On-chip cavity electro-acoustics using lithium niobate phononic crystal resonators

This paper demonstrates an on-chip cavity electro-acoustic platform using lithium niobate phononic crystal resonators that leverages electrical modulation to emulate atomic-like transitions, enabling the observation of quantum phenomena such as Autler-Townes splitting and Rabi oscillations, as well as achieving tunable non-reciprocal frequency conversion.

The Gist

Imagine you have a tiny, invisible drum made of a special crystal called Lithium Niobate. This drum is so small it fits on a computer chip, and it vibrates at a frequency so high (about 1 billion times per second) that it's in the "microwave" range.

In the world of quantum physics and advanced computing, these vibrating drums are incredibly useful. They can store information, act as memory, or help different parts of a computer talk to each other. But there's a problem: usually, these drums vibrate in a very rigid, predictable way. If you want to make one note turn into another, it's like trying to force a piano key to change its pitch just by hitting it harder—it doesn't work well.

This paper describes a breakthrough where the researchers built a "smart drum" that can be controlled with electricity to do something magical: it can change its notes on the fly, just like a human voice.

Here is how they did it, explained with some everyday analogies:

1. The "Uneven Staircase" (The Phononic Crystal)

Normally, if you have a drum, the notes it can play are like steps on a ladder: they are all the same distance apart. This makes it hard to pick just two specific notes to interact with without accidentally hitting the others.

The researchers built their drum using a Phononic Crystal. Think of this as a staircase where the steps are uneven.

• Step 1 (Mode 0): Low note.
• Step 2 (Mode 1): A medium note, but the gap between Step 1 and 2 is small.
• Step 3 (Mode 2): A high note, but the gap between Step 2 and 3 is much larger.

Because the gaps are different, the researchers can use electricity to talk specifically to "Step 1 and Step 2" without accidentally bothering "Step 3." It's like having a remote control that can change the channel on your TV without accidentally turning on the radio.

2. The "Electric Conductor" (Electro-Acoustics)

The researchers placed metal electrodes (like tiny wires) over half of this drum. When they send an electrical signal through these wires, it creates a "push and pull" force on the crystal.

Because the crystal is special (piezoelectric), this electrical push changes the stiffness of the drum. It's like a conductor waving a baton, telling the drum, "Hey, vibrate faster!" or "Hey, vibrate slower!"

3. The Magic Tricks They Performed

By using this electrical "baton," they demonstrated three famous physics tricks, but with sound waves instead of atoms:

• The Split Personality (Autler-Townes Splitting):
  Imagine a single musical note. When they apply a specific electrical rhythm, that single note suddenly splits into two distinct notes. It's like a magician pulling two rabbits out of one hat. This proves they have successfully "coupled" the two energy levels.

• The Weighted Swing (AC Stark Shift):
  Imagine a child on a swing. If you push the swing at the exact right time, it goes higher. If you push it at the wrong time, it slows down or changes its rhythm. By applying an electrical signal that is slightly "out of tune," they made the notes shift their pitch slightly (one goes up, one goes down) without splitting them. It's like adding weight to the swing to change how it moves.

• The Energy Dance (Rabi Oscillation):
  This is the coolest part. They put energy into the first note (Mode 0). Then, they applied an electrical pulse. Suddenly, the energy started dancing back and forth between the first note and the second note.

  • Imagine a bucket of water being poured back and forth between two cups.
  • They could control exactly how much water was in each cup by timing the pour. This is the foundation of a "quantum switch" or a logic gate for a future quantum computer.

4. The One-Way Street (Non-Reciprocity)

Finally, they used three notes to create a one-way street for sound.

• If you send a signal from Note A to Note C, it flows smoothly.
• If you try to send a signal from Note C back to Note A, it gets blocked.

They achieved this by timing two electrical pulses perfectly, like a traffic light. If the light turns green for traffic going North, it turns red for traffic going South. This is huge because usually, sound waves travel both ways. Making them travel only one way without using magnets (which are bulky and hard to put on a chip) is a major step forward for making tiny, efficient acoustic devices.

Why Does This Matter?

Think of this technology as the transistor for sound. Just as transistors allowed us to build tiny, fast electronic computers, this "electro-acoustic" control allows us to build tiny, fast acoustic computers.

• Sensing: These drums are so sensitive they could detect the weight of a single virus or a tiny magnetic field.
• Quantum Computing: They can act as a "bridge" to connect different types of quantum computers (like connecting a superconducting qubit to a photon).
• Signal Processing: They could filter and process radio waves in your phone much more efficiently than current technology.

In short: The researchers took a tiny crystal drum, made its notes uneven so they could be picked individually, and used electricity to make those notes dance, split, and flow in only one direction. It's a new way to control sound at the smallest scale imaginable.

Technical Summary

1. Problem Statement

Mechanical systems are crucial for quantum technologies due to their long coherence times and versatile coupling capabilities. However, achieving dynamic, direct, and selective control between different acoustic modes at microwave frequencies (GHz range) remains a significant challenge.

• Limitations of existing methods: Previous approaches often rely on mediation by other systems (e.g., superconducting qubits) or optomechanical/electromechanical coupling, which are typically limited to lower (MHz) frequencies.
• Spectral constraints: Standard acoustic resonators (like ring resonators) usually support modes with nearly constant frequency spacing (Free Spectral Range), making it difficult to selectively drive transitions between specific non-adjacent modes without exciting others.
• Goal: The authors aim to create an integrated platform that mimics atomic energy levels using acoustic modes, allowing for selective, direct, and coherent control via electrical fields, analogous to atomic physics phenomena.

