Multifunctional on-chip storage at telecommunication wavelength for quantum networks

Quantum networks will enable a variety of applications, from secure communication and precision measurements to distributed quantum computing. Storing photonic qubits and controlling their frequency, bandwidth and retrieval time are important functionalities in future optical quantum networks. Here we demonstrate these functions using an ensemble of erbium ions in yttrium orthosilicate coupled to a silicon photonic resonator and controlled via on-chip electrodes. Light in the telecommunication C-band is stored, manipulated and retrieved using a dynamic atomic frequency comb protocol controlled by linear DC Stark shifts of the ion ensemble's transition frequencies. We demonstrate memory time control in a digital fashion in increments of 50 ns, frequency shifting by more than a pulse-width ($\pm39$ MHz), and a bandwidth increase by a factor of three, from 6 MHz to 18 MHz. Using on-chip electrodes, electric fields as high as 3 kV/cm were achieved with a low applied bias of 5 V, making this an appealing platform for rare earth ions, which experience Stark shifts of the order of 10 kHz/(V/cm).

In parallel with efforts to increase the efficiency [20] and storage time [18,19] of quantum memories, several works have focused on new types of multifunctional devices [24][25][26] in which control fields are used to modify the state of the light during storage.
In many quantum repeater protocols [27], quantum memories act as interfaces between emitters such as quantum dots [28] or individual atoms [7]. Dynamic control of the optical pulses stored in these memories can correct for differences between individual emitters, leading to higher indistinguishably for Bell State measurements at the entanglement swapping stage of quantum repeater protocols [1]. In addition, with control over the frequency of stored light, one can map an input mode to a different output mode in a frequency multiplexed quantum memory, which enables quantum networks with fixed-time quantum memories [29].
In this work, we use a silicon resonator evanescently coupled to 167 Er 3+ :Y 2 SiO 5 ions and gold electrodes to realize a multifunctional on-chip device which can not only store light, but also dynamically modify its frequency and bandwidth. Electrodes create a DC electric field that can be rapidly switched, which enables control of the 167 Er 3+ ions' optical transition frequency via the DC Stark shift [30]. Using a resonator increases the interaction between light and the ion ensemble, allowing on-chip implementation of the atomic frequency comb (AFC) memory protocol [31]. This protocol allows multiplexing in frequency, which offers a significant advantage in quantum repeater networks [32]. Additionally, the on-chip electrodes are patterned close together to achieve the high electric fields required for Stark shift control with CMOS compatible, applied voltages. We demonstrate dynamic control of memory time in a digital fashion, as well as modification of the frequency and bandwidth of stored light.
II. HYBRID αSi-167 Er 3+ :Y 2 SiO 5 RESONATOR WITH ELECTRODES The multifunctional device consists of an optical resonator coupled to 167 Er 3+ :Y 2 SiO 5 ions between gold electrodes. Using the AFC quantum storage protocol [34] and the ions' Stark shift, light can be stored and manipulated in this device. Figure 1a shows a schematic  Quality factors of up to 10 5 were measured for weakly coupled resonators, where the photonic crystal mirrors on both sides were designed to be highly reflective. The device used in this work is made one-sided for more efficient quantum storage [14,34] by using fewer photonic crystal periods in one mirror to make it less reflective. Light is sent into and measured from the side with the lower reflectivity mirror. The intrinsic quality factor for this device is also lower than the weakly coupled resonators, leading to a quality factor of 3 × 10 4 and a coupling ratio of κ in /κ = 0.2, where κ in is the coupling rate through the lower reflectivity mirror and κ is the total decay rate [35].
Electrodes are used to apply electric fields to those ions coupled to the optical resonator.
