A variety of nanomechanical systems can now operate at the quantum limit1,2,3,4, making quantum phenomena more accessible for applications and providing new opportunities for exploring the fundamentals of quantum physics. Such mechanical quantum devices offer compelling opportunities for quantum-enhanced sensing and quantum information5,6,7. Furthermore, mechanical modes provide a versatile quantum bus for coupling hybrid quantum systems, supporting a quantum-coherent connection between different physical degrees of freedom8,9,10,11,12,13. Here, we demonstrate a nanomechanical interface between optical photons and microwave electrical signals, using a piezoelectric optomechanical crystal. We achieve coherent signal transfer between itinerant microwave and optical fields by parametric electro-optical coupling using a localized phonon mode. We perform optical tomography of electrically injected mechanical states and observe coherent interactions between microwave, mechanical and optical modes, manifested as electromechanically induced optical transparency. Our on-chip approach merges integrated photonics with microwave nanomechanics and is fully compatible with superconducting quantum circuits, potentially enabling microwave-to-optical quantum state transfer, and photonic networks of superconducting quantum bits14,15,16.
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In engineered quantum systems, the interactions between different physical degrees of freedom can be strongly enhanced by mode confinement in nanoscale structures. In the field of optomechanics17, this has recently enabled quantum-coherent coupling between optical and mechanical modes, and quantum control of mechanical motion2,3,4. The emerging possibility of mechanically mediated state transfer11,18,19,20,21,22 promises a new type of quantum transducer, using nanomechanical motion to translate electrical or spin-based quantum states to photonic states, thereby creating an optical quantum interface.
Here, we present a nanomechanical transducer in which a purpose-designed microwave-frequency mechanical mode generates a coupling between electrical signals at 4 GHz and optical photons at 200 THz. Strong coherent interactions between the electrical, mechanical and optical modes are enabled by combining electromechanical and optomechanical coupling in a piezoelectric optomechanical crystal. Fabricated from aluminium nitride (AlN) and monolithically integrated on-chip, the transducer is fully compatible with superconducting quantum circuits and is well suited for cryogenic operation. Operating at microwave mechanical frequencies, this device in principle allows quantum ground-state control of the mechanical mode1 and state transfer between quantum microwave and optical channels.
The transducer is illustrated in Fig. 1. A mechanically suspended beam of AlN (0.33×1×100 μm3) is patterned as an optomechanical crystal, designed to support a highly localized phonon mode at 4.2 GHz and a co-localized optical mode at 196 THz with strong optomechanical coupling3,23. The beam also includes a pair of aluminium electrodes connected to an on-chip, broadband microwave transmission line, enabling strong electromechanical coupling through the piezoelectric effect in AlN (refs 1, 24, 25). The transducer is connected optically using an evanescently coupled rib waveguide, with signals routed to a pair of optical fibres by means of on-chip grating couplers. The optical design wavelength is 1,550 nm, matching a fibre-optic telecommunication band. The 4–5 GHz design frequency of the confined mechanical mode is compatible with the operating frequency of superconducting quantum bits1,15,16.
The dynamics of the integrated system are described by the Hamiltonian of equation (1),
where the first term is the energy in the optical cavity mode, with photon operators a(a†), the second term is the energy in the microwave-frequency mechanical mode, with phonon operators b(b†), the third term is the usual optomechanical interaction term with optomechanical interaction strength gom (refs 3, 17), and the last term represents electrical actuation of the mechanical mode, using a Jaynes–Cummings interaction with coupling strength gem and an electrical driving field with operators c(c†) (refs 1, 26).
We characterized the room-temperature optomechanical properties of the device using a tunable diode laser. The optical transmission signal, shown in Fig. 1d, exhibits a high-quality-factor photonic crystal resonance at 1,531.5 nm (intrinsic quality factor Qopt = 130,000, optical linewidth κ/2π = 2.5 GHz) indicative of the confined optical mode shown in Fig. 1b.
