1. INTRODUCTION

A. Background

As quantum technologies become more developed and the need to process and exchange quantum information grows, we will need to find ways to expand the Internet to include quantum links [1]. The advantages of a future quantum Internet include distributed quantum computation, provably secure communication, and long baseline quantum sensing [2–4]. Already, significant progress has been made towards realizing quantum networks, including terrestrial and satellite-based demonstrations of distant entanglement generation [5,6], commercially available quantum key distribution [7], and loophole-free Bell tests [8].

Quantum systems with optical frequency transitions, such as defect centers in diamond [9], quantum dots [10], and trapped ions [11], naturally interact with visible or infrared light, so connecting these systems with optical links is comparatively straightforward. In contrast, superconducting qubits [12,13], a leading technology for near-term quantum information processing [14], operate at microwave frequencies in the few gigahertz range and are not readily addressable with light. There has been a tremendous effort to create entanglement between increasingly distant superconducting qubits using microwave channels [15–18], culminating in a recent demonstration by Magnard et al. of entangled qubits in two dilution refrigerators separated by 5 m [19]. However, for links at microwave frequencies to operate with an acceptably low probability of adding thermal noise photons, the physical links must be cooled to cryogenic temperatures [20,21], likely making them impractical for links longer than a few tens of meters. On the other hand, optical fiber links are inherently free from thermal noise at room temperature due to their high carrier frequency and low loss, and optical fiber can be cheaply deployed over distances of many kilometers. Millimeter wave (60 to 300 GHz) interconnects may prove useful for intermediate distances (e.g., data centers or intracity connections) [22], but as in today’s Internet, for many applications, long-haul optical links are required.

The benefits of networking superconducting qubits with optical links has spurred a great deal of research on coherent conversion between optical and microwave photons [23,24]. There have been a variety of approaches, including electro-optomechanics [25–27], piezo-optomechanics [28–32], direct electro-optic (EO) coupling [33–36], magnons in yttrium iron garnet [37], Rydberg atoms [38,39], and rare-earth-doped crystals [40–42]. To date, the highest conversion efficiencies have been achieved using the electro-optomechanical approach [43]; however, the approach demonstrated here using the direct EO effect (aka the Pockels effect) has the advantages that it can be microfabricated on a chip, has high conversion bandwidth, and operates at a wavelength that is readily voltage-tunable.

Several different protocols have been considered for quantum communication between distant superconducting qubits [16–18,44], including some heralding protocols that are robust in the presence of nonunity photon conversion efficiency [45–47]. Figure 1(a) shows an example heralding scheme using beam splitters and a pair of single-photon detectors to generate entanglement in a probabilistic fashion. In this demonstration, we implement the circled portion of Fig. 1(a), which is a key component for a future long-distance heralding experiment.

 

Fig. 1. (a) Schematic showing a two-node quantum network connected with EO converters. The EO converter produces entangled microwave and optical photons. When a photon is detected by one of the SPDs, the superconducting qubits are projected into an entangled state. The tunable filters are required to remove the pump light from the EO converters. (b) Schematic illustration of the coupled microwave and optical modes; (c) diagram of the EO conversion process in the case of red-side pump detuning, with the optical modes tuned to be fully hybridized. Microwave photons are upconverted into the anti-Stokes sideband.

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B. Basic Theory of Operation

Our EO converter consists of a triply resonant system utilizing two optical modes and one microwave mode, similar to the proposals in [48,49] and demonstration in [34]. Figures 1(b) and 1(c) illustrate the device operation. Two nominally identical racetrack resonators evanescently couple to form optical modes. After diagonalizing the Hamiltonian in the coupled-mode basis (see Supplement 1, Section A), the interaction Hamiltonian for this triply resonant system is given by

 

Fig. 2. (a) Image of the chip with four EO converter devices, before wirebonding and fiber gluing; (b) optical micrograph of the converter device, which consists of two coupled optical racetrack resonators and a quasi-lumped-element LC microwave resonator. The ${+}$ and ${-}$ indicate the polarity of the modulation electrodes. (c) Zoomed-in image showing the optical waveguide between the capacitor electrodes, with the LN crystal axes indicated; (d) diagram illustrating the cross-section geometry of the device (approximately to scale). The exact waveguide dimensions can be found in Supplement 1.

