Gigahertz-frequency Lamb wave resonator cavities on suspended lithium niobate for quantum acoustics

TL;DR

Phonons in piezoelectric materials offer strong confinement and versatile interfaces to quantum systems, but bulk LiNbO3 devices suffer surface leakage. This work demonstrates GHz Lamb-wave resonator cavities on a 200 nm suspended LiNbO3 membrane with Bragg mirrors, identifying the antisymmetric $A_0$ mode near $f_0 \approx 2$ GHz and characterizing them at room temperature and $\sim 10$ mK. A Butterworth–van Dyke model yields lumped parameters and shows intrinsic $Q_i$ up to $\approx 6600$, with TLS-related losses modulated by phonon occupancy. By proposing a flip-chip inductive coupling to superconducting transmons and evaluating coupling strengths, the study outlines a viable path toward strong qubit-phonon interfaces and quantum acoustic devices based on gigahertz Lamb waves in LiNbO3.

Abstract

Phononic nanodevices offer a promising route toward quantum technologies, as phonons combine strong confinement within matter with broad coupling capabilities to various quantum systems. In particular, the piezoelectric response of materials such as lithium niobate enables coupling between superconducting qubits and gigahertz-frequency phonons. However, bulk lithium niobate phononic devices typically rely on surface acoustic waves and are therefore inherently subject to leakage from the surface into the bulk substrate. Here, we explore the acoustic behavior of resonator cavities supporting GHz-frequency Lamb waves in a 200 nm-thick suspended lithium niobate layer. We characterize the acoustic response at both room and millikelvin temperatures. We find that our resonator cavities with strong confinement reach intrinsic quality factors of approximately 6000 at the single phonon level. We use the measured parameters of the resonators to model their coupling to a superconducting transmon qubit, allowing us to evaluate their potential as quantum acoustic devices.

Figures (5)

• Figure 1: Lamb wave resonator cavities on suspended lithium niobate. (a) Optical microscope image and magnified detail of a representative suspended resonator cavity, consisting of a central IDT terminated along each emission direction by a set of acoustic mirrors, the whole patterned on a suspended 200-nm-thick Y-cut lithium niobate plate. For the cavity here, the IDT–mirror spacing is 5 $\mu$m. (b) Measured room-temperature $|S_{21}|$ transmission through the IDT of a resonator cavity with an IDT-mirror spacing of 10 $\mu$m. The fit is based on the Butterworth-van Dyke (BvD) model chou2020measurements, whose equivalent electrical circuit is shown inset; ports 1 and 2 correspond to the VNA ports used for this measurement. (c) Model for the resonator cavity used for finite element simulations. (d) Real and imaginary parts of the simulated admittance, calculated via a finite element simulation for a resonator cavity with an IDT–mirror spacing of 10 $\mu$m. The resonance frequency agrees well with experimental measurements. (e) Displacement field magnitude for the simulated resonant mode, showing the confined antisymmetric $A_0$ Lamb mode from a top-view perspective of the entire cavity (top) and from a cross-sectional view of the cavity center (bottom).
• Figure 2: Suspended resonator cavities measured at room temperature. (a) $|S_{11}|$ reflection measurement using the configuration shown inset in the panel equivalent circuit, for different IDT-mirror spacings. (b) $|S_{21}|$ transmission measurements with the configuration shown inset in the panel equivalent circuit, for different IDT-mirror spacings. (c) $|S_{21}|$ transmission measurements with the configuration shown inset in Fig.\ref{['fig:1']}(b), for different IDT-mirror spacings. All spectra are normalized to the absolute value of their main dip and vertically offset for clarity. (d) Imaginary part of the inverse scattering parameter $1/S$ for the measurements in panels (a) and (b), for two resonator cavities with IDT–mirror spacing of 5 $\mu$m, together with the corresponding fits. The scattering parameter subscripts $11$ and $21$ are omitted. The normalized magnitude of these fits are shown as dashed lines in panels (a) and (b) for the corresponding spectra. (e) Fit intrinsic quality factors $Q_i$ for all measured cavities with different IDT–mirror spacings, obtained from both reflection and transmission measurements. When multiple $Q_i$ values are shown for a given IDT–mirror spacing, these correspond to distinct resonant dips of a single resonator cavity.
• Figure 3: Suspended resonator cavities measured in the millikelvin regime. (a–c) Transmission spectra for resonator cavity RC-A (tee configuration, panel a), RC-B (through configuration, panel b) and RC-C (through configuration, panel c) measured at $\sim$10 mK. Spectra are vertically offset for clarity. Measurement power (color scale) corresponds to the signal output from VNA, which is heavily attenuated in the cryostat. (d) Inverse $1/S_{21}$ signal in the complex plane for RC-A (tee measurement; see Table \ref{['table:Devices']}) with a VNA power of -60 dBm, together with the corresponding fit. The magnitude of the fit is shown in panel (a) superposed on the corresponding spectrum. (e) Fitted intrinsic quality factors of modes in each of the three cavities as a function of phonon occupation. For RC-A and RC-B, only a single resonance is present, whereas for RC-C, the $Q_i$ for three resonances is displayed. (f) Same data as in (e), with the quality factors normalized to their respective values at the highest input power. For both (e) and (f) panels, the power scale on the bottom axis is from the VNA power combined with an estimate of the line attenuation (see discussion), with a roughly 10 dB uncertainty in the actual attenuation.
• Figure 4: Coupling between a transmon qubit and a suspended resonator cavity. (a) Transmission spectrum $|S_{21}|$ in the millikelvin regime for RC-B and corresponding BvD fit. (b) Schematic illustration and equivalent circuit diagram using the BvD model for a transmon qubit inductively coupled to a suspended resonator cavity. (c) Calculated coupling as a function of the coupler junction inductance $L_{c0}$ for a suspended resonator cavity with an aperture of 10 $\mu$m ($C_0=0.07$ pF) and of 100 $\mu$m ($C_0=0.7$ pF).
• Figure 5: Schematic of the circuitry in the dilution refrigerator, together with a photograph of the sample wire-bonded to the printed circuit board.