For mechanical modes with sufficient overlap with the optical mode, thermomechanical motion of the photonic crystal induces phase and intensity modulations on the transmitted probe laser light, detected as resonances at the mechanical frequencies in the optical noise power spectrum. We observe several thermally excited flexural, torsional and extensional beam modes, shown in Fig. 2. The most relevant spectral feature is the resonance at ωm/2π = 4.24 GHz, induced by the mechanical breathing mode localized at the centre of the optomechanical crystal, shown in Fig. 2b (mechanical quality factor Qmech = 2,500, linewidth Γmech/2π = 1.7 MHz). Probed in thermal equilibrium at room temperature (Nth≈1,500 phonons), the integral over the resonance in the noise spectral density yields an optomechanical coupling gom/2π = 30±5 kHz, in agreement with numerical simulations (Supplementary Information). We note that the mechanical mode frequency ωm is significantly larger than the optical linewidth κ, meeting the crucial requirement for operation in the resolved sideband regime, and allowing access to the rich toolbox of cavity optomechanics17. These performance metrics, achieved using a strong piezoelectric material, provide an excellent outlook for quantum electro-optomechanics.
We use piezoelectric actuation of the optomechanical crystal to generate a strong optical response. When applying a fixed voltage difference V dc to the electrodes (Fig. 2c), piezoelectric dilatation shifts the photonic crystal resonance frequency ωcav/2π and we measure dωcav/dV dc = 2π×310 MHz V−1, in agreement with numerical simulations. The shift is linear and preserves the sign of the applied voltage, in contrast to capacitive actuation27. When applying radiofrequency electrical signals to the transducer electrodes, we induce a complex, frequency-dependent displacement field, generating a series of distinct electro-optomechanical resonances. Sweeping the electrical excitation frequency Ω while monitoring the mechanically induced optical sideband power at frequency ωlaser±Ω yields the electro-optic transfer function S21(Ω), shown in Fig. 2a,b (Supplementary Information). Comparison of this transfer function with the thermomechanical spectrum and numerical simulations allows us to identify the most prominent resonances (Fig. 2a,b,d). Resonances between 20 and 200 MHz correspond to electrically actuated in-plane extensional beam modes. The fundamental breathing mode of the optomechanical crystal appears as a resonance at 4.24 GHz (Fig. 2b), with an effective electro-optomechanical frequency shift dωcav/dV rms = 2π×300 MHz/V rms. We focus on this mode for the remainder of this work.
A prerequisite for quantum state transfer is the faithful mapping of phase and amplitude from the electrical to the optical field through the mechanical mode. We investigate this by performing optical homodyne tomography of the electrically generated localized phonon state, shown schematically in Fig. 3a. We downconvert the optomechanically induced optical sidebands of the 196 THz optical carrier to 4.24 GHz through optical beat note detection, and further downconvert to a homodyne signal by quadrature-sensitive mixing with the radiofrequency drive signal (see Supplementary Information). Figure 3b shows the measured homodyne signal when exciting the breathing mode electromechanically at a frequency Ωexc = ωm with Nexc≈106 phonons, while sweeping the laser frequency across the optical cavity resonance. The characteristic antisymmetry of the homodyne signal provides confirmation of frequency modulation, as expected for parametric optomechanical coupling, in contrast to intensity modulation (see Supplementary Information).
Homodyne tomography allows us to reconstruct the quadrature probability distributions of different mechanical states. We electrically inject classical mechanical states at Ωexc = ωm with a mean phonon number Nexc≈ 1,100 at phases of 0, π/2, π and 3π/2 with respect to the local oscillator, and obtain four distinct quadrature distributions (Fig. 3c), illustrating phase-preserving mapping from the electrical to the optical channel by way of the mechanical mode. The spread in the measured distributions reflects the combination of technical and thermal noise in the system. We then reduced the excitation signal to achieve on average Nexc≈100, 7 and 1 phonons (Fig. 3d). The successful detection of these few-phonon excitations on top of an incoherent thermal background of Nth≈1,500 phonons is aided by the narrow measurement bandwidth (200 Hz), yielding a detection noise floor comparable to the displacement amplitude of one phonon.