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When the cooperativity $C \ll 1$, as is the case in this work, the on-chip efficiency can be expressed as (see Supplement 1, Section B)

Our device primarily uses the ${r_{33}}$ (contracted notation) component of the EO tensor and transverse electric (TE)-polarized fields along the extraordinary $z$ axis of the crystal with index ${n_e}$, so we can approximate ${g_0}$ as (see Supplement 1, Section C)

If we want to use the device as an entangled pair source instead of a frequency converter, we put the optical pump on the higher frequency mode $b$. In this case, the device probabilistically generates pairs of entangled microwave and optical photons with rate [50]

2. LITHIUM-NIOBATE-ON-SAPPHIRE PLATFORM

A. Motivation

In order to achieve efficient on-chip microwave-to-optical conversion, it is necessary to use a material system that supports high optical and microwave quality (Q) factors as well as large EO coupling. Lithium niobate (LN) has long been a workhorse material for the telecommunications industry because of its large EO coefficient (${r_{33}} \approx 31\,\,{\rm pm}/{\rm V}$ [52]) and low optical loss. The recent commercial availability of thin-film LN wafers has enabled the development of nanofabricated LN resonators with optical Q factors well above one million [53–56]. These properties make LN an ideal candidate for microwave-to-optical conversion; however, the details of the material stack have a substantial impact on the device performance.

One commonly available thin-film LN platform, lithium-niobate-on-insulator (LNOI) [57], consists of thin-film LN bonded to an LN or silicon substrate with a silicon dioxide buffer layer. Although this platform has proven useful for classical modulator technology [58], the piezoelectric effect of the LN substrate can cause energy to be lost to acoustic radiation, presenting a significant loss channel for superconducting microwave resonators. The silicon substrate variant also has challenges because the interface between the oxide and silicon layers can exhibit large conductivity, which also leads to microwave losses [59]. Lithium-niobate-on-silicon (LNOS), consisting of thin-film LN directly bonded to silicon, is an alternative stack that avoids these issues. However, since the refractive index of silicon is higher than LN, the LN film must be undercut in order to achieve optical guiding [30,60], making the design and fabrication more challenging.

Lithium-niobate-on-sapphire (manufactured by NGK Inc.), which we abbreviate as LiSa, consists of a thin LN film directly bonded to a sapphire substrate without any oxide layer, and it offers a promising alternative to both LNOI and LNOS for hybrid microwave/optical applications. Sapphire is a commonly used microwave substrate with low dielectric and optical loss and is not a source of piezoelectric loss, due to its centrosymmetric crystal structure. The higher refractive index of LN relative to sapphire (approximately 2.2 compared to 1.7) makes it possible to confine light without the need for an intermediate buffer layer or suspended structures.

B. Device Overview

The EO converter device is pictured in Fig. 2. The optical portion of the device consists of two coupled racetrack resonators, with the left resonator coupled to a feed waveguide. Grating couplers are used to couple light into and out of the chip from a pair of angle-polished fibers. The microwave resonator is a quasi-lumped-element LC circuit, with a meandering wire acting as the inductor and the modulator electrodes acting as the capacitor. The microwave mode must have odd parity in the overlap region for the integral in Eq. (4) to be nonzero because modes $a$ and $b$ are the symmetric and antisymmetric supermodes formed by coupling two resonators. To realize odd parity, we arrange the electrodes as shown in Fig. 2(b). The LC resonator is inductively coupled to a microwave coplanar waveguide (CPW) feedline. Bias electrodes span a segment of the right optical resonator and are used to provide DC tuning to compensate for frequency mismatch. The coupling between the optical resonators is carefully chosen to match the microwave resonator frequency when the optical modes are tuned to the symmetric operating point, i.e., when the modes are fully hybridized.

