This paper is available on arxiv under CC 4.0 license. Authors: (1) Terence Blésin, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (2) Wil Kao, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (3) Anat Siddharth, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL); (4) Alaina Attanasio, OxideMEMS lab, Purdue University; (5) Hao Tian, OxideMEMS lab, Purdue University; (6) Sunil A. Bhave, OxideMEMS lab, Purdue University; (7) Tobias J. Kippenberg, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL). Table of Links Introduction Results A. Physics and design B. Device characterization C. Bidirectional microwave-optical transduction D. Pulsed transduction Discussion Acknowledgments Appendix A: Theory Appendix B: Fabrication process flow Appendix C: Optical characterization Appendix D: Characterization of acoustic resonances Appendix E: Characterization of bidirectional transduction Appendix F: Optimization of optical extraction efficiency III. DISCUSSION Non-classically correlated microwave-optical photon pairs can be generated through spontaneous parametric down-conversion in our transducer. These correlated photon pairs constitute a key ingredient toward entangling distant quantum processors via the Duan-LukinCirac-Zoller protocol [4, 45]. With the current device parameters, the pair generation rate on chip amounts to 190 Hz, which is well above the thermal decoherence rate for 3.5 GHz at 10 mK as explained in Appendix A 4. However, losses in the measurement setup specific to such an experiment, as well as the gating of the optical pump required to alleviate the effective heat load, are expected to limit further the final heralding rate. Quasi-free-standing structures, such as 1D OMCs, do not readily thermalize and are thus more susceptible to heating effects. Even though our transducer also utilizes a suspended acoustic resonator, it may be feasible to operate at a higher duty cycle than what is presented in Fig. 4. It has been shown that a buffer gas environment can facilitate thermalization of a 1D OMC, at the cost of increased damping of the mechanical breathing mode [46]. On the contrary, the HBAR mode of interest here should be relatively insensitive to such viscous damping, as the acoustic wave propagates predominantly along the longitudinal direction inside the cladding. Therefore, a sample cell affixed to the mixing chamber flange and filled with buffer superfluid helium—an inviscid fluid that is both an excellent thermal conductor and electrical insulator—could potentially improve the heralding rate without hampering the conversion efficiency [47]. The present design is also suited for tasks beyond quantum state transfer. The transducer can be a key component of photonic interconnects for superconducting qubits [7, 8], where laser lights routed through optical fibers are used to encode microwave signals directly inside the dilution refrigerator during qubit readout. It may be challenging for traveling-wave EOMs to attain the requisite half-wave voltage to be competitive in noise performance against conventional all-electrical readout scheme utilizing high-electron-mobility transistor amplifiers [8]. Our triply resonant approach affords a path towards a scalable optically controlled cryogenic waveform generator for both qubit readout and control. The multimode nature of the transducer is particularly suited for frequency-multiplexed dispersive readout. Transduction leveraging multiple HBAR modes is already demonstrated in Fig. 3e. One can additionally utilize line-type instead of point-type dimer coupling for the photonic molecule, which gives rise to a dispersion in the supermode splitting [48]. In combination with the multitude of acoustic overtones, a single transducer can therefore support several spectrally distinguishable triply resonant systems that serve as qubit multiplex channels. Finally, since the transducer requires no superconducting element to function, it may be pertinent for applications in classical microwave photonics. Optimization of design and fabrication should engender further improvement on device performance. The conversion efficiency, proportional to microwave extraction efficiency (Eq. 2), can be improved by replacing AlN with scandium-doped AlN [49], which features a piezoelectric coefficient d33 about five times larger than AlN [50, 51] while preserving CMOS compatibility. There is likewise additional upside on the photonics (Appendix C 1). Bending radiation loss can be significantly reduced by increasing the micro-ring radius r. In particular, intrinsic quality factor exceeding 107 has been demonstrated with an r approximately ten times larger using the same fabrication process [52]. It may be anticipated that the efficiency gain here may be chiefly compensated by the reduction in optomechanical coupling rate g0 ∼ 1/ √ r. Nevertheless, by thinning the waveguide to 200 nm that approaches half of the acoustic wavelength, g0 is expected to remain unchanged. As in the thick-core waveguide fabricated using the photonic Damascene process, such a thin-core waveguide on a subtractive manufacturing platform is expected to exhibit negligible bending loss [53]. Assuming critical coupling conditions (Appendix F), we therefore expect another 1.5- time gain in η tot. Finally, optical insertion loss can be nearly eliminated by employing a spot-size converter to facilitate mode-matching with lensed fiber [54–56]. Combining these improvements, our transducer could achieve a total efficiency η tot = 6 × 10−3 . In conclusion, we have designed, fabricated, and characterized a compact piezo-optomechanical microwaveoptical transducer that integrates wafer-scale, CMOScompatible HBAR and Si3N4 photonic technologies. Free of any superconducting components, this triply resonant transducer attains a bidirectional off-chip photon number conversion efficiency of 1.6 × 10−5 and a bandwidth of 25 MHz, with an input pump power of 21 dBm at room temperature. Multimode transduction leveraging distinct HBAR modes have been demonstrated, suggesting prospects for designing frequency-multiplexed photonic interconnects for superconducting qubits. Realistic design and fabrication improvements may even allow access to experiments in the quantum regime.

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