Strong coupling between collective electron oscillations and photons in vacuum

A foundation for electron-photon hybrid systems toward quantum information technology

Note: This post explains our research in plain language for a general audience.

Summary

We have realized a strong-coupling regime linking the collective oscillation (“plasmon”[1]) of electrons floating in vacuum above the surface of liquid helium with a radio-frequency photon confined in an electrical (LC) circuit, at a coupling strength exceeding the rate at which each system loses energy.

This achievement is expected to contribute to the foundational technology needed for quantum information processing using electrons floating in vacuum, as well as for highly sensitive sensing techniques that exploit plasmons and light.

We fabricated a device that integrates a two-dimensional electron system — floating in vacuum roughly 10 nanometers (one nanometer is one billionth of a meter) above the surface of liquid helium — with an LC resonator circuit made of a ring-shaped electrode and a microfabricated coil.

By adjusting the voltage applied to the electrodes, the frequency of the electrons’ collective oscillation (plasmon) can be tuned; when it is brought into resonance with the LC circuit’s resonant frequency, the reflected microwave spectrum splits into two peaks — an “avoided crossing” — confirming that the two systems are coupled. The resulting coupling strength (coupling constant) was about 4.9 megahertz (1 megahertz means one million oscillations per second), exceeding the rate at which both the plasmon and the circuit lose energy, satisfying the condition for “strong coupling.” Furthermore, injecting a short, 20-nanosecond (one nanosecond is one billionth of a second) microwave pulse and tracking the circuit’s energy afterward revealed energy oscillating back and forth between the plasmon and the photon as it decayed. Using this LC circuit as a sensitive sensor, the team also precisely captured the transition to a “Wigner crystal[2],” in which electrons arrange into a regular lattice at low temperature, and the plasmon decay caused by interaction with “ripplons[3],” ripples on the liquid helium surface.

This work was published online in the journal Nature Communications on September 10.

The collective oscillation of many electrons in vacuum appears as a plasmon

Background

In matter, a phenomenon in which many electrons oscillate collectively through Coulomb interaction is called a “plasmon,” and it appears across a wide range of systems, from metal nanoparticles to semiconductors and two-dimensional materials. Because plasmons interact strongly with light and radio waves, they are expected to find applications in photocatalysis, chemical sensing, and quantum information processing.

However, in ordinary metals and semiconductors, electrons are scattered by impurities and lattice disorder, causing plasmon energy to dissipate quickly. This has made it difficult to clearly realize a state in which plasmons and photons (radio waves) exchange energy while maintaining wave coherence, free from the effects of disorder.

A layer of electrons floating in vacuum can instead be created above the surface of liquid helium. Because this electron system is free of both impurities and lattice disorder, electron scattering is extremely low, making it one of the cleanest two-dimensional electron systems known.

Plasmons of electrons on liquid helium have been studied since the 1970s through microwave absorption measurements, but their quantum mechanical properties, and coupling them coherently to a photon in an electrical circuit, had not been explored.

We therefore reasoned that strongly coupling the plasmon of this exceptionally clean electron system to a photon confined in an electrical circuit could realize a new “electron-photon hybrid system” as a foundation for quantum information technology, while also serving as a highly sensitive sensor for probing the physics of electrons on liquid helium.

Methods and results

We fabricated a device in which liquid helium about 1 millimeter thick is sandwiched between two disk-shaped electrodes, with electrons floating in vacuum roughly 10 nanometers above its surface (Figure 1).

The lower electrode is divided into three concentric regions — center, middle, and outer — so that adjusting the voltage on each controls the area over which electrons accumulate, their density, and the frequency of their collective oscillation (plasmon). A small, microfabricated coil is connected to the upper center electrode; together, the electrode and coil form an LC resonator circuit with a resonant frequency of about 121 megahertz.

As the plasmon frequency was brought closer to the LC circuit’s resonant frequency, the reflected microwave spectrum split into two peaks — an “avoided crossing.” This indicates the formation of new hybrid oscillation modes in which the plasmon and the circuit’s photon are mixed, providing evidence that the two are coupled.

The coupling constant, which quantifies the coupling strength, was about 4.6 megahertz from frequency-domain measurements and about 4.9 megahertz from time-domain measurements. Both values exceed the rate at which the plasmon and circuit lose energy (a few megahertz), satisfying the strong-coupling condition in which energy can be exchanged between the two multiple times before it is lost.

