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Quantum acoustics with superconducting qubits
Yiwen Chu, Prashanta Kharel, William H. Renninger, Luke D. Burkhart, Luigi Frunzio, Peter T. Rakich, Robert J. Schoelkopf
TL;DR
Sophisticated quantum control of mechanical motion requires long coherence times, sufficient interaction strength, and simple, scalable systems. This paper experimentally demonstrates a strongly coupled bulk acoustic wave resonator and superconducting qubit, achieving microsecond-scale coherence and basic qubit–phonon operations.
Problem
Quantum control of mechanical motion requires systems combining long coherence times with sufficient interaction strength, simple fabrication, and future scalability.
Method
The authors experimentally demonstrate strong coupling between a high-frequency bulk acoustic wave resonator and a superconducting qubit using piezoelectric transduction.
Results
The device provides qubit coherence of many microseconds, controllable access to multiple phonon modes, and basic quantum operations on the coupled qubit–phonon system.
Takeaways & Limitations
The system provides a resource for hybrid quantum technologies and may support advanced protocols analogous to those demonstrated in optical and microwave resonators.
Takeaways & Limitations
More subtle characteristics require simulation using more sophisticated methods, and reported fidelity is likely limited by the swap operation, making it a lower bound.
Abstract
from arXiv · showhide
The ability to engineer and manipulate different types of quantum mechanical objects allows us to take advantage of their unique properties and create useful hybrid technologies. Thus far, complex quantum states and exquisite quantum control have been demonstrated in systems ranging from trapped ions to superconducting resonators. Recently, there have been many efforts to extend these demonstrations to the motion of complex, macroscopic objects. These mechanical objects have important applications as quantum memories or transducers for measuring and connecting different types of quantum systems. In particular, there have been a few experiments that couple motion to nonlinear quantum objects such as superconducting qubits. This opens up the possibility of creating, storing, and manipulating non-Gaussian quantum states in mechanical degrees of freedom. However, before sophisticated quantum control of mechanical motion can be achieved, we must realize systems with long coherence times while maintaining a sufficient interaction strength. These systems should be implemented in a simple and robust manner that allows for increasing complexity and scalability in the future. Here we experimentally demonstrate a high frequency bulk acoustic wave resonator that is strongly coupled to a superconducting qubit using piezoelectric transduction. In contrast to previous experiments with qubit-mechanical systems, our device requires only simple fabrication methods, extends coherence times to many microseconds, and provides controllable access to a multitude of phonon modes. We use this system to demonstrate basic quantum operations on the coupled qubit-phonon system. Straightforward improvements to the current device will allow for advanced protocols analogous to what has been shown in optical and microwave resonators, resulting in a novel resource for implementing hybrid quantum technologies.
experimentally demonstrate a high frequency bulk acoustic wave resonator that is strongly
The paper demonstrates strong coupling between a superconducting qubit and a high-frequency bulk acoustic resonator, combining microsecond-scale coherence with access to many phonon modes and basic quantum control.
- Device and motivation: The system addresses the challenge of combining long coherence, sufficient coupling strength, and a robust, easily implemented electromechanical platform.The strong-coupling regime requires g to exceed the qubit and oscillator loss rates.
- Device and motivation: Strong coupling is demonstrated between a superconducting qubit and the phonon modes of a high-overtone bulk acoustic wave resonator using piezoelectric transduction.The device incorporates a piezoelectric transducer into a standard 3D transmon geometry.
- Scalability and applications: C = g^2/κγ = 260, and the device provides individually addressable acoustic modes that could form a multimode quantum-information register.The reported cooperativity is more than an order of magnitude higher than in previous qubit-coupled mechanical systems.
- Spectroscopy and coupling: 13.2 MHz is the measured free spectral range between evenly spaced qubit-phonon anticrossings associated with different longitudinal phonon modes.The anticrossings appear while tuning the transmon frequency with applied flux.
- Quantum control and coherence: T1 = 17 ± 1 µs and T2 = 27 ± 1 µs characterize the phonon coherence, while the qubit exhibits vacuum Rabi oscillations near anticrossings.The phonon T1 data include a decaying sinusoidal component, and the phonon T2 is measured with a modified Ramsey sequence.
- Scalability and applications: The authors identify straightforward improvements toward advanced quantum-acoustics protocols, including higher phonon Fock states and hybrid microwave-to-optical transduction.The device is presented as a resource for hybrid quantum technologies and more sophisticated operations analogous to those in optical and microwave resonators.
1 Fabrication procedures
The device uses a relatively simple fabrication procedure to integrate AlN transducer disks with a standard 3D transmon geometry. The process defines and thins the AlN disks, aligns the qubit, and fabricates the transmon by standard lithography and evaporation.
- Substrate preparation: The fabrication uses commercially purchased double-side-polished 2-inch sapphire as the substrate.
- AlN disk fabrication: A 1 µm c-axis AlN film on sapphire is patterned into circular disks using chromium masking and reactive ion etching.The AlN is subsequently thinned to approximately 900 nm, with a slight sapphire etch during the process.
- Alignment: Chromium alignment markers are fabricated alongside the disks and used to align the qubit to the AlN.The markers are physically protected during subsequent etching steps.
- Qubit fabrication: The transmon qubit is fabricated with standard electron-beam lithography and Dolan-bridge evaporation.The deposited aluminum electrically connects the top of the AlN disk to the surrounding structure.