There are four independently biased gold electrodes, each comprised of a 70 µm diameter circle connected to a 20 µm × 60 µm rectangle. They are patterned onto the 167 Er 3+ :Y 2 SiO 5 after the αSi resonators using electron-beam lithography followed by electron-beam gold evaporation and lift-off. Figures 1e-g show simulations of the two electrode biasing configurations: parallel, which applies a nearly constant electric field to all ions (E(x) = a), and quadrupole, which applies an electric field gradient along the resonator (approximating , where a and b are constants. The electrode geometry was designed to best approximate these two electric field profiles with four independently biased electrodes, while providing a large electric field for a given applied bias (E/V ). In the 167 Er 3+ :Y 2 SiO 5 region where ions are coupled to the optical mode, the E y component of the electric field is domi- , and it does not vary significantly in the z and y directions. Therefore only E y (x), which is aligned to the b-axis of the Y 2 SiO 5 crystal, is considered.
The device is thermally connected to the coldest plate of a dilution refrigerator, the temperature of which is ∼ 100 mK. A static magnetic field of 0.98 T is applied along the Y 2 SiO 5 D 1 -axis with a superconducting electromagnet. Trim coils are used to cancel any magnetic field component along the b-axis. The remainder of the measurement setup was similar to the one described in Ref. [14].
Er 3+ :Y 2 SiO 5 has been extensively studied for quantum applications [4, 5, 7, 11-14, 36, 37], including demonstrations of AFC storage [11,12,14]. Erbium ions substitute for yttrium ions in Y 2 SiO 5 in 2 crystallographic sites, each of which has four different orientations due to the C 6 2h crystal symmetry [38]. In this work, we use crystallographic site 2, which has an optical transition near 1539 nm [4]. 167 Er 3+ has a nuclear spin I = 7/2, which together with an effective electron spin, leads to 16 hyperfine levels in both the optical ground and excited states. At high fields and low temperatures, the lowest 8 ground-state hyperfine levels are long-lived [8,14], enabling the spectral holeburning that is required to create atomic frequency combs. Dynamic control is enabled by the DC Stark shift. When a rare earth ion in a crystal interacts with a DC electric field E, its optical transition frequency is shifted due to the difference between the permanent electric dipole moments in the optical excited and optical ground states δ µ = µ e − µ g . For non-centrosymmetric sites such as the yttrium sites in Y 2 SiO 5 for which Er 3+ ions substitute, the linear Stark shift term δf = − 1 h δ µ ·L · E dominates, whereL is the local field correction tensor [30].
The Stark shift is dependent on the orientation of the applied field relative to δ µ [39].
Without knowing δ µ orL, the Stark shift can be empirically characterized for an electric field applied in a particular directionn using the Stark shift parameter sn given δf = snEn.
In an ensemble of 167 Er 3+ :Y 2 SiO 5 ions, four different Stark shifts will be observed for an arbitrary electric field due to the four orientations of each crystallographic site [38]. For electric fields parallel or perpendicular to the b-axis, the Stark shifts of the four subclasses are pair-wise degenerate, resulting in two equal and opposite Stark shifts δf ± = ±sE. In this work, all electric fields are applied parallel to the b-axis, so we will simply refer to two 167 Er 3+ subclasses.

TIME CONTROL
After a photon is absorbed by an ensemble of ions, the ensemble of ions is described by a Dicke state [34]: Each ion has a different transition frequency f j and position r j . For AFC storage, the transition frequencies {f j } form a frequency comb with period ∆. When a photon is absorbed at t = 0, the ensemble of ions first dephase then rephase every t = m ∆ , m ∈ N, leading to a coherent re-emission of the light [34]. A Stark shift δf j (t) enables dynamic control of light stored in the AFC by changing the optical transition frequencies of the ions. δf j (t) can be varied over time by changing the amplitude of the applied electric field (slowly relative to optical frequencies). This enables two types of control: electric field pulses applied between the absorption and emission of light modify the phase of the output, while electric field pulses applied during emission of light modify the frequency profile of the output light.
To achieve dynamic control of storage time, the electrodes are biased in a parallel configuration as shown in the top panel of Figure 1a. When an electric pulse is applied, the two 167 Er 3+ :Y 2 SiO 5 subclasses experience equal and opposite frequency shifts, ±δf (t) = ±s b E.