C. Fabrication and Packaging

We fabricate the device using a LiSa wafer with 500 nm initial thickness of congruently grown $X$-cut LN on a $C$-cut sapphire substrate. The waveguides are defined with electron beam lithography (JEOL JBX-6300FS, 100-keV) in a hydrogen silsesquioxane (HSQ) resist. The pattern is transferred to the LN with an argon ion mill etch that etches 300 nm of the LN. Next, we use photolithography and another argon ion mill etch to remove the remaining 200 nm of LN that would otherwise lie below the microwave circuit. We leave a $6\,\,\unicode{x00B5}{\rm m}$ wide pedestal of LN around the waveguide. A $1.5\,\,\unicode{x00B5}{\rm m}$ thick oxide cladding is deposited on the die using plasma-enhanced chemical vapor deposition (PECVD) and annealed at ${500 ^ \circ}\!{\rm C}$. Next, we RF sputter approximately 300 nm of niobium onto the die, pattern the microwave circuits using photolithography, and etch the niobium using a combination of argon ion milling and ${{\rm SF}_6}$ reactive ion etching (RIE). After dicing the die into smaller chips, the chips are then wirebonded into copper printed circuit boards (PCBs). Angle-polished fibers are used to provide optical access to the device. The fibers are aligned to the on-chip grating couplers and glued to the chips using the technique described in [51]. The device is mounted at the 1 K still plate of a helium dilution refrigerator. Although the thermal occupancy of the microwave mode ($\approx\! 3$ photons) is not relevant to the current demonstration, future quantum experiments will require reducing the thermal occupancy by mounting the sample at a lower temperature location in the dilution refrigerator or thermalizing the microwave mode with radiative cooling [61].

3. EO CONVERSION RESULTS

To prepare for EO conversion, the detuning between the optical modes must be adjusted to match the microwave frequency using the DC bias electrodes. The color plot in Fig. 3(a) shows optical transmission spectra as the bias voltage is swept, showing the avoided crossing between the two optical modes. The inset shows an example spectrum where the modes are tuned to be fully hybridized. The optical modes used for the conversion process are undercoupled, and the splitting between the modes at the fully hybridized point is approximately 6.8 GHz. Device details are shown in Table 1.

 

Fig. 3. (a) Optical spectra of a representative coupled racetrack device plotted versus bias voltage. The avoided crossing between the two modes is clearly visible. Inset, an example spectrum showing the optical modes tuned to be fully hybridized. In this case, the separation between the modes is approximately 6.8 GHz. (b) Microwave frequency characterization of the converter device. The top curve (blue) shows an ${S_{21}}$ (transmission) measurement through the microwave feedline, taken using a vector network analyzer (VNA). The four resonances (marked with dashed lines) correspond to the four converter devices on the chip. The bottom curve (red) is an EO ${S_{21}}$ measurement showing the optical response on a high-speed photoreceiver when the converter device is driven with a VNA. The ${S_{21}}$ is normalized to the peak EO response. For this measurement, light is going through the third device on the chip, which is why the EO response is strongly peaked at the frequency of the third microwave mode. The data in this figure are taken from a different chip than the conversion data in Fig. 4, but with nominally identical microwave circuits.

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The microwave ${S_{21}}$ (transmission) spectrum is shown in Fig. 3(b). The four resonances correspond to the four LC resonators coupled to the feedline on the chip. The microwave modes have total Qs in the range of 200–700. The EO response of the device can be measured by driving the microwave resonator and sending laser light through the feed waveguide to the coupled racetrack resonators. The electric field on the capacitor modulates the light and creates an optical sideband that can be detected by sending the outgoing light to a high-speed photoreceiver. The EO response is highly peaked at 6.8 GHz, since it is the third converter device on the chip that is being optically addressed. From these data, we conclude that the 3-dB conversion bandwidth is approximately 20 MHz.

In order to demonstrate sideband selective conversion of microwave photons to optical photons, we use two different experimental techniques. A heterodyne measurement shown in Fig. 4(a) allows us to resolve the upper and lower sidebands with high-frequency resolution and large dynamic range. We send a resonant microwave tone and a pump laser to the device and beat the modulated outgoing light with a frequency-shifted local oscillator (LO) on a high-speed photoreceiver whose signal is fed to a real-time spectrum analyzer. By calibrating the measured spectra (see Supplement 1, Section G for details) we can obtain the efficiency of conversion into the two sidebands as a function of the pump laser detuning [Fig. 4(b)] and compare to the predicted curve from theory. The theory curve uses independently measured parameters such as the DC tuning response and Q factors and does not include any fit parameters from the heterodyne experiment. Based on the measured efficiency we infer ${g_0}/2\pi = 1.2\;{\rm kHz} $, which very closely matches the value that we obtain from DC tuning measurements and is about 40% lower than the value predicted from finite-element simulations [see Eq. (4)].