The coherent interaction of photons and phonons in cavity optomechanics manifests itself through the phenomenon of optomechanically induced transparency28,29 (OMIT). With the phonon mode coupled to an electrical mode, we expect a similarly striking effect in the electrically driven optical response: electro-optomechanically induced transparency. We add optical probe sidebands at frequencies ωp = ωlaser±Δp to the optical carrier signal at ωlaser and monitor the sideband transmission through the device. The laser carrier is red-detuned from the cavity resonance by the breathing mode frequency (ωcav−ωlaser = Δ = ωm = 2π×4.24 GHz), and the mechanical breathing mode is driven electrically at frequency Ωexc. This situation is similar to OMIT, except the mechanical motion is driven electrically instead of optically, and we control the mechanical phase, amplitude and frequency independently. The measured optical sideband transmission signals are shown in Fig. 4. A theoretical analysis is given in the Supplementary Information.
When scanning the optical sideband frequency Δp across the cavity resonance (at fixed Ωexc), we observe a narrow transparency dip in the sideband transmission (Fig. 4b). As in OMIT, this occurs when Δp = Ωexc, and is caused by destructive interference between the electromechanical and optical excitation paths of the coupled system. However, when the phase of the electrical excitation signal and hence the mechanical motion is changed by π, the sideband transmission exhibits a peak as the interference becomes constructive. In contrast to OMIT, this mechanical phase is an externally controlled parameter, and the width of the transparency window is limited only by the measurement bandwidth, which can be much narrower than the mechanical linewidth. This is exemplified when the electromechanical excitation frequency Ωexc is swept while keeping the optical sideband fixed at Δp (Fig. 4c). The Lorentzian envelope of the mechanical sideband transmission is given by the mechanical susceptibility of the system, and the characteristic transparency again occurs at Δp = Ωexc. The envelope function of all possible transparency dips (peaks) is measured by synchronously sweeping the probe sideband Δp and mechanical drive frequency Ωexc (Fig. 4d), giving extinction ratios as high as 25 dB in the transparency window.
The controlled interactions between electrical signals, phonons and optical photons realized in this device provide an excellent outlook for quantum electro-optomechanics. The mechanical frequency of more than 4 GHz gives access to the single quantum regime at temperatures below about 0.3 K, and is well suited for integration into a superconducting quantum bit architecture. From the transducer geometry and extrapolation from previous work1, we can expect electromechanical coupling rates up to gem/2π = 40 MHz when coupled to a single superconducting qubit1, exceeding the expected qubit decoherence rate γ/2π<1 MHz. Operating in the resolved-sideband regime of optomechanics, the measured optomechanical coupling of gom/2π = 30 kHz should enable mechanical-to-optical quantum swap operations at a rate Ωom/2π = 6 MHz at moderate laser power, faster than the intrinsic decoherence rate of the mechanical resonator Γ/2π = 1.7 MHz (Supplementary Information). Our transducer concept thus opens a potentially viable path towards microwave-to-optical quantum state transfer. This should allow mapping of on-chip synthesized microwave quantum states30 to optical modes, thereby providing a unique source of non-classical light and enabling long-range quantum networks of superconducting quantum circuits.
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Devices were made at the UCSB Nanofabrication Facility, a part of the NSF-funded National Nanotechnology Infrastructure Network. This work was supported by DARPA ORCHID under contract HR0011-10-1-0067. J.B. acknowledges support from a Harvey Karp Discovery Award. We thank O. Painter and S. Bhave for valuable conversations and R. Ilic for fabrication assistance.
The authors declare no competing financial interests.
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Bochmann, J., Vainsencher, A., Awschalom, D. et al. Nanomechanical coupling between microwave and optical photons. Nature Phys 9, 712–716 (2013). https://doi.org/10.1038/nphys2748
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