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Standing Waves in a Cavity

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A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:

Capacitor With A Dielectric

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Parallel plate capacitors consist of two conducting plates separated by a certain distance. However, it is mechanically difficult to hold the large plates parallel to each other without actual contact. Hence, a dielectric layer is commonly placed between the plates, which provides an easy solution for holding the plates together with a small gap and increases the capacitance of the capacitor.
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Oscillations In An LC Circuit

Oscillations In An LC Circuit

An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by

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Double Resonance Techniques: Overview

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Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
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Related Experiment Video

Updated: Jun 24, 2026

Fabrication of Nanoheight Channels Incorporating Surface Acoustic Wave Actuation via Lithium Niobate for Acoustic Nanofluidics

Fabrication of Nanoheight Channels Incorporating Surface Acoustic Wave Actuation via Lithium Niobate for Acoustic Nanofluidics

Published on: February 5, 2020

On-Chip Cavity Electroacoustics Using Lithium Niobate Phononic Crystal Resonators.

Jun Ji¹, Joseph G Thomas¹, Zichen Xi¹

¹Virginia Tech, Bradley Department of Electric and Computer Engineering, Blacksburg, Virginia, USA.

Physical Review Letters

|June 22, 2026

Summary

We demonstrate on-chip cavity electroacoustic dynamics in lithium niobate resonators. This platform enables precise control of acoustic modes for quantum technologies and signal processing.

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Fabrication of Nanoheight Channels Incorporating Surface Acoustic Wave Actuation via Lithium Niobate for Acoustic Nanofluidics

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Published on: February 5, 2020

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Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators

Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators

Published on: August 8, 2025

Area of Science:

Quantum Acoustics
Solid-State Physics
Materials Science

Background:

Mechanical systems are crucial for quantum technologies due to their long coherence times and coupling capabilities.
Current control of gigahertz mechanical modes often uses optomechanical or piezoelectric coupling to superconducting qubits.

Purpose of the Study:

To demonstrate on-chip cavity electroacoustic dynamics using electrically modulated phononic crystal resonators.
To explore atomiclike transitions and control of acoustic modes via nonlinear piezoelectricity.
To investigate applications in quantum acoustics and microwave signal processing.

Main Methods:

Fabrication of microwave-frequency phononic crystal resonators on lithium niobate.
Utilizing high dispersion of phononic crystals to create unevenly spaced acoustic modes.
Applying electrical fields to modulate acoustic modes via nonlinear piezoelectricity.
Demonstrating Autler-Townes splitting, ac Stark shift, and Rabi oscillation in two-mode systems.
Achieving nonreciprocal frequency conversions in three-mode systems.

Main Results:

Selective atomiclike transitions between acoustic modes were achieved.
Maximum cooperativity of 4.18 was observed in two-mode demonstrations.
Nonreciprocal frequency conversions with up to 20 dB isolation were demonstrated.
Tunable nonreciprocity was achieved by adjusting the time delay between modulating pulses.

Conclusions:

The developed cavity electroacoustic platform offers precise control over acoustic modes.
This platform shows potential for advancements in quantum acoustics, sensing, and microwave signal processing.
The use of nonlinear piezoelectricity in lithium niobate provides a versatile approach for electroacoustic dynamics.