Table 1. Summary of Measured Device Parameters^a

View Table

 

Fig. 4. (a) and (b) show the system diagram and measurement results for the heterodyne setup. (c) and (d) show the system diagram and measurement results for the SPD setup. (a) The system diagram for the heterodyne measurement setup. A 50/50 beam splitter divides the light into two paths: one path pumps the device and the other path serves as the LO path. The pump light drives the conversion process, which results in Stokes and anti-Stokes sideband generation. The modulated light exits the device and combines with the LO with a 90/10 beam splitter. An acousto-optic modulator (AOM) offsets the LO frequency by 40 MHz to allow for sideband discrimination in the beat signals of the high-speed photoreceiver. A 60 meter delay line is used in the LO path to reduce laser phase noise in the measurement. (b) Experimental on-chip conversion efficiency versus the pump frequency. The device produces Stokes and anti-Stokes optical sidebands at ${\omega _p} - {\omega _\mu}$ and ${\omega _p} + {\omega _\mu}$, respectively, and the conversion efficiency into these sidebands is plotted versus pump frequency. The black line shows the theoretical efficiency of the device. The theory curve uses measured parameters of the device and does not use any free fit parameters. The device resonantly enhances conversion while suppressing unwanted sideband generation. At location A, only the anti-Stokes sideband is resonantly enhanced. At location B, the pump and anti-Stokes sideband are resonantly enhanced. At location C, the pump and Stokes sideband are resonantly enhanced. At location D, the Stokes sideband is resonantly enhanced. The Stokes to anti-Stokes suppression ratio is 24.2 dB. (c) The system diagram for the single-photon detection setup that uses optical sideband filtering and a SNSPD. The laser source is power stabilized using an electro-optic modulator (EOM) and is frequency-stabilized to a high-finesse optical filter controlled by a thermo-electric cooler (TEC). The pump here is tuned to the anti-symmetric mode of the device (mode $b$). A variable optical attenuator (VOA) controls the amount of pump power to the device. The on-chip conversion process produces a Stokes sideband that is filtered by two high-finesse filters with a combined linewidth of around 30 MHz. The filters are temperature-stabilized to the Stokes sideband frequency ${\omega _p} - {\omega _\mu}$. The SNSPD detects the filtered sideband signal and counting electronics measure the photon flux. (d) Experimental photon count rate versus the microwave drive frequency for a range of input microwave powers. The inset figure shows the count rate as a function of filter detuning. The count rate is maximum when the filter is tuned to ${\omega _p} - {\omega _\mu}$. Other abbreviations, fiber polarization controller (FPC); optical isolator (ISO).

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The maximum total on-chip photon number conversion efficiency is $6.6 \times {10^{- 6}}\,\,{\rm dB}$ ($3.9 \times {10^{- 7}}$ off-chip), measured with 1.2 mW incident on the input grating coupler. The efficiencies reported generally have an uncertainty of ${\pm}3.3\;{\rm dB} $, which comes from an ambiguity in assigning the measured total losses to the input and output grating coupler losses. The insertion loss through both grating couplers is well known (24.4 dB), but decoupling the losses results in uncertainty. See Supplement 1, Section G for more details. The off-chip conversion efficiency includes the loss from the output grating coupler, but not the loss of the upstream microwave lines or downstream optical components. The maximum on-chip conversion efficiency normalized to the pump power in the feed waveguide is $9.5 \times {10^{- 8}}\,\unicode{x00B5} {W^{- 1}}$ ($5.7 \times {10^{- 9}}\,\unicode{x00B5} {W^{- 1}}$ off-chip). Figure 4(b) shows the large advantage of incorporating an optical mode to resonate the pump. When the pump is set off-resonant with modes $a$ and $b$ by ${\omega _c}$, the converter operates with only a single optical resonance, and the efficiency is 24.2 dB lower than when utilizing both optical resonances. We define the selectivity as the ratio of the Stokes to anti-Stokes sideband efficiency with the pump tuned on resonance. As viewed in Fig. 4(b), we achieve a selectivity of 24.2 dB with the pump tuned on mode $a$, in good agreement with the theoretical prediction of 24.6 dB given our device parameters. Optical mode drift causes the peaks in efficiency to imperfectly match the theoretical predictions. The modes drifted by a larger amount towards the beginning of the experiment, when the pump frequency was set to higher frequencies near mode $b$. We did not measure the photon conversion efficiency in the reverse direction (optical to microwave), but expect it to be the same based on the reciprocal nature of the device.

