Multifunctional on-chip storage at telecommunication wavelength for quantum networks

Optical quantum memories will enable long distance quantum communication using quantum repeater protocols [1, 2, 3]. A quantum memory device which can control the bandwidth and frequency of stored light is additionally useful, as it can interface between optical elements which have different optimal operating points. Erbium-doped materials are a promising solid-state platform for ensemble-based optical quantum memories because of their long-lived optical transition in the telecommunication C-band that is highly coherent at cryogenic temperatures [4, 5]. This allows for integration of memory systems with low-loss optical fibers, opening up opportunities for repeaters over continental distances, as well as integration with silicon photonics [6, 7] one of the most advanced platforms for integrated photonics. Spin transitions in ¹⁶⁷Er³⁺-doped yttrium orthosilicate (¹⁶⁷Er³⁺:Y₂SiO₅) have also been shown to have long relaxation and coherence lifetimes at cryogenic temperatures and high magnetic fields [8] which opens the possibility for long term spin wave memories.

There have been several demonstrations of optical storage in erbium-doped materials [9, 10, 11, 12, 13, 14], including storage at the quantum level [9, 10, 14], and on-chip storage [10, 14]. These results are part of a larger body of optical quantum memory research [15, 3], using rare-earth-ion-doped crystals [16, 17, 18, 19], atomic gases [20, 21], and single atoms or defects [22, 23]. In parallel with efforts to increase the efficiency [20] and storage time [19, 18] 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 ¹⁶⁷Er³⁺:Y₂SiO₅ 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 ¹⁶⁷Er³⁺ 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.

The multifunctional device consists of an optical resonator coupled to ¹⁶⁷Er³⁺:Y₂SiO₅ 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 of the device and the three functionalities demonstrated in this work: memory time control, frequency control, and bandwidth control. Different electric field configurations are created by applying a positive (blue) or negative (red) bias to each electrode. For the true device dimensions, see the micrograph in Fig. 1h.

The optical resonator used in this work is a Fabry-Perot resonator comprised of a 100 $\mu$m amorphous silicon ($\alpha$Si) waveguide on ¹⁶⁷Er³⁺:Y₂SiO₅ with photonic crystal mirrors on either end. Figures 1b-d show simulations and micrographs of this resonator. The waveguide is $h=310$ nm tall and $w=605$ nm wide. Ten percent of the energy of the transverse-magnetic optical waveguide mode penetrates into the ¹⁶⁷Er³⁺:Y₂SiO₅ and evanescently couples to the ¹⁶⁷Er³⁺ ions. Photonic crystal mirrors on either side are formed by a repeating pattern of elliptical air holes in the $\alpha$Si waveguide with period $a_{\circ}=370$ nm. A grating coupler is used to couple light from a free-space mode into and out of the resonator. The amorphous silicon resonator is fabricated on top of an ¹⁶⁷Er³⁺:Y₂SiO₅ chip using a deposition and etching process similar to Ref. [6]. The ¹⁶⁷Er³⁺:Y₂SiO₅ substrate is doped with isotopically purified ¹⁶⁷Er³⁺ ions at 135 ppm, measured by secondary ion mass spectrometry, and cut perpendicular to the $D_{1}$ crystal axis, such that the electric field of the transversal magnetic (TM) optical mode is polarized along this axis.

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 [34, 14] 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 $3\times 10^{4}$ and a coupling ratio of $\kappa_{\mathrm{in}}/\kappa=0.2$, where $\kappa_{\mathrm{in}}$ is the coupling rate through the lower reflectivity mirror and $\kappa$ 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 $\mu$m diameter circle connected to a $20\>\mu\mathrm{m}\times 60\>\mu\mathrm{m}$ rectangle. They are patterned onto the ¹⁶⁷Er³⁺:Y₂SiO₅ after the $\alpha$Si 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 $\frac{\mathrm{d}E(x)}{\mathrm{d}x}=b$), 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 ¹⁶⁷Er³⁺:Y₂SiO₅ region where ions are coupled to the optical mode, the $E_{y}$ component of the electric field is dominant ($E_{y}\gg E_{x},E_{z}$), 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 Y₂SiO₅ crystal, is considered.

The device is thermally connected to the coldest plate of a dilution refrigerator, the temperature of which is $\sim 100$ mK. A static magnetic field of 0.98 T is applied along the Y₂SiO₅ $D_{1}$-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].