2 Frequency dependence of phonon modes
Spectroscopy and vacuum Rabi measurements reveal regularly spaced longitudinal phonon modes with frequency-dependent transverse-mode substructure. The observed features provide a longitudinal phonon velocity and show that transverse confinement varies with mode number.
- Longitudinal modes: 13.2 MHz anticrossings recur across the spectrum, corresponding to the longitudinal free spectral range of the phonon Fabry–Perot resonator.
- Mode spectroscopy: Spectroscopy and vacuum Rabi measurements around l = 429 reveal a dominant anticrossing and additional higher-frequency subfeatures.The substructure differs qualitatively from that observed around the l = 503 mode.
- Longitudinal modes: A linear fit across nine investigated free spectral ranges gives a longitudinal phonon velocity of v_l = 1.11×10^4 m/s.
- Transverse-mode dependence: The relative locations and intensities of transverse-mode subfeatures change with longitudinal mode number l, rather than following simple overall frequency scaling.The behavior could be explained by frequency-dependent transverse confinement from the AlN.
3 Phonon T1 versus swap operation parameters
The experiments examine how swap-pulse parameters affect phonon T1 measurements in a multimode qubit–phonon system. The data show interference and coherent qubit–phonon operations, including a phonon memory that can outlive the qubit.
- Swap-pulse dependence: The measurements show slow oscillations from the m = 0 and m = 1 frequency difference and fast oscillations at approximately 3 MHz.The fast oscillations correspond to the detuning difference between the swap pulse and the delay period.
- Quantum interference: When the qubit is returned to resonance for a second swap pulse, qubit and phonon populations interfere and produce oscillations.
- Effective T1: Phonon T1 is maximal when the qubit population is most efficiently swapped into the phonon and gradually returns to the uncoupled-qubit value away from strongly coupled modes.
- Coherent operations: The data demonstrate coherent operations between the qubit and phonon, with the phonon serving as a quantum memory that is longer lived than the qubit.
4 Analysis of phonon modes
The analysis combines lossy-resonator and semi-infinite radiation pictures to model phonon propagation, diffraction, and qubit coupling. A discrete-mode quantum simulation reproduces the observed vacuum Rabi behavior reasonably well.
- Physical pictures: The system can be viewed both as a phonon box with two ends and as a piezoelectric transducer radiating into bulk-crystal free space.The transverse boundaries are effectively open, while the large AlN diameter limits diffraction beneath the transducer.
- Physical pictures: The analysis models diffraction loss using semi-infinite-system modes and models confined strain using a fictitious cylindrical box with a high quality factor.Both descriptions can represent systems with geometric or radiation loss, depending on the chosen boundaries.
- Coupling model: The qubit–phonon interaction is derived from piezoelectric stress and electric-field overlap, then mapped under the rotating wave approximation to a Jaynes–Cummings coupling.The model assumes dominant tensor components perpendicular to the substrate surface and a constant electric field across the transducer.
- Quantum simulation: The few-mode quantum simulation agrees reasonably well with experiment, indicating that the system can be modeled using a few discrete phonon modes.The simulation initializes the qubit excited and phonons in vacuum, then evolves the system with mode detunings, couplings, and phenomenological phonon losses.
- Quantum simulation: 2π×260 kHz is the extracted l,m=0 coupling strength after scaling the simulated couplings to match vacuum Rabi data.The estimated unscaled coupling was g ∼2π × 300 kHz, and the fit used an overall scale factor.
- Experimental comparison: The fitted qubit coherence parameters are T1 ∼4 µs and T2 ∼7µs.The broader modeling framework is intended to qualitatively reproduce the experimental results, while more exact geometry simulations are presented separately.
5 Beam propagation simulations: Finding acoustic modes with AlN
Beam propagation and resonant acoustic excitation are used to find acoustic resonances and mode profiles while including the AlN disk. The simulations reproduce measured mode-spacing trends and show energy concentration within AlN, but the modes remain leaky.
- Simulation method: Resonances are identified by repeatedly propagating the field, summing round-trip fields at z = 0, and sweeping drive frequency for resonant intensity buildup.An additional phase accounts for the AlN disk during each round trip.
- Simulation method: The simulation starts with a longitudinally polarized field that is constant in the AlN region and zero elsewhere, then propagates it through the crystal.This initial condition follows the assumption of constant piezoelectric stress or drive in AlN.
- Mode extraction: The converged complex field sum yields standing-wave mode profiles at resonance, which are then used to calculate quantities such as qubit coupling rates.The method is intended to find acoustic modes for arbitrary geometries, including future shaped resonators.
- Comparison with experiment: At lower longitudinal mode number, corresponding to smaller phonon frequencies, higher-order transverse modes separate more strongly as observed experimentally.The analysis focuses on comparing frequency spacings because maximum-value plots are not direct measurements of total acoustic intensity.
- Mode properties: Most acoustic energy near l = 503 is confined within the AlN region, although the modes extend across the domain and lose energy at absorbing boundaries.Their leaky character appears as finite resonance widths in the simulated spectrum.
- Future improvements: Future simulations will guide plano-convex boundary designs to laterally confine thickness modes and shape the AlN drive region for single-mode coupling.The stated goal is to increase phonon coherence and tailor coupling to one phonon mode.