In our second measurement technique [illustrated in Fig. 4(c)], the converted optical sideband photons are directly detected using a superconducting nanowire single-photon detector (SNSPD). A pair of cascaded, tunable Fabry–Perot filters (Micron Optics) are used to select the sideband of interest and provide approximately 110 dB suppression of pump light leaving the device. The data are shown in Fig. 4(d). We achieve a maximum on-chip conversion efficiency normalized to the pump power in the feed waveguide of $8.2 \times {10^{- 7}}\,\unicode{x00B5} {W^{- 1}}$ ($4.9 \times {10^{- 8}}\,\unicode{x00B5} {W^{- 1}}$ off-chip), with a pump power of $5.8\,\unicode{x00B5}{\rm W}$ incident on the grating coupler. The background count rate is 4.8 kHz, due primarily to stray pump and environmental light reaching the SNSPD. We note that there is a discrepancy between the efficiency per $\unicode{x00B5}{\rm W}$ obtained using the two measurement techniques. Although the exact source of the discrepancy is not clear, the two experiments were performed with different pump powers incident on the input grating coupler (1.2 mW versus $5.8\,\unicode{x00B5}{\rm W}$), and also during separate cooldowns of the fridge about 1 month apart.

 

Fig. 5. Strategy used for reducing acoustic loss in the device. (a) and (d) show a comparison of the device cross section with and without the additional LN slab etch. (b) and (e) show microwave ${S_{21}}$ spectra from two nearly identical microwave LC resonators. The device in (b) with an unetched slab has no clear resonances corresponding to the LC circuit, but there are a large number of small mechanical resonances corresponding to BAWs. In contrast, the device in (e) with an etched slab has sharp resonances at the designed frequencies and no mechanical resonances are visible. (c) and (f) show COMSOL simulations of acoustic radiation from a device with an unetched slab and etched slab, respectively, simulated with an excitation frequency of 6.5 GHz. Etching the slab greatly reduces the excitation of shear waves. The color shows the displacement in the crystal $Z$ direction and the color scales in the two figures are the same.

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The incorporation of single-photon detectors (SPDs) in this experimental setup provides greater sensitivity and is an important step towards future quantum experiments such as heralded entanglement generation. Based on our peak on-chip conversion efficiency, we estimate that this device operated without a microwave drive could generate entangled optical–microwave photon pairs at a rate of 20 Hz [see Eq. (5)].

A summary of the relevant device parameters is given in Table 1.

4. OTHER DESIGN CONSIDERATIONS

There are a few design choices with the present device that are worth highlighting because of their broader applicability to microwave-to-optical converters.

