# Microwave-to-optics conversion using a mechanical oscillator in its quantum ground state

## Abstract

Conversion between signals in the microwave and optical domains is of great interest both for classical telecommunication and for connecting future superconducting quantum computers into a global quantum network. For quantum applications, the conversion has to be efficient, as well as operate in a regime of minimal added classical noise. While efficient conversion has been demonstrated using mechanical transducers, they have so far all operated with a substantial thermal noise background. Here, we overcome this limitation and demonstrate coherent conversion between gigahertz microwave signals and the optical telecom band with a thermal background of less than one phonon. We use an integrated, on-chip electro-optomechanical device that couples surface acoustic waves driven by a resonant microwave signal to an optomechanical crystal featuring a 2.7 GHz mechanical mode. We initialize the mechanical mode in its quantum ground state, which allows us to perform the transduction process with minimal added thermal noise, while maintaining an optomechanical cooperativity >1, so that microwave photons mapped into the mechanical resonator are effectively upconverted to the optical domain. We further verify the preservation of the coherence of the microwave signal throughout the transduction process.

## Main

Research into novel quantum technologies is receiving significant attention for its potential to fundamentally transform how we receive, process and transmit information. In particular, major endeavours into building quantum processors and quantum simulators are currently underway. Many leading efforts, including superconducting qubits1 and quantum dots2, share quantum information through photons in the microwave regime. While this allows for an impressive degree of quantum control3, it also limits the distance the information can realistically travel before being lost4. At the same time, the field of optical quantum communication has already seen demonstrations over distance scales capable of providing real-world applications5. In particular, by transmitting information in the optical telecom band, fibre-based quantum networks over tens or even hundreds of kilometres can be envisaged6. To connect several quantum computing nodes over large distances into a quantum internet7, it is therefore vital to be able to convert quantum information from the microwave to the optical domain, and back.

Several promising approaches have been taken to realize such a microwave-to-optics converter, most notably by trying to directly couple the fields inside a nonlinear crystal8,9,10,11, or by using rare-earth-ion-doped crystals12, magnons13 or mechanical systems as a transducer14,15,16,17,18,19,20. Recent milestones include bi-directional operation21, coherent coupling22 and efficient conversion23, all of which make use of a mechanical oscillator as the transducer. While high conversion efficiency has been a particular success with some mechanically mediated frequency converters, the demonstration of intrinsic noise sources compatible with conversion of a quantum state has remained an outstanding challenge. For quantum information protocols, particularly those that can tolerate optical loss, the requirement of subphoton added noise necessitates that the converter contains less than one thermal excitation24. To this end, several experiments have recently demonstrated cooling of mechanical oscillators into the quantum ground state of motion25,26,27. The low thermal occupation forms the basis for quantum control over mechanical states, with demonstrations including quantum-state preparation28,29,30 and entanglement between multiple mechanical degrees of freedom31,32,33. Reaching this occupation regime is challenging because the absorption of optical photons has to be avoided, while at the same time a sufficiently strong optomechanical cooperativity needs to be realized in order to suppress additional noise sources34. To date there has been no demonstration of a system with mechanically mediated interfaces in both the microwave and optical domains that operates in the quantum ground state.

In this work, we demonstrate microwave-to-optics conversion with an electro-optomechanical device, which contributes less than one quantum of thermal noise. We cryogenically cool a gigahertz-frequency piezoelectric optomechanical crystal (OMC) device into its quantum ground state of motion and excite the mechanical mode using a microwave circuit through surface acoustic waves (SAWs). Crucially, our system remains in the ground state while a drive of sufficient strength for upconversion from the mechanical to the optical domain is applied. This allows for conversion of a microwave pulse to the optical telecom band in a regime where we excite on average one phonon. As our converter features a noise source containing less than one photon, optimizing the electromechanical cooperativity28,35, the main efficiency bottleneck in our platform, will allow for the faithful transduction of a single photon from the microwave to the optical domain.

Our microwave-to-optics converter consists of a one-dimensional OMC36, which is mechanically coupled to an interdigital transducer (IDT) through SAWs (see Fig. 1a). We fabricate the devices from a 250-nm-thick GaAs layer, on a 3 μm Al0.7Ga0.3As sacrificial layer, both epitaxially grown on a GaAs substrate. This material combines a large refractive index (nGaAs = 3.37 at λ = 1,550 nm)37 and a non-zero piezoelectric coefficient (ϵ14 = −0.16 C m−2), with well-established fabrication processes. The optomechanical device, shown in the lower inset of Fig. 1a, is designed using finite-element modelling, such that the patterned nanobeam confines light in the telecom band, while at the same time exhibiting a co-localized mechanical breathing mode at ωm = 2π × 2.7 GHz (Fig. 1b). The electromechanical coupling in our device is due to the piezoelectric effect that allows for the excitation of travelling acoustic waves that drive the OMC22. The optomechanical coupling, on the other hand, is facilitated by the parametric coupling between the mechanical excitation and the intracavity photon number owing to the combination of photoelastic coupling and moving boundary conditions36. Both effects can intrinsically operate in a bi-directional and noiseless fashion. The device fabrication consists of a two-stage lithography process to define the IDT and then pattern the nanobeams, followed by a hydrogen fluoride etch to remove the AlGaAs sacrificial layer. A final deposition of 5 nm of AlOx passivates the surfaces and reduces the effect of unwanted drive-laser absorption38 (see Supplementary Information for details). The lower inset of Fig. 1a displays a scanning electron micrograph of an optomechanical device, and an evanescently coupled waveguide that provides optical-fibre access to the confined optical mode29.