Er³⁺:Y₂SiO₅ has been extensively studied for quantum applications [4, 5, 36, 11, 12, 13, 7, 14, 37], including demonstrations of AFC storage [11, 12, 14]. Erbium ions substitute for yttrium ions in Y₂SiO₅ 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]. ¹⁶⁷Er³⁺ 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 $\vec{E}$, its optical transition frequency is shifted due to the difference between the permanent electric dipole moments in the optical excited and optical ground states $\delta\vec{\mu}=\vec{\mu}_{\mathrm{e}}-\vec{\mu}_{\mathrm{g}}$. For non-centrosymmetric sites such as the yttrium sites in Y₂SiO₅ for which Er³⁺ ions substitute, the linear Stark shift term $\delta f=-\frac{1}{h}\,\delta\vec{\mu}\cdot\hat{L}\cdot\vec{E}$ dominates, where $\hat{L}$ is the local field correction tensor [30].

The Stark shift is dependent on the orientation of the applied field relative to $\delta\vec{\mu}$ [39]. Without knowing $\delta\vec{\mu}$ or $\hat{L}$, the Stark shift can be empirically characterized for an electric field applied in a particular direction $\hat{n}$ using the Stark shift parameter $s_{\hat{n}}$ given $\delta f=s_{\hat{n}}E_{\hat{n}}$. We measured $s_{\hat{n}}=11.8\pm 0.2$ kHz/(V/cm) for $\hat{n}$ nominally aligned with the Y₂SiO₅ crystal $b$-axis (see Appendix A).

In an ensemble of ¹⁶⁷Er³⁺:Y₂SiO₅ 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 $\delta f_{\pm}=\pm sE$. In this work, all electric fields are applied parallel to the $b$-axis, so we will simply refer to two ¹⁶⁷Er³⁺ subclasses.

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 $\vec{r}_{j}$. For AFC storage, the transition frequencies $\{f_{j}\}$ form a frequency comb with period $\Delta$. When a photon is absorbed at $t=0$, the ensemble of ions first dephase then rephase every $t=\frac{m}{\Delta}$, $m\in\mathbb{N}$, leading to a coherent re-emission of the light [34]. A Stark shift $\delta f_{j}(t)$ enables dynamic control of light stored in the AFC by changing the optical transition frequencies of the ions. $\delta f_{j}(t)$ 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 ¹⁶⁷Er³⁺:Y₂SiO₅ subclasses experience equal and opposite frequency shifts, $\pm\delta f(t)=\pm s_{b}E$. By appropriately choosing the length in time $t$ and amplitude $E$ of the electric pulse, a $\pi$ phase difference between subclasses can be introduced $\pi=2\pi\times(+s_{b}E-(-s_{b}E))\times t$, 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 Pr³⁺:Y₂SiO₅ [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 [14, 8]. First, an AFC with period $\Delta$ is created by repeatedly burning away population between the teeth of the comb, $n_{\mathrm{comb}}=20$ 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 $t=\frac{m}{\Delta}$. Without electric field control, the output of the memory (the first and largest emission), would be centered at $t=\frac{1}{\Delta}$ ($m=1$). The schematic shows instead an emission in red at $t=\frac{3}{\Delta}$ ($m=3$), 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 $19.7\pm 0.1$ MHz, which corresponds to a minimum storage time of $t=\frac{1}{\Delta}=50$ 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 $t_{\mathrm{pulse\,1}}=25$ ns. The second was 10 ns long with an opposite amplitude of -2.0 kV/cm, and its center position was varied as $t_{\mathrm{pulse\,2}}=25$ ns $+\,(m-1)\times 50$ ns to allow the emission at $t_{\mathrm{memory}}=\frac{m}{\Delta}$. 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 $t_{\mathrm{memory}}=\frac{m}{\Delta}$. The data is fit to the dephasing term in the theoretical storage efficiency for a comb with Gaussian teeth: $\mathrm{exp}\left(-\frac{\pi^{2}}{2\mathrm{ln}2}\frac{m^{2}}{F^{2}}\right)$ [34, 12], where $F=\Delta/\gamma$ is the comb finesse, and $\gamma$ is the full-width at half maximum (FWHM) of each tooth. The $m=1$ data point is excluded from the fit because the approximately 100 ns dead time of the single photon detector after the input pulse is thought to lead to undercounting in that time bin. A comb finesse of $F=12.2\pm 0.2$ ($\gamma=1.6$ MHz) is extracted from this fit. This corresponds to a $1/e$ point of 240 ns ($m=4$ for digital storage time). To improve on this scaling requires a smaller tooth width $\gamma$. The grey data in Fig. 2d show the total counts in the $m^{th}$ time bin when the previous output pulses are not suppressed.

