US-12620972-B2 - Minimally diffracting surface-acoustic-wave resonator

Abstract

A surface-acoustic-wave (SAW) resonator includes a substrate formed from an anisotropic crystal and first and second acoustic reflectors disposed on a surface of the substrate. The first and second acoustic reflectors face each other to form an acoustic cavity whose axis is aligned with a crystallographic orientation of the anisotropic crystal such that the SAW resonator is minimally diffracting at cryogenic temperatures. The substrate may be a piezoelectric crystal, in which case the acoustic cavity can be excited by driving electrodes located on the surface of the substrate. Since the SAW resonator is minimally diffracting, it has less loss, and therefore can achieve higher Qs, than SAW resonators based on other crystallographic orientations.

Inventors

• Konrad Lehnert
• Alec Emser
• Lucas Sletten
• Brendon Rose

Assignees

• THE REGENTS OF THE UNIVERSITY OF COLORADO, A BODY CORPORATE
• Government of the United States of America as represented by the Secretary of Commerce

Dates

Publication Date

20260505

Application Date

20230228

Claims (20)

1. 1 . A surface-acoustic-wave (SAW) resonator, comprising: a substrate comprising an anisotropic crystal; and first and second acoustic reflectors disposed on a surface of the substrate, the first and second acoustic reflectors facing each other to form an acoustic cavity; wherein an axis of the acoustic cavity is aligned with a crystallographic orientation of the anisotropic crystal such that the SAW resonator is minimally diffracting at cryogenic temperatures.
2. 2 . The SAW resonator of claim 1 , having a diffraction parameter γ such that −2<γ<0 at the cryogenic temperatures.
3. 3 . The SAW resonator of claim 2 , the diffraction parameter γ being equal to −1.
4. 4 . The SAW resonator of claim 1 , having a beam-steering angle near zero at the cryogenic temperatures.
5. 5 . The SAW resonator of claim 1 , being minimally diffracting at temperatures less than or equal to 10 K.
6. 6 . The SAW resonator of claim 1 , each of the first and second acoustic reflectors being a Bragg reflector.
7. 7 . The SAW resonator of claim 1 , each of the first and second acoustic reflectors being flat.
8. 8 . The SAW resonator of claim 1 , the anisotropic crystal comprising a piezoelectric crystal.
9. 9 . The SAW resonator of claim 8 , further comprising first and second electrodes located on the surface of the substrate between the first and second acoustic reflectors.
10. 10 . The SAW resonator of claim 9 , the first and second electrodes comprising first and second arrays of interdigitated transducers.
11. 11 . The SAW resonator of claim 8 , the piezoelectric crystal comprising quartz.
12. 12 . The SAW resonator of claim 11 , the quartz comprising α-quartz.
13. 13 . The SAW resonator of claim 11 , wherein the crystallographic orientation of the quartz is given by Euler angles (ψ, φ, θ)=(0°, 40.2°, 23.4°).
14. 14 . The SAW resonator of claim 8 , the piezoelectric crystal being selected from the group consisting of silicon carbide (SiC), gallium arsenide (GaAs), zinc oxide (ZnO), aluminum nitride (AlN), lithium niobate (LiNbO 3 ), and lithium tantalate (LiTaO 3 ), and potassium niobate (KNbO 3 ).
15. 15 . The SAW resonator of claim 1 , the axis of the acoustic cavity being parallel to a length of the substrate.
16. 16 . The SAW resonator of claim 1 , wherein the crystallographic orientation corresponds to a singly rotated cut of the anisotropic crystal.
17. 17 . The SAW resonator of claim 1 , wherein the crystallographic orientation corresponds to a doubly rotated cut of the anisotropic crystal.
18. 18 . The SAW resonator of claim 1 , the acoustic cavity having an acoustic aperture with a width of 40λ or less, λ being an acoustic wavelength.
19. 19 . A method comprising exciting a mode of the acoustic cavity of the SAW resonator of claim 1 .
20. 20 . The method of claim 19 , wherein: the SAW resonator comprises first and second electrodes located on the surface of the substrate between the first and second acoustic reflectors; and exciting the mode of the acoustic cavity comprises electrically driving the first and second electrodes.