By appropriately choosing the length in time t and amplitude E of the electric pulse, a π phase difference between subclasses can be introduced π = 2π × (+s b E − (−s b E)) × t, which will prevent any coherent emission from the ensemble. An equal and opposite electric pulse can then rephase the two subclasses, and allows coherent re-emissions from the AFC. This procedure of dephasing and rephasing the ensemble works even if the electric field distribution is not perfectly homogeneous, as shown in the context of Stark Echo Modulation Memory in Reference [40]. Recently, dynamic control of memory time in AFC was demonstrated using this same procedure in Pr 3+ :Y 2 SiO 5 [41]. Reference [12] proposed a similar protocol but using an electric field gradient.
The pulse sequence used to achieve dynamic control of AFC storage is shown in Figure   2a. Not shown is the initialization to move most of the population into one hyperfine state, which is performed before every experiment [8,14]. First, an AFC with period ∆ is created by repeatedly burning away population between the teeth of the comb, n comb = 20 times.
Then, an input pulse indicated by the red laser pulse is sent into the resonator at t = 0 and is absorbed by the AFC. Shown in light red are possible emissions corresponding to rephasing events of the AFC at times t = m ∆ . Without electric field control, the output of the memory (the first and largest emission), would be centered at t = 1 ∆ (m = 1). The schematic shows instead an emission in red at t = 3 ∆ (m = 3), obtained when a first electric pulse is applied before the first emission and a compensating pulse is applied immediately before the third emission. Figure 2b shows the AFC used in this experiment. The period of the comb, extracted from the fit, is 19.7 ± 0.1 MHz, which corresponds to a minimum storage time of t = 1 ∆ = 50 ns. Figure 2c shows dynamically controlled storage for various values of m. Two electric pulses were used to control memory time. The first was a 10 ns long pulse with amplitude 2.0 kV/cm centered at t pulse 1 = 25 ns. The second was 10 ns long with an opposite amplitude of -2.0 kV/cm, and its center position was varied as t pulse 2 = 25 ns + (m − 1) × 50 ns to allow the emission at t memory = m ∆ . For the m = 1 case, no electric pulses were applied. Between the two electric pulses, emission was suppressed down to the dark counts level, a factor of 100 lower than peak emission counts. The presence of multiple smaller pulses following the output pulse is a feature of the high finesse and low efficiency of the memory (see Appendix B). For higher efficiency, high finesse AFCs, subsequent emissions are significantly suppressed [41]. Figure 2d shows the energy emitted in the m th time bin for t memory = m ∆ . The data is fit to the dephasing term in the theoretical storage efficiency for a comb with Gaussian teeth: [12,34], where F = ∆/γ is the comb finesse, and γ is the full-width at half

V. DYNAMIC FREQUENCY CONTROL
The frequency of light stored in an AFC can be dynamically modified during emission.
The atomic frequency comb is shifted in frequency during the emission of stored light by biasing the electrodes in the parallel configuration as shown in the middle panel of Figure   1a. The pulse sequence used to achieve AFC storage with frequency control is shown in Figure 3a. The first step is to eliminate one of the two 167 Er 3+ subclasses from the spectral window, leaving only ions which experience a positive Stark shift, δf + = +s b E (the choice of subclass is arbitrary). This is accomplished using a two-part comb burning procedure. With the first burning step, a normal AFC containing both subclasses is created using a sequence of laser pulses. For the second burning step, the two subclasses are split by ∆/2 using a parallel electric field, and a similar sequence of laser pulses is used, but with a frequency shift of ∆/4. This burns away ions with a negative shift δf − = −s b E.