A. Managing Acoustic Loss

An issue we encountered while building the present converter device was the generation of acoustic waves by the microwave resonators. Our initial devices had an LN slab that covered the entire chip underneath the microwave resonators [see Fig. 5(a)]. These devices, with an unetched slab, had no clear microwave resonances at the designed frequencies; instead, we observed a large number of weakly coupled resonances with a free spectral range (FSR) of about 6.2 MHz. We identify these resonances as being due to acoustic shear waves in the sapphire substrate. Transverse acoustic waves in sapphire have a velocity of approximately 6000 m/s [62], and the sapphire substrate has a thickness of $500\,\unicode{x00B5}{\rm m}$, so the predicted FSR would be roughly 6 MHz, in line with what we observe. The next iteration of microwave resonators was fabricated with a nearly identical design, except that the LN slab was etched everywhere except for a narrow $6\,\unicode{x00B5}{\rm m}$ strip around the optical waveguides. These test devices were observed to have microwave resonances at the target frequencies with total Q factors of 2000–3000 [Fig. 5(e)]. Note that one microwave resonator fabricated on the same chip had all of the LN completely etched away and had a Q factor in the same range, indicating that the Q is likely limited by another factor, such as the dielectric losses in the oxide cladding rather than acoustic loss. The dramatic difference in loss between the etched and unetched slab can be understood through simulations of the piezoelectric effect in our devices. Figures 5(c) and 5(f) show a 2D COMSOL simulation of bulk acoustic waves (BAWs) generated when an AC voltage at 6.5 GHz is applied to the electrodes. The dominant form of radiation is shear waves radiating downwards into the substrate. These waves are generated by the vertical component of the electric field (along the LN $X$ direction) directly underneath the electrodes, which interacts with the largest component of the LN piezoelectric tensor (${d_{15}} \approx 7 \times {10^{- 11}}\,\,{\rm C}/{\rm N}$). Since the electric field has this orientation only underneath the electrodes, removing the LN slab in this region is an effective way to reduce acoustic radiation.

B. Choice of Superconductor

The choice of superconductor is very important to the converter operation. Here we use niobium rather than aluminum because of its higher critical temperature ($\approx\! 8\! -\! 9\,\,{\rm K}$ rather than $\approx 1\,\,{\rm K}$) and much lower quasi-particle lifetime ($\approx$ nanoseconds compared to milliseconds). This allows us to operate the device at the 1 K still plate of the dilution fridge and to use significantly higher pump powers. Niobium titanium nitride (NbTiN) would likely be an even better choice than niobium because it has a similarly short quasi-particle lifetime and would also allow for the fabrication of high-kinetic inductance resonators to boost the EO coupling rate. Future work will explore the integration of high-quality NbTiN films. For more information on the effect of light on the microwave resonators, refer to Supplement 1, Section H.

5. OUTLOOK

We have demonstrated sideband-resolved microwave-to-optical signal transduction in a dilution refrigerator environment. Our device operates with an on-chip conversion efficiency of $6.6 \times {10^{- 6}}$ and a large bandwidth of 20 MHz.

There are several straightforward ways in which the conversion efficiency of our transducer can be improved. First, we note that the microwave quality factor seems to be limited by the presence of the PECVD silicon dioxide cladding—test devices made with the same niobium film and similar circuit geometry, but without the oxide cladding, have intrinsic Qs above 100,000. This is not surprising; dielectric loss in amorphous materials often limits the Q factor of superconducting circuits, particularly at low microwave photon numbers where two-level system (TLS) effects become important [63]. Creating devices without the oxide should be straightforward in the LiSa platform by using air bridges [64] instead of oxide cladding, allowing the microwave circuits to be directly on the sapphire. Additionally, the optical Q factors of our resonators are similar, with and without the cladding. Other possibilities to improve the conversion efficiency include using higher impedance microwave resonators to enhance the EO coupling rate (for example, by incorporating NbTiN nanowire kinetic inductors [65–67]), increasing the optical Q by optimizing the electron beam lithography and ion mill etch, and improving fiber-to-chip coupling efficiency by either optimizing the grating coupler design or by switching to end-fire coupling using a lensed fiber [68].

It is also important to note that the optical modes in our experiment tended to drift, usually towards shorter wavelengths. This drift depends on both the optical pump power and the applied bias voltage, and it is the limiting factor on how much pump power we can use in the experiment. We believe this drift is due to a combination of photorefraction and optically induced conductivity in the LN, an effect which has been studied for several decades (see, e.g., [69–72]). This effect is likely to be important for a broad class of thin-film LN modulators—it is described in more detail in Supplement 1, Section I and will be investigated carefully in future publications. Mitigating this effect will greatly improve device performance by allowing us to send up to 10 times more optical pump power to the device.

While there is still much work to be done in increasing conversion efficiency, this demonstration addresses some of the challenges in EO photon conversion and highlights the potential of EO transducers in playing a key role in future quantum networks.