2. Methodology

The researchers developed an on-chip platform utilizing Lithium Niobate (LiNbO₃, LN) and Phononic Crystals (PnC).

• Device Architecture:

  • Substrate: X-cut Lithium Niobate with a patterned Silicon Nitride (SiN) thin film.
  • Resonator Design: A 1D PnC resonator formed by SiN pillars in an acoustic waveguide. The design leverages the high dispersion at the upper edge of the PnC bandgap.
  • Mode Engineering: By utilizing the strong dispersion, the device supports multiple acoustic modes that are spectrally unevenly spaced. This mimics the anharmonic energy levels of an atom, allowing specific transitions to be addressed without exciting others.
  • Symmetry & Selection Rules: The resonator is designed such that the fundamental mode (Mode 0) and second-order mode (Mode 2) have symmetric strain profiles, while the first-order mode (Mode 1) is anti-symmetric. This symmetry-based selection rule allows transitions between neighboring modes (0↔1, 1↔2) but forbids direct transitions between next-neighboring modes (0↔2).
  • Modulation: Modulation electrodes cover half the resonator, utilizing the nonlinear piezoelectric effect of LN. An applied electrical field modulates the acoustic modes, acting as a coherent drive for transitions.

• Experimental Setup:

  • Devices were fabricated using electron-beam lithography and reactive-ion etching.
  • Measurements were performed using a Vector Network Analyzer (VNA) for spectral dynamics and custom high-voltage amplifiers (up to ~300 Vpp) for temporal control.
  • A microwave-frequency optical vibrometer was used to visualize displacement profiles.

3. Key Contributions

1. Atomic-Like Acoustic System: Demonstrated a solid-state system where discrete, unevenly spaced acoustic modes act as artificial atomic energy levels.
2. Direct Electro-Acoustic Control: Achieved direct, selective coupling between microwave-frequency acoustic modes (approx. 1 GHz) using electrical fields, bypassing the need for intermediate quantum systems.
3. Observation of Quantum Analogues: Experimentally demonstrated acoustic counterparts of fundamental quantum phenomena:
   • Autler-Townes Splitting (ATS): Splitting of energy levels under resonant driving.
   • AC Stark Shift: Frequency shifting of modes under off-resonant driving.
   • Rabi Oscillations: Coherent energy exchange between modes.
4. Programmable Non-Reciprocity: Extended the system to a three-level configuration to achieve magnetic-free, programmable non-reciprocal frequency conversion.

4. Key Results

• Device Performance:

  • Supported three high-Q modes at ~1.005 GHz with frequencies $f_0 = 1004.620$ MHz, $f_1 = 1005.306$ MHz, and $f_2 = 1006.347$ MHz.
  • Achieved loaded Quality (Q) factors up to 12,020 and lifetimes up to 1.966 µs.
  • Mode spacing was uneven: $\Delta f_{01} = 0.686$ MHz and $\Delta f_{12} = 1.041$ MHz, enabling selective addressing.

• Two-Level System Dynamics (Mode 0 ↔ Mode 1):

  • ATS: Observed splitting of transmission peaks when modulation frequency matched the mode spacing ($f_m \approx f_{01}$).
  • AC Stark Shift: Observed frequency shifts (up to 13–14 kHz) when modulation was detuned.
  • Rabi Oscillations: Demonstrated coherent energy exchange with a period of 13.9 µs (Rabi frequency $\Omega_1/2\pi = 72$ kHz). The Rabi frequency scaled linearly with modulation amplitude.
  • Strong Coupling: Achieved a maximum cooperativity of 4.18, indicating strong coupling between the two acoustic modes.

• Three-Level System & Non-Reciprocity (Mode 0 ↔ Mode 1 ↔ Mode 2):

  • Implemented a sequence of two $\pi$-pulses (frequencies $f_{01}$ and $f_{12}$) with a tunable time delay ($t_{delay}$).
  • Forward Conversion: Efficiently converted signals from Mode 0 to Mode 2.
  • Backward Conversion: Suppressed conversion from Mode 2 to Mode 0 due to time-reversal symmetry breaking via the pulse sequence.
  • Isolation: Achieved a maximum non-reciprocity (isolation) of 20.1 dB at an optimal delay time ($t_{delay} = 11$ µs). Non-reciprocity vanished when the delay was zero (time-reversal symmetric).

5. Significance and Future Outlook

• Quantum Acoustics: This platform provides a pathway to manipulate single phonons and build phononic quantum gates, memories, and transducers. The high Q-factors and strong cooperativity suggest potential for exploring the ultra-strong coupling regime.
• Signal Processing: The ability to perform non-reciprocal frequency conversion without magnetic fields is a breakthrough for microwave signal processing, enabling compact isolators and circulators for integrated circuits.
• Acoustic Computing: The programmable nature of the transitions supports applications in analog computing and synthetic frequency dimension computing.
• Scalability: The design allows for engineering the number of modes and their spacing by tuning the cavity length, offering a scalable route to complex multi-level acoustic systems.

In summary, this work establishes a robust, electrically controllable platform for cavity electro-acoustics, bridging the gap between classical acoustic devices and quantum coherent control, with immediate applications in sensing, computing, and quantum networking.