Repeating the comb burning procedure n comb = 5 times, an AFC with width 145 MHz, and a period ∆ = 5 MHz is created. An input pulse is sent in and the rephasing of the

VI. DYNAMIC BANDWIDTH CONTROL
The bandwidth of stored light can be dynamically controlled by biasing the electrodes in a quadrupole configuration as shown in the bottom panel of Figure 1a. Figure 4a shows the pulse sequence used to achieve AFC storage with bandwidth control. First, an AFC with ∆ = 1.6 MHz and bandwidth 144 MHz is created by repeatedly burning away population n comb = 20 times. Next, an input pulse is sent into the device, leading to an output pulse at t = 1 ∆ = 630 ns. In the quadrupole configuration, electric pulses create a gradient electric field across the ions so that each ion experiences a different Stark shift. Electric pulses are applied during the input and output optical pulses, and also during the wait time. The first electric field pulse, applied during the absorption of the input pulse, and the third electric field pulse, applied during the emission of stored light, induce changes to the atomic frequency comb which lead to a change in the output light frequency profile. The second pulse during the wait time is used to add phase compensation, accounting for the fact that AFC storage is first-in-first-out [24,42].  Figure 4c shows the trend of output bandwidth as a function of the maximum electric field applied during the third pulse E max (the electric field across the resonator ranges from −E max to E max ). To confirm that the trend observed in the data is expected given the atomic frequency comb profile, the input pulse, and the electric field distribution E y (x), a simulation of the experiment was performed by numerically integrating the time-evolution equations of the atoms and cavity (see Appendix C). The simulation data reproduces the trend in FWHM as a function of field. The only previously unknown parameter used in this simulation was the distance that the optical mode penetrates into the photonic crystal mirrors, which modifies the effective resonator length and changes the value of E max . This parameter was found to be x eff = 6 µm for each mirror by coarsely sweeping x eff in 1 µm increments in the simulation to find the best fit to the data. 3 kV/cm are generated with just ±5 V of applied bias in the parallel configuration. Such biases were easily supplied by a function generator with no additional amplification. In the quadrupole configuration, electric field gradients of up to 50 V/cm/µm were generated, corresponding to gradient of 0.58 MHz/µm in 167 Er 3+ :Y 2 SiO 5 transition frequencies.
For the dynamically controlled memory times in Fig. 2d, an excellent match was found between the amplitude of stored light as a function of time and the theoretical limit due to the dephasing of a comb with finesse F = 12.2, indicating that the two electric field control pulses did not introduce any irreversible dephasing. This was also confirmed using a two pulse photon echo measurement, where inserting two equal and opposite electric field pulses between the first and second optical pulses was found not to decrease the optical coherence time T 2 , which was measured in this device to be 108 ± 13 µs.
Frequency control was demonstrated for up to ±39 MHz. In this work, the maximum shift was set by the maximum applied electric field of 3 kV/cm. One technical difficulty is that ions from the other subclass that are outside of the comb will act as an absorbing background when the comb is shifted in frequency and the other subclass experiences an opposite frequency shift. Assuming that the comb can be sufficiently separated in frequency from the other subclass using high electric fields, a more fundamental limit is set by the inhomogeneity of the Stark shifts, which leads to a decrease in storage efficiency with increasing frequency shift. In this device, the Stark shift inhomogeneity was dominated by an electric field distribution that was not perfectly homogeneous (see Fig. 1g). Even in a perfectly homogeneous field, however, some inhomogeneity in Stark shifts will exist due to crystal field variations throughout the crystal [30].
The bandwidth of stored light was changed by a factor of three from 6 MHz to 18 MHz.
The maximum broadening in this case was limited by the maximum electric field gradient of 50 V/cm/µm. With higher gradients, stored pulses could be broadened up to half the value of the bandwidth of the comb, and the bandwidth of combs in this material is limited to ∼ 150 MHz [14]. Decreasing the bandwidth of a stored pulse is not possible with this procedure, because the AFC cannot be made narrower with a gradient electric field, only wider. Narrowing the AFC could be accomplished with a frequency selective shift such as the AC Stark shift. Note that while digital memory time and frequency control theoretically do not affect the storage efficiency, the bandwidth control procedure has some associated loss. This is because the AFC rephasing does not always finish within the window defined by the third electric pulse, so the edges of the emitted pulse's temporal envelope are clipped.