We perform an initial characterization of the device properties at room temperature with the set-up depicted in Fig. 1c, the results of which are presented in Fig. 1d. An S11 measurement of the IDT shows a 10-MHz-wide microwave resonance centred at 2.76 GHz. The mechanical mode of the OMC is then measured by locking a laser onto the blue sideband (ωl = ωc + ωm) of the optical cavity resonance ωc (ωc = 2π × 194.3 THz, with a loaded optical quality factor Qo = 3.3 × 104; see Supplementary Information), and monitoring the high-frequency noise in the reflected signal. The peak in the noise spectrum at 2.744 GHz corresponds to the thermally occupied mechanical mode (~1 × 103 phonons) and has a linewidth of several megahertz. The small mismatch between the IDT and mechanical resonances of ~10 MHz is a result of fabrication-based inhomogeneities. As we apply a radio-frequency (RF) tone to the IDT at the mechanical frequency ωm, we observe an additional narrow peak on top of the thermal noise, corresponding to the transduced coherent signal from the IDT. The height of this peak is dependent on the RF power and the detuning from the mechanical resonance22.

The room-temperature characterization highlights that the large initial thermal occupation of the mechanical mode is a significant source of noise in this conversion process. Especially at low RF drive powers, the thermal noise dominates over the transduced signal22. By placing our device in a dilution refrigerator (base temperature ~20 mK), we can in principle reduce the thermal occupation of the mechanical mode to nth ≈ 10−3. In practice, the achievable occupation is limited by residual heating through laser absorption and finite thermalization to the cryostat29. With the device cooled to millikelvin temperatures, we measure the actual thermal occupation of the mechanical mode by monitoring cavity-enhanced Stokes (blue sideband) and anti-Stokes (red sideband) scattering rates (ΓB and ΓR, respectively), when we drive the cavity with laser pulses detuned by ±ωm (ref. 27). We suppress the reflected pump light through spectral filtering, such that only scattered photons on cavity resonance are detected by superconducting nanowire single-photon detectors (SNSPDs) as shown in Fig. 2a. Specifically, the rates we measure are set by ΓBnth + 1 and ΓRnth (ref. 39). Figure 2b shows a histogram of the single-photon count rates measured for 40-ns-long pulses set to the two detunings with a peak power of 107 nW at the device. For this power, we find an optomechanical cooperativity of C = 1.7 (see Supplementary Information)40. We extract a thermal occupation of nth = 0.90 ± 0.01, which verifies the initialization of the mechanical mode close to its quantum ground state. This value is higher than the theoretical value set by the cryostat temperature, limited by residual heating of the structure during the laser pulse29. A sweep of the pulse power reveals that lower occupations can be achieved (for example, nth = 0.36 ± 0.03; see Supplementary Information), at the cost of a lower conversion efficiency.

We now proceed to verify the conversion from microwave to optical telecom signals at millikelvin temperatures. Red-detuned (ωl = ωc − ωm) optical pulses, which realize an optomechanical state-swap41, are sent into the OMC to read out the state of the mechanical mode, which is coherently excited by sweeping the frequency of an RF drive tone (1 μW) across the mechanical resonance (see Fig. 2c). The data are fitted with a Lorentzian, from which we extract a mechanical linewidth of γm/2π = 197 kHz, an expected improvement in mechanical quality factor of about one order of magnitude compared to the value at room temperature. Furthermore, we observe a blueshift of both the mechanical mode and the IDT resonance by about 35 MHz compared to room temperature due to the temperature dependence of the GaAs elastic constants.