The team also injected a short, 20-nanosecond microwave pulse into the circuit and measured how the accumulated energy changed over time. Energy was observed oscillating periodically between the plasmon and the photon as it decayed, directly confirming — through time-resolved measurement — that coherent energy exchange was taking place.

This LC resonator circuit also functions as a highly sensitive sensor of the electron state on liquid helium. As the temperature was lowered, the plasmon frequency changed abruptly near about 0.25 kelvin (a unit of absolute temperature; 0 kelvin is about −273°C), revealing a transition to a “Wigner crystal,” in which electrons arrange into a regular triangular lattice. Detailed measurements of the plasmon decay rate as a function of temperature also quantitatively confirmed that electron scattering by “ripplons” — ripples on the liquid helium surface — is the dominant cause of the decay, in good agreement with theoretical calculations.

Figure 1: Strong coupling between the plasmon of electrons on liquid helium and a resonator-circuit photon.
Liquid helium (light blue cylinder) is held between upper and lower disk electrodes, with electrons (light blue circles) floating in vacuum roughly 10 nanometers above its surface. A coil connected to the upper center electrode forms an LC resonator circuit together with the electrode, confining a roughly 121 megahertz radio-frequency photon. When the voltage on the electrodes tunes the frequency of the electrons' collective oscillation (plasmon) to match the circuit's resonant frequency, a strong-coupling state arises in which the plasmon and photon periodically exchange energy. This circuit also serves as a sensitive sensor for measuring the transition to a Wigner crystal and the decay of the plasmon.

The measurements were carried out in a dilution refrigerator (a device for producing extremely low temperatures), cooled to about 0.18 kelvin. The areal density of the electrons was about 100 million per square centimeter.

Outlook

This work is a first step toward realizing, in an exceptionally clean system with minimal disorder, experiments combining the plasmon of electrons floating in vacuum with the photon of an electrical circuit.

Because a plasmon acts electrically like a large “antenna,” it is expected to serve as a “quantum information bus” linking qubits based on the spin or motional states of single electrons via photons. If a plasmon confined in the circuit is sent out as a wave (a plasmon wave packet) traveling along the electron layer, it could also carry quantum information to another, distant qubit.

In the future, confining the plasmon to a smaller region to raise its oscillation frequency into the gigahertz range (roughly one billion oscillations per second) would allow it to operate in the same frequency band as superconducting quantum circuits, enabling information exchange with a single microwave photon at the quantum mechanical level.

Furthermore, “parametric driving” — periodically modulating the electron confinement — is expected to enable devices that amplify weak signals or generate states with suppressed quantum noise. This achievement is expected to become a foundational technology toward realizing a quantum computer based on electrons floating on liquid helium.

Paper information

Strong Coupling Between RF Photons and Plasmons of Electrons on Liquid Helium Asher Jennings*, Ivan Grytsenko, Thomas Giovansili, Itay Josef Barabash, Oleksiy Rybalko, Yiran Tian, Jun Wang, Hiroki Ikegami, and Erika Kawakami* Nature Communications (2026)

Notes

[1] Plasmon A collective oscillation in which many electrons in a metal, semiconductor, or similar material move back and forth together in the same direction. It interacts strongly with radio waves and light. In electron systems on liquid helium, it appears as a wave of electron-density modulation arising from Coulomb repulsion between electrons.

[2] Wigner crystal A state in which, once the Coulomb repulsion energy between electrons exceeds their thermal energy, the electrons arrange into a regular triangular lattice and behave like a solid. It was theoretically predicted by the physicist Eugene Wigner.

[3] Ripplon The quantum mechanical description of ripples (surface-tension waves) on the surface of liquid helium. Electrons floating on liquid helium interact with ripplons, which disturb the electrons’ motion and cause the plasmon to decay.

Acknowledgments

This work was supported by the RIKEN Hakubi Program, the RIKEN Center for Quantum Computing, JST-FOREST, and the Hattori Hokokai Foundation. We are grateful to Prof. Jaw-Shen Tsai for granting us access to the Kelvinox 400HA dilution refrigerator, and to Prof. Denis Konstantinov for useful discussions. Asher Jennings was supported by a RIKEN Incentive Research Project.