An on-chip resonator allows for storage efficiencies approaching unity if the impedance matching condition is met [31]. In this device, the storage efficiency was up to 0.4%, depending on the finesse of the comb created, and was mainly limited by the low coupling between the ensemble of ions and the optical mode of the resonator, characterized by an ensemble cooperativity C < 1. The storage time on an optical transition is ultimately limited by the optical coherence time T 2 . However, in 167 Er 3+ :Y 2 SiO 5 , superhyperfine coupling to yttrium nuclear spins in the crystal prevents the creation of narrow spectral features, which means a low storage efficiency for storage times longer than ∼ 500 ns [14]. Superhyperfine coupling is a major limitation to high-efficiency long lived storage in 167 Er 3+ :Y 2 SiO 5 when using memory protocols based on spectral tailoring such as AFC.
For quantum repeater applications, the duration and efficiency of on-chip storage must be improved. Improvements to the intrinsic quality factor of the resonator are required to reach the impedance matching condition. Creative solutions such as using clock transitions in 167 Er 3+ :Y 2 SiO 5 [37,43,44], which are less sensitive to superhyperfine coupling, or finding new crystal hosts for erbium ions [45] can be used to overcome the superhyperfine limit.
Another requirement of quantum memories is to store quantum states of light with high fidelity. This has already been demonstrated with the AFC protocol [9]. Storage of weak coherent states using the AFC protocol with DC Stark shift control of storage time has also been recently demonstrated [41]. Future work should include demonstrations of on-chip storage of light at the quantum level with dynamic frequency and bandwidth control. More generally, this type of device could work with different absorbers that experience linear Stark shifts, or with other quantum storage protocols that do not require spectral tailoring such as Stark echo modulation memory [40].
The functionality of the device is not limited to the demonstrations in this work. For example, a gradient field could be used instead of a homogeneous field to dynamically control the storage time. The bandwidth or frequency of emissions at any time t = m ∆ could be modified, frequency and bandwidth control could be combined, and the order of two pulses could be reversed. A device which enables Stark shift control of an ion's transition frequency is useful for other technologies as well. For example, a gradient electric field could be used to tune two 167 Er 3+ ions coupled to the same resonator into resonance with one another. This would enable entangling gates between the two ions, a key step in quantum repeater protocols using single ions [46].

VIII. CONCLUSION
In this work we demonstrated a multifunctional on-chip device that can store light while  The Stark shift parameter for electric fields applied along the Y 2 SiO 5 crystal b-axis was estimated in the same device using spectral holeburning with electrodes biased in the parallel configuration (see Fig. 1e). A comb consisting of four narrow teeth 27.5 MHz apart was created in the 167 Er 3+ :Y 2 SiO 5 optical transition. The frequency profile of the transition was then measured while a variable electric field was applied, which led to a field-dependent twofold splitting of each tooth, as shown in Figure 5a. This splitting results from the equal and opposite Stark shifts experienced by the two subclasses of 167 Er 3+ :Y 2 SiO 5 ions δf ± = ±s b E. Figure 5b shows the observed splitting as a function of electric field. The slope of the straight-line fit is 2s b , from which s b = 11.8 ± 0.2 kHz/(V/cm) is extracted. This uncertainty does not take into account any misalignment between the electric field and the b-axis. To align E y to the b-axis, the device coordinate axes (x and y) were visually aligned to the Y 2 SiO 5 chip edges (b and D 2 crystal axes), with an estimated error of < 5 • . The following section expands upon the analysis by Afzelius et al. in References [31,34] to consider multiple emissions. An ensemble of ions is coupled to a cavity with field decay rate κ. An AFC is created in this ensemble of ions, which leads ion distribution to be n(ω), where n(ω)dω = N , and N is the number of ions. Each ion has a detuning ω relative to cavity center frequency, coherent decay rate γ h , and ion-cavity coupling rate g. After sending a photon into the cavity that is resonant with it, the dynamic equations [31,47] of cavity field E and atomic polarization σ ω in the rotating frame of photon frequency arė σ ω = −(iω + γ h )σ ω + igE.

(B2)
The input output formalism gives where κ in is the cavity decay rate to the input channel. We can solve Eq. (B2) and get Then, inserting Eq. (B4) into Eq. (B1), we finḋ where n(t) is the Fourier transform of n(ω) [34].