While the optical absorption can be reduced through tuning of the power of the input light as well as by pulsed operation, thus far little is known about the potential heating due to the RF tone that drives the IDT. To investigate the amount of heating resulting from the RF drive, we measure the second-order correlation function $$g^{(2)}(\tau ) = \langle \hat b^\dagger (0)\hat b^\dagger (\tau )\hat b(0)\hat b(\tau )\rangle /(\langle \hat b^\dagger (0)\hat b(0)\rangle \langle \hat b^\dagger (\tau )\hat b(\tau )\rangle )$$ of the mechanical resonator mode29, by swapping mechanical excitations into optical photons at the cavity resonance frequency. Here $$\hat b$$ ($$\hat b^\dagger$$) is the annihilation (creation) operator of the mechanical mode. We expect the coherence of the RF drive to be mapped first onto the mechanical state in our resonator and then onto the light field. Any sign of heating due to the RF drive should result in bunching of the g(2)(τ) during the mechanical lifetime (~1.5 μs). For this measurement, both the laser (locked onto the red sideband) and the RF source are operated in a continuous-wave mode. The scattered optical photons are detected on a Hanbury Brown and Twiss (HBT)-type set-up with two SNSPDs. The time τ here is the relative delay between clicks from the two detectors. We observe a near-flat g(2)(τ) over the entire range of the RF power sweep (see Fig. 2d), clearly indicating that the coherent part of the mechanical state dominates any thermal contribution across the entire power sweep. As a reference, we also perform a measurement without an RF drive but with high enough optical power for absorption-induced heating to occur. In this case, a clear signature of photon bunching is visible, indicating, as expected, a thermal state of the mechanical resonator.

To demonstrate the potential of these devices as transducers of microwave to optical signals at the quantum level, we now operate both the RF driving and optical readout in a pulsed mode42. We send a resonant RF pulse (1 μs long) to the IDT to excite our oscillator and access the mechanical state through a 40-ns-long red-detuned state-swap pulse. This allows us to minimize the effects of heating due to optical absorption. The pulsed experiment enables us to quantify the absolute number of coherent phonons added to our initial state by comparing the scattering rate in the presence of an RF drive (ΓR,RF) to the scattering rate we obtain from the remaining thermal population (ΓR) (inset in Fig. 3b). By measuring the photon rate with and without a resonant RF drive, we recover an RF-phonon conversion efficiency of 3.57 × 10−10 phonons per RF photon.

Using the same HBT-type set-up as above, we detect the second-order correlation of the scattered photons, which allows us to compare the coincidences between detection events originating from the same (Δi = 0) or different (Δi ≠ 0) pulse sequences. A selection of the histograms of these correlations is shown in Fig. 3a for various coherent phonon occupations (ncoh). The full set of g(2)(0) values for increasing coherent phonon occupation is shown in Fig. 3b. We expect the value of g(2)(0) to be determined by the ratio ncoh/nth (see the Supplementary Information). We extract this number from the relative count rate we recover with and without the RF pulse, ΓR,RF/ΓR, displayed in the inset of Fig. 3b, making use of ΓRn. The dashed curve in Fig. 3b displays the expected g(2)(0) values for our RF power sweep based on the theory for a displaced thermal state (see the Supplementary Information), which are in good agreement with our measured values. An increase in RF power results in a larger coherent displacement of the thermal state, which in turn leads to a decreased value for g(2)(0).

While our pulsed experiments clearly demonstrate conversion between a coherent state in the microwave and the telecom domain, they do not imply the retention of the input-state phase. To access the coherence of the transduction process, we use a modified version of the set-up (for a detailed sketch, see Supplementary Fig. 5). We split the red-detuned excitation laser into two branches of a phase-stabilized Mach–Zehnder interferometer, one of which contains our device and the other an amplitude electro-optic modulator. We drive both the IDT and the electro-optic modulator with a single RF source, such that a coherent transduction process results in a fixed phase relationship between the upconverted light in the two interferometer arms. We then mix the light on a beamsplitter, matching the photon rate in the two arms. Figure 4a displays the count rate at one output port of the Mach–Zehnder interferometer when we vary the phase of the interferometer for several coherent phonon occupations. We observe a clear interference pattern with a visibility of 44 ± 3% for powers corresponding to a coherent phonon occupation of ncoh = 1.1, which increases to 85 ± 7% as the coherent contribution dominates over the small thermal background. Figure 4b displays these experimentally retrieved visibilities for several coherent phonon occupations, showing the expected modelled behaviour assuming only thermal noise (nnoise = nth, solid line), as well as additional incoherent noise sources (nnoise = nth + nother, dashed line). These respective trends are given by $$\sqrt {n_{{\mathrm{coh}}}{\mathrm{/}}\left( {n_{{\mathrm{coh}}} + n_{{\mathrm{noise}}}} \right)}$$ and scaled by the maximally achievable interference visibility in our set-up of 90%. Here, nother represents the equivalent noise figure for any other source than the thermal occupation of the resonator, including imperfections in the measurement set-up. We estimate the upper bound of these sources to be nother ~ 2.5. The main contributions to this remaining part are drifts of the interferometer free spectral range over the duration of the measurement, imperfect sideband resolution ((κ/4ωm)2 = 0.27), and mechanical decoherence16,24. With this measurement, we confirm the phase-preserving nature of the conversion process down to the single-phonon level.