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 ¹⁶⁷Er³⁺ subclasses from the spectral window, leaving only ions which experience a positive Stark shift, $\delta f_{+}=+s_{b}E$ (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 $\Delta/2$ using a parallel electric field, and a similar sequence of laser pulses is used, but with a frequency shift of $\Delta/4$. This burns away ions with a negative shift $\delta f_{-}=-s_{b}E$.

Repeating the comb burning procedure $n_{\mathrm{comb}}=5$ times, an AFC with width 145 MHz, and a period $\Delta=5$ MHz is created. An input pulse is sent in and the rephasing of the AFC causes an emission at $t=\frac{1}{\Delta}=200$ ns. During this emission, an electric field pulse with amplitude $E_{\mathrm{pulse}}$ applied in the parallel configuration will cause the ions to emit with a frequency shift of $f=+s_{b}E_{\mathrm{pulse}}$. Figures 3b-c show the light emitted from the memory, with and without a frequency shift. A heterodyne measurement is used to measure the frequency of the output pulse directly. Figure 3d shows the linear frequency shift as a function of electric field. The decrease in output amplitude with frequency shift evident in Figures 3b-c is mainly due to the inhomogeneity of Stark shifts experienced by the ions (see Appendix A).

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 $\Delta=1.6$ MHz and bandwidth 144 MHz is created by repeatedly burning away population $n_{\mathrm{comb}}=20$ times. Next, an input pulse is sent into the device, leading to an output pulse at $t=\frac{1}{\Delta}=630$ 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 [42, 24].

Figure 4b shows AFC storage with no broadening (top) and with the maximum achieved bandwidth broadening (bottom). A broadening in frequency space is seen as a narrowing of the output pulse in time. By fitting the output pulses to Gaussians, the temporal FWHMs ($\Delta t$) of input and output pulses are extracted and converted to bandwidth or frequency FWHMs ($\Delta f$) using: $\Delta f=\frac{4\mathrm{ln}2}{2\pi}(\Delta t)^{-1}$. Figure 4c shows the trend of output bandwidth as a function of the maximum electric field applied during the third pulse $E_{\mathrm{max}}$ (the electric field across the resonator ranges from $-E_{\mathrm{max}}$ to $E_{\mathrm{max}}$). 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 $E_{\mathrm{max}}$. This parameter was found to be $x_{\mathrm{eff}}=6$ $\mu$m for each mirror by coarsely sweeping $x_{\mathrm{eff}}$ in 1 $\mu$m increments in the simulation to find the best fit to the data.

In this work, we have demonstrated the capabilities of an on-chip optical storage device with DC Stark shift control. Taking this technology on-chip has two main advantages. First, it allows miniaturization and future integration with other optical components on chip. Second, it enables simple generation of large electric fields. Because the distance between electrodes across the resonator is small (a minimum of 20 $\mu$m), electric fields of $3$ kV/cm are generated with just $\pm 5$ 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/$\mu$m were generated, corresponding to gradient of 0.58 MHz/$\mu$m in ¹⁶⁷Er³⁺:Y₂SiO₅ 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 $108\pm 13\>\mu$s.

Frequency control was demonstrated for up to $\pm 39$ 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/$\mu$m. 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 $\sim 150$ 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 ¹⁶⁷Er³⁺:Y₂SiO₅, 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 $\sim 500$ ns [14]. Superhyperfine coupling is a major limitation to high-efficiency long lived storage in ¹⁶⁷Er³⁺:Y₂SiO₅ 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 ¹⁶⁷Er³⁺:Y₂SiO₅[43, 44, 37], 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 $t=\frac{m}{\Delta}$ 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 ¹⁶⁷Er³⁺ 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].

In this work we demonstrated a multifunctional on-chip device that can store light while dynamically modifying its storage time, frequency and bandwidth. Dynamic control of the memory time and the frequency profile of the output light was achieved via the linear DC stark shift of ¹⁶⁷Er³⁺ ions in Y₂SiO₅ . We demonstrated dynamic control of memory time in a digital fashion with storage times that were multiples of $50$ ns, for up to $400$ ns. The frequency of stored light was changed by up to $\pm 39$ MHz, and the bandwidth of stored light was increased by up to a factor of three, from 6 MHz to 18 MHz. This on-chip platform, comprising a resonator evanescently coupled to an ensemble of atoms that experience a DC Stark shift and on-chip electrodes, can be adapted to other materials and other quantum memory protocols.