We have an atomic frequency comb with period ∆, and each tooth has a shape described by f (ω), so n(ω) can be written as The Fourier transform of n(ω) is n(t): Inserting Eq. (B7) into Eq. (B5), we finḋ where Γ comb is the absorption rate of atomic frequency comb [14], and Γ comb ∝ g 2 .
Consider the time after the ensemble of ions absorb the light (t > 0). There are no input pulses after t = 0, so E in (t > 0) = 0. Applying adiabatic elimination of the cavity mode (Ė(t) = 0) leads to The cavity field at time t = m ∆ goes as From this, we can see that the amplitude of the cavity field at time t = m ∆ is determined by the cavity field at all earlier times t = k ∆ , where k = 0, 1, ..., m − 1. We can theoretically find the amplitude of the cavity field at any time, which depends on how we modulate the cavity field at previous times. In our case, γ h is much smaller than the teeth width [14], so we can ignore the term e −γ h k ∆ . We assume each tooth has Gaussian shape, which gives where γ is the FWHM of the Gaussian peak, and F = ∆/γ as we defined in the main text, We also know from Eq. (B3) that the amplitude of the k th emission (for k > 0) is At time t = 0 we have From the above three equations, the emission at time t = m ∆ has the following amplitude The m th emission is the sum of 1 st to (m − 1) th emission and the input. In the case where we don't apply electric fields to prevent any emissions, the first and second emitted field amplitudes are As Eq. (B17) shows, the amplitude of the second emission is composed of two parts. The first part is from the light absorbed at t = 0, and the second part is from the light reabsorbed at the first emission time t = 1/∆. The competition between these two terms determines the amplitude and the phase of the output at t = 2 ∆ . When we operate in the high finesse regime (since we always want the dephasing term exp − π 2 2ln2 1 F 2 to be close to 1), if the amplitude of the first output is small, the amplitude of the second output will be dominated by the first term in Eq. (B17), so it will still have an observable amplitude. If the amplitude of the first output is high, the amplitude of the second output will be small due to the minus sign between the two terms in Eq. (B17). In particular, when the impedance matching condition [31] holds where 2Γ comb κ+Γ comb → 1, the second emission will be zero. This trend also holds for higher order emissions, as can be seen by extending the analysis of Eq. (B15. In the case where we apply an electric field to kill all the lower order emissions (from 1 to m − 1), we find the m th output amplitude to be Then, we can find the efficiency of the m th output pulse to be form of Eq. (B1) and Eq. (B2) for the cavity field E and the atomic polarization σ i of a number n of ions in the rotating frame, following Reference [48]: where ∆ω a is the cavity detuning and ∆ω i (t) is the detuning of each ion, which can vary in time as a function of applied electric field at the location of the ion ∆ω i (t) = ∆ω i,0 ± sE y (x i , t). ∆ω i,0 is the detuning of each ion in the absence of an applied electric field and the ± sign depends on which subclass the ion is in. The cavity field is coupled to external fields as described by input-output formalism (see Equation B3). The initial conditions are E(0) = 0, σ i (0) = 0.
For the simulation, a system of n + 1 differential equations (Equations C2 and C1) are numerically solved. To keep the number of equations to a reasonable size, the number of ions simulated n ∼ 10 4 is significantly smaller than the true number of ions coupled to the cavity ∼ 10 7 . To accurately represent the strength of the interaction between the ion ensemble and the cavity, g in the simulation is chosen such that g 2 total = ng 2 , where g total = 2π × 0.6 GHz is measured from the cavity reflectance curve [14]. The time-independent frequency distribution of the ions (frequency comb) is described as a continuous distribution, and n values of ∆ω i,0 are sampled from it. A time dependent scalar ±sE y (x i , t) representing the Stark shift is added to all ion detunings. E y (x i , t) for each ion is given by randomly sampling the x-position along the resonator, and obtaining the corresponding electric field from Figure   1g, then varying it in amplitude and time to represent each electric pulse.
Using this simulation, the output pulse profile E out (t) can be computed given E in (t), the input pulse profile centered around t = 0, and certain set of electric field control pulses. [2] H. J. Kimble, The quantum internet, Nature 453, 1023 (2008).