The total efficiency of our device is the product of two parts: the loading efficiency of the mechanical mode from the microwave side (3.57 × 10−10, measured from the attenuator output at the mixing chamber to the excitation of phonons in the mechanical mode) and the optical readout efficiency of the mechanical mode (1.55 × 10−5). The latter one can itself be separated into two parts: ηro = pr × ηdet, with ηdet = 1.41 × 10−3 (see Supplementary Information). The state-swap probability pr = 1.1% is a function of the power with which the optical readout is performed and can be increased through improvements with respect to optical absorption. Note that the current performance of our device is already sufficient to read out a non-classical state of the mechanical mode29. The low loading efficiency of the mechanical mode can be attributed to the design and size of the electromechanical transducer. We estimate the efficiency of transferring a SAW from the IDT (150 μm wide) into a single, narrow (~1 μm), suspended beam to be less than 2.5 × 10−5. Additional contributions arise from the difference in the polarizations of the incoming SAW and the mechanical mode, the discrepancy between the IDT and mechanical frequencies, and the large electrical impedance of the IDT. These factors can be improved by tailoring the size and design of the electromechanical transducer specifically to the purpose of exciting the breathing mode of a single nanobeam43. While the small-scale piezo-resonator required to mode-match the nanobeam will necessitate careful electrical impedance matching, the required network falls into the range accessible with coplanar resonator technology43. The relatively small optomechanical state-swap probability and detection efficiency reported here, on the other hand, can be circumvented with post-selection techniques routinely used in quantum optics experiments29,44.

We have demonstrated faithful conversion of a microwave to an optical signal with only a small added thermal contribution due to the ground state occupation of the mechanical resonator. Furthermore, these measurements show our ability to detect the displacement amplitude of the initial state in our mechanical resonator down to one phonon (corresponding to our lowest measured RF power), marking a crucial benchmark for applications in the quantum regime24. The device used for this experiment is a fully integrated, on-chip hybrid electro-optomechanical system with a mechanical mode as the transducer. We cool this mode to its quantum ground state using a dilution refrigerator, which allows us to operate directly at the quantum noise limit. This work allows for the on-chip integration of a single-photon RF source, such as a superconducting qubit35,45, which paves the way for building a true quantum network over large distances, based on superconducting nodes. The device we consider here is specifically suited towards heralded entanglement generation between remote superconducting qubits, a protocol that is described in ref. 24.

While we demonstrate quantum-limited noise performance in the readout of the mechanical state, the conversion efficiency is currently limited by low microwave-phonon excitation efficiency. We note that this is not a fundamental limit but rather a result of design choices for this proof-of-principle demonstration. The material itself imposes some limitations on the efficiency, such as the remaining absorption heating and the relatively low piezoelectric coupling. However, demonstrations of coherent coupling between superconducting qubits and SAWs in GaAs (refs. 35,45) suggest that the latter are highly suitable choices for noise-free carriers of quantum information. Importantly, our system is already operating in the range of optical drive strengths expected for mediating efficient conversion. In particular, the optomechanical cooperativity of C ≈ 1.7 (see Supplementary Information) is sufficient for efficiently converting gigahertz phonons into telecom photons.

Note added in proof: During the submission process, we became aware of a related work demonstrating a GaAs OMC in the low thermal occupation regime46.

## Data availability

The data represented in the figures are available as Supplementary information files. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

We thank V. Anant, J. Davis, M. Jenkins and C. Schäfermeier for valuable discussions and support. We also acknowledge assistance from the Kavli Nanolab Delft, in particular from M. Zuiddam and C. de Boer. The sample growth was realized in the NanoLab@TU/e cleanroom facility. This project was supported by Foundation for Fundamental Research on Matter (FOM) Projectruimte grants (15PR3210, 16PR1054), the European Research Council (ERC StG Strong-Q, 676842) and by the Netherlands Organisation for Scientific Research (NWO/OCW), as part of the Frontiers of Nanoscience programme, as well as through a Vidi grant (680-47-541/994), the Gravitation programme Research Center for Integrated Nanophotonics and the ARO/LPS CQTS programme.

## Author information

M.F., R.S., K.S. and S.G. planned the experiment and performed the device design. M.F., R.S., C.G. and R.A.N. fabricated the sample and F.v.O. and A.F. supplied the material. M.F., R.S., A.W. and I.M. performed the measurements, while M.F., R.S., K.S. and S.G. analysed the data and wrote the manuscript with input from all authors. S.G. supervised the project.

Correspondence to Simon Gröblacher.

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### Competing interests

M.F., R.S. and S.G. declare that there is a pending patent application related to this research.

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