latter normalized by the transmission through the pit [85%, see inset in Fig. 5(a)]. The resulting efficiency is the internal efficiency of the process ${\eta }_{\mathrm{AFC}}$. The total efficiency of our device, i.e., the ratio between the output signal and the input signal before entering the waveguide, is calculated multiplying ${\eta }_{\mathrm{AFC}}$ by the coupling into the waveguide ($\sim 40\%$). 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 increasing $\tau$ is fitted with an exponential decay $e^{-4/(T_2^{*}\mathrm{\Delta })}$ [45], from which we extract the effective coherence time of our storage protocol $T_2^{*}=8\mathrm{\mu s}$, which is much smaller than $T_2$ (see Section 4). This suggests that our storage time is at the moment limited by technical issues and not yet by the coherence time $T_2$ of the ${\mathrm{Pr}}^{3+}$ in the waveguide. We estimate that a factor of 2 could be given by instantaneous spectral diffusion because, due to the time limit imposed by the cryostat cycle, we implement the optical pumping for the AFC preparation with relatively high power. The remaining mismatch between $T_2^{*}$ and $T_2$ is likely due to the finite laser linewidth (see Section 3) and power broadening.

The $g_{\mathrm{AFC},i}^{(2)}$ 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 ${\eta }_{\mathrm{AFC}}$); $p_s·p_i$ is measured integrating the accidental coincidences after the AFC echo up to the last stored noise count $t_{\mathrm{P}}^{\mathrm{off}}+\tau$ [light orange rectangle in Fig. 5(a)], renormalized to a 400 ns window. Figure 5(c) shows the $g_{\mathrm{AFC},i}^{(2)}$ values for AFC echoes measured at different $\tau$. The cross-correlation increases after the storage up to $61\pm 12$ for a storage time of 1.5 μs with respect to $36\pm 3$ after the pit. This could be explained by the presence of broadband noise from the SPDC source, which is not in resonance with the inhomogeneous absorption line of the ${\mathrm{Pr}}^{3+}$ 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 $g_{\mathrm{AFC},i}^{(2)}$ should remain constant for different $\tau$, as the storage efficiency is the same for the AFC echo and for the stored noise. But for longer storage times, as ${\eta }_{\mathrm{AFC}}$ decreases, our signal-to-noise ratio is limited by the background noise. Nevertheless, the $g_{\mathrm{AFC},i}^{(2)}$ remains higher than the classical bound (orange dashed line) for all the measured storage times up to $\tau =5.5\mathrm{\mu s}$, for which we violate the CS inequality with $R=34\pm 18$ (above the classical bound by almost 2 standard deviations), effectively demonstrating the longest quantum storage in an integrated solid-state optical memory (100 times longer than the previous demonstrations of single-photon storage in waveguides [7,8]). Moreover, thanks to the convenient energy level scheme, our system enables the full spin-wave AFC storage, thus giving access to both longer storage times and on-demand read-out [44,46,47].

6. 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 ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal using FLM in a new writing regime. We showed that the fabrication of type I waveguides preserves the measured spectroscopic properties of ${\mathrm{Pr}}^{3+}$. We implemented a quantum storage protocol for heralded single photons, observing high non-classical correlations for storage times 100 times longer than in previous waveguide demonstrations. The use of type I waveguides in ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ gives several advantages with respect to type II ones. In type I waveguides, the guided mode is in general sensibly smaller than what is 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 the ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ samples directly to fiber patch cords with low coupling losses, sensibly simplifying the procedure of light coupling inside the cryostat and avoiding the temporal constraints on the photon storage given by the cryostat vibrations. High-quality type I waveguides will also allow us to produce linear cavities with high-quality factors by directly writing Bragg gratings superimposed to the waveguide [48]. In addition, type I waveguides in ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ 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 [49] embedding quantum memories. Remarkably, taking advantage of the intrinsic three-dimensional capabilities of FLM, one can envision high spatial multiplexing by an efficient exploitation of the substrate volume with matrices of quantum memories interconnected to linear fiber arrays by glass circuits. Finally, for this kind of waveguide, 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 us to easily inscribe optical circuits in ${\mathrm{Pr}}^{3+}\text{:}{\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystals embedding directional couplers and other integrated optics devices, for performing complex tasks besides quantum light storage, fully on-chip.