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Circuit quantum acoustodynamics with surface acoustic waves
R. Manenti, A. F. Kockum, A. Patterson, T. Behrle, J. Rahamim, G. Tancredi, F. Nori, P. J. Leek
TL;DR
The paper addresses how superconducting qubits can interact with propagating surface acoustic waves confined in a cavity. It measures a tuneable transmon coupled to a SAW resonator, characterizes dispersive interactions and time-delayed shifts, and finds a 5.7 ± 0.5 MHz acoustic coupling. The work demonstrates a cavity-QED-like acoustic device and identifies possible uses of trapped SAWs.
Problem
Propagating SAWs can couple piezoelectrically to superconducting qubits and be confined in Fabry-Perot cavities, but their interaction in a cavity-QED device remains to be characterized.
Source: p. 1Method
The authors measure a tuneable transmon piezoelectrically coupled to a SAW cavity, probing qubit- and acoustic-mode frequency shifts and time-delayed Stark shifts.
Source: pp. 1–2Results
The measured acoustic coupling is λm2 = 5.7±0.5 MHz at fq = 2.52 GHz, and an independent Stark-shift estimate is λm2 = 5.9 ± 0.2 MHz.
Source: pp. 3–4Takeaways & Limitations
The slow travel of SAWs permits time-delayed control in a compact cavity-QED-like device and may support quantum memories, time delays, and signal filtering.
Source: p. 5The prototype uses a relatively weak piezoelectric substrate, and undesired bulk acoustic emission likely limits qubit coherence.
Source: p. 5
Abstract
from arXiv · showhide
The experimental investigation of quantum devices incorporating mechanical resonators has opened up new frontiers in the study of quantum mechanics at a macroscopic level$^{1,2}$. Superconducting microwave circuits have proven to be a powerful platform for the realisation of such quantum devices, both in cavity optomechanics$^{3,4}$, and circuit quantum electro-dynamics (QED)$^{5,6}$. While most experiments to date have involved localised nanomechanical resonators, it has recently been shown that propagating surface acoustic waves (SAWs) can be piezoelectrically coupled to superconducting qubits$^{7,8}$, and confined in high-quality Fabry-Perot cavities up to microwave frequencies in the quantum regime$^{9}$, indicating the possibility of realising coherent exchange of quantum information between the two systems. Here we present measurements of a device in which a superconducting qubit is embedded in, and interacts with, the acoustic field of a Fabry-Perot SAW cavity on quartz, realising a surface acoustic version of cavity quantum electrodynamics. This quantum acoustodynamics (QAD) architecture may be used to develop new quantum acoustic devices in which quantum information is stored in trapped on-chip surface acoustic wavepackets, and manipulated in ways that are impossible with purely electromagnetic signals, due to the $10^{5}$ times slower speed of travel of the mechanical waves.
I. DEVICE PARAMETERS
The device combines a tuneable transmon with a two-port SAW cavity and an auxiliary CPWR. Its resonator geometry balances acoustic coupling, losses, and the number of supported modes, with measured parameters characterizing the acoustic and microwave resonances.
I. DEVICE PARAMETERS
- A 6 µm-periodicity IDT-and-grating layout forms the two-port acoustic cavity around a central tuneable transmon.Each grating has 400 shorted strips; the transmon's interdigitated capacitance has the same periodicity as the IDTs.Source: §I · p. 7, Figure S1 · p. 7
- The cavity length and grating spacing were chosen to balance high internal quality factor, stronger qubit coupling, and fewer longitudinal modes.The design uses n2 = 158 and a grating separation of 1260 µm; increasing grating distance raises internal quality factor and the number of supported modes, while coupling decreases with cavity area.Source: §I · pp. 7, 9
- Assuming fm2 is the central resonance, the effective speed of sound is 3140.6 m/s, calculated as λ0 × fm2; optimal transduction occurs when wavelength λ equals λ0.The longitudinal cavity length extracted from the frequency difference between fm3 and fm2 is 1370 µm, in agreement with time-domain measurements.Source: §I · p. 8
- The auxiliary CPWR resonates at 5.83 GHz, with a 3.41 MHz linewidth and qubit coupling strength g = 69 MHz.The reported internal and external quality factors are 3240 and 3630.Source: §I · pp. 8–9
- The SAW cavity has three modes at 522.825, 523.426, and 524.575 MHz, with linewidths of 108, 75, and 69 kHz, respectively.The fitted internal quality factors are 4830, 7020, and 7600; the corresponding external quality factors are 2.34 × 10^6, 1.33 × 10^6, and 2.33 × 10^6.Source: §I · pp. 8–9
- The qubit has relaxation time T1 = 46 ns at fq = 2.9 GHz, and its Rabi frequency varies linearly with drive amplitude.The supplementary measurements also report T2 = 67 ns at fq = 2.6 GHz.Source: §I · p. 9
II. COUPLING STRENGTH BETWEEN A CHARGE QUBIT AND A SAW CAVITY
The section derives the transmon–SAW cavity coupling from the single-phonon acoustic potential and transmon charge, then compares the calculated value with experiment.
II. COUPLING STRENGTH BETWEEN A CHARGE QUBIT AND A SAW CAVITY
- A SAW crossing a matching-periodicity interdigitated capacitor generates an oscillating electrode voltage, providing the basis for coupling to the transmon.The calculation considers the charge and potential difference generated by a single phonon.Source: §II · p. 9
- The zero-point electric potential is derived from the cavity’s zero-point mechanical motion and scaled by a normalized array factor for the transmon capacitance.At f = f0, A(f) = 1, so the potential difference is V0 = φ0A(f); epz/ε ≈ 2.0 V/nm for ST-X quartz.Source: §II · p. 10
- For the first two transmon levels, the charge-operator matrix element is ⟨1|q̂|0⟩ ≈ eβ (EJ(φ)/2EC)^(1/4); β is a prefactor.Source: §II · p. 10
- The prefactor β accounts for acoustic-wave charge distributed across the gate, junction, strain, and transmon capacitances.The cited capacitances include C2, CJ, Cs, and Cq.Source: §II · p. 10
- The calculated coupling strength agrees well with the experimental value extracted from measurements.The calculation uses a qubit frequency of 2.52 GHz and assumes β ≈ 1 and A(f) ≈ 1.Source: §II · p. 11
III. CRYOGENIC SETUP AND FABRICATION PROCEDURE
The device was measured at cryogenic temperature with attenuated microwave and IDT lines; its ground planes, waveguides, SAW resonator, and qubit were fabricated using lithography and metal deposition.
III. CRYOGENIC SETUP AND FABRICATION PROCEDURE
- The chip was anchored to a dilution refrigerator’s 10 mK plate, and the CPWR readout line had measured attenuation of −67 dB.The reflected signal passed through two 4–8 GHz circulators and a 1–12 GHz HEMT amplifier; the IDT lines had estimated attenuation of −16 dB.Source: §III · pp. 11–12
- Ground planes, alignment marks, and waveguides were patterned first, followed by joint electron-beam patterning of the SAW resonator and qubit.The ground-plane and waveguide metal structures were 100 nm thick.Source: §III · p. 12
- The 200 × 200 nm2 junctions used Dolan-bridge double-angle evaporation, yielding a total qubit and SAW resonator height of 90 nm.The aluminium layers were 30 nm and 60 nm, separated by in-situ oxidation.Source: §III · p. 12