Description

RELATED APPLICATIONS This application claims priority to U.S. Provisional Patent Application No. 63/268,630, filed on Feb. 28, 2022, the entirety of which is incorporated herein by reference. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT This invention was made with government support under grant number N00014-20-1-2833 awarded by the Office of Naval Research. The government has certain rights in the invention. BACKGROUND A surface-acoustic-wave (SAW) resonator uses a cavity to confine acoustic modes along the surface of an elastic substrate. SAW resonators have long been an important component in the telecommunications industry, with applications including filters and delay lines, among others. More recently, low-temperature applications of SAW devices and resonators have gained interest in the field of quantum computing, where applications include isolating superconducting qubits from unwanted interference and implementing long-lived quantum memories. Additionally, in the field of quantum acoustics, acoustic devices can be integrated with superconducting qubits to implement quantum control over mechanical degrees of freedom. Acoustic systems offer quantum technologies a favorable combination of long on-chip delays, competitive coherence times, and the ability to connect disparate quantum systems. SUMMARY The present embodiments include surface-acoustic-wave (SAW) devices that reduce diffraction loss for operation at cryogenic temperatures (e.g., less than 10 K). These embodiments achieve this benefit by fabricating the device on a substrate such that SAWs propagate along a particular crystalline orientation of the substrate. This orientation is also referred to herein as a minimally-diffracting (MD) orientation. Some of the present embodiments include a SAW resonator in which a pair of acoustic reflectors (e.g., Bragg mirrors) face each other to create an acoustic cavity. The longitudinal axis of the acoustic cavity coincides with the MD orientation of the substrate at cryogenic temperatures. In other embodiments, a SAW filter or delay line is fabricated such that SAWs propagate parallel to the MD orientation. BRIEF DESCRIPTION OF THE FIGURES FIGS. 1A and 1B are functional diagrams of surface-acoustic-wave (SAW) resonators for two orientations of quartz. FIG. 2A is a functional diagram of an interdigitated transducer launching SAWs on an anisotropic substrate that exhibits beam-steering. FIG. 2B illustrates minimal diffraction. FIG. 2C is a perspective view of a quartz crystal showing a wafer oriented relative to quartz crystallographic axes: φ determines the angle at which the wafer is cut from a monocrystalline bar and θ determines the planar rotation of a device about the wafer normal. FIG. 2D is a plot of SAW velocity as a function of planar rotation for minimally diffracting (MD) and ST quartz. FIG. 2E is a plot of beam-steering angle η calculated from simulated velocity profiles for all θ and φ. FIG. 2F is a plot of diffraction parameter γ calculated from the simulated beam-steering for all θ and φ. FIG. 2G is a plot of contours for minimal beam-steering and diffraction. The six unique intersections of the curves represent MD orientations. FIG. 3A illustrates a reflection measurement from a one-port SAW resonator fabricated at φ, θ=(40.2°, 23.4°) and cooled to 20 mK. The resonator (see inset) includes a double-finger IDT and Bragg mirror gratings which are designed with a narrow acoustic aperture (10λ). Aluminum is etched away to define the coplanar waveguide, IDT, and SAW cavity. The lower portion of the figure is a plot of internal linewidth for each mode. FIG. 3B illustrates the simulated diffraction parameter γ for SAWs on φ=40.2° quartz at 293 K and 5 K. Minimal diffraction is predicted at θ=22.5° (23.4°) for warm (cold) devices. The lower portion of the figure is a plot of the measured internal linewidth of the central resonator mode of each device as θ is incremented across many devices. The fit error bars for all data points are smaller than the marker size. FIG. 4 is a plot showing measurements of the diffraction parameter γ. The internal linewidths of SAW resonators were measured at room temperature and 20 mK which sweep the width of the acoustic aperture. The solid lines are best fits. The open circles show widths for which asymmetric diffraction becomes comparable to the residual second-order diffraction. Fit error bars are smaller than the marker size. FIG. 5A shows the unit cell geometry used for unit-cell simulations. FIG. 5B shows a typical meshing for a unit-cell simulation. The longitudinal dimension is meshed more finely. FIG. 5C shows the eigenmode for the COLD quartz orientation. Deformation shows displacement in the z dimension. FIG. 5D shows the coordinate system for the simulations (top) and the crystallographic axes xc, yc and zc rotated for COLD quartz (bottom). FIG. 6 is a plot of the simulated electromechanical coupling coefficient k2 in the ψ=0° paramet