What Is Strong Coupling Between Microwave Photons and Nanomagnet Magnons?

Strong coupling is a condition in quantum physics where two different systems exchange energy back and forth faster than that energy can leak out into the environment. When applied to microwave photons and nanomagnet magnons, it means the quanta of light in a microwave cavity and the quanta of spin waves in a tiny magnetic disk become so tightly linked that they form hybrid quantum particles. This state is essential for building quantum transducers that can connect superconducting qubits to magnetic memory or spin-based devices.

The Basic Players: Photons and Magnons

A microwave photon is a single quantum of electromagnetic energy in the gigahertz frequency range. In a typical experiment, these photons are trapped inside a small superconducting cavity that confines the microwave field to a tiny volume.

A magnon is the quantum of a spin wave. In a nanomagnet, the magnetic moments of atoms are arranged in an ordered pattern. When you disturb that order, the disturbance travels through the material as a wave. A magnon is the particle-like packet of that wave. Magnons carry spin angular momentum, which makes them useful for information processing without moving electrical charge.

The key difference between the two is that photons interact strongly with electric fields, while magnons interact with magnetic fields. To get them to couple, you need a geometry where the magnetic component of the microwave field overlaps with the magnetic material of the nanomagnet.

How Strong Coupling Works

Strong coupling occurs when the rate of energy exchange between the two systems exceeds the loss rate of both systems. This is described by the cooperativity parameter:

[ C = \frac{g^2}{\kappa \gamma} ]

Here, (g) is the coupling strength, (\kappa) is the photon decay rate (how fast energy leaves the cavity), and (\gamma) is the magnon damping rate (how fast the spin wave dissipates). When (C > 1), the system is in the strong coupling regime.

In practice, researchers measure strong coupling by looking at the transmission spectrum of the microwave cavity. Without coupling, there is a single dip at the cavity resonance frequency. When the magnon mode is tuned to match that frequency, the dip splits into two separate peaks. This splitting is called the vacuum Rabi splitting, and its size is proportional to (2g).

For a typical nanomagnet, the coupling strength (g) might be on the order of tens to hundreds of megahertz, while the loss rates are in the range of a few megahertz. That ratio allows strong coupling to be achieved in carefully designed experiments.

Why Nanomagnets Are Used

The size of the magnet matters because the coupling strength depends on the overlap between the microwave magnetic field and the magnetic material. A smaller magnet concentrates the spin-wave mode into a smaller volume, which can increase the coupling per magnon.

Nanomagnets, often made from yttrium iron garnet (YIG) or other ferromagnetic materials, can be as small as 100 nanometers in diameter. At that scale, the magnon modes become discrete and well-separated in frequency, making it easier to address a single mode.

YIG is a common choice because it has very low magnetic damping. The damping parameter (\alpha) for YIG can be as low as (10^{-5}), meaning the magnons can travel for many cycles before losing energy. This low damping is what makes the strong coupling condition achievable. Other materials, such as permalloy or cobalt, have higher damping but can be easier to integrate into existing fabrication processes.

Experimental Setup

A typical experiment for observing strong coupling between microwave photons and nanomagnet magnons uses a coplanar waveguide resonator. This is a thin strip of superconducting metal on a substrate, with gaps on either side that define the resonant frequency. The nanomagnet is placed on top of the waveguide, often at a point where the microwave magnetic field is strongest.

The sample is cooled to millikelvin temperatures inside a dilution refrigerator. This reduces thermal noise and keeps the superconducting cavity in its low-loss state. A vector network analyzer sends a microwave signal through the cavity and measures the transmitted power as a function of frequency.

When the external magnetic field is swept, the magnon frequency changes due to the Zeeman effect. At the field value where the magnon frequency matches the cavity frequency, the transmission spectrum shows the characteristic avoided crossing. The size of the gap between the two peaks tells you the coupling strength.

A concrete example: with a 1-micrometer-diameter YIG sphere placed on a 3D microwave cavity, researchers have measured (g/2\pi \approx 10) MHz while the cavity linewidth (\kappa/2\pi) was about 1 MHz and the magnon linewidth (\gamma/2\pi) was about 1 MHz. That gives a cooperativity of roughly 100, well into the strong coupling regime.

Applications in Quantum Information

The main motivation for studying this system is to build a quantum transducer. Superconducting qubits operate at microwave frequencies and require cryogenic temperatures. They are excellent for computation but poor for long-distance communication. Magnons, on the other hand, can interface with spin-based systems that operate at higher temperatures or with different wavelengths.

A strong-coupled photon-magnon system allows a quantum state to be transferred from a superconducting qubit to a magnon, and then potentially to an optical photon for transmission over fiber. This is a step toward a quantum network that connects remote superconducting processors.

Another application is quantum memory. Magnons can store quantum information for longer times than photons in a cavity because the magnon damping can be very low in high-quality materials. The strong coupling ensures that the information can be written from the photon to the magnon and read back out with high fidelity.

Challenges and Current Limits

The main challenge is scaling. A single nanomagnet coupled to a single cavity works well, but building a multi-qubit system requires many magnon modes that can be individually addressed. The magnon modes in a nanomagnet are closely spaced in frequency, and cross-talk between modes can be hard to avoid.

Material imperfections also limit performance. Even in YIG, surface roughness and defects can increase damping. For nanomagnets below 100 nanometers, the surface-to-volume ratio is high, and surface spins can cause additional relaxation.

Thermal noise is another concern. While cryogenic operation reduces it, magnons can still be excited by thermal energy at millikelvin temperatures if the magnon frequency is low enough. Careful design is needed to keep the magnon mode well above the thermal energy scale.

Key Takeaways

• Strong coupling between microwave photons and nanomagnet magnons occurs when the energy exchange rate exceeds the loss rates of both systems, producing hybrid quantum states.
• The coupling is observed as a vacuum Rabi splitting in the microwave transmission spectrum when the magnon frequency matches the cavity frequency.
• Nanomagnets made from low-damping materials like YIG allow strong coupling to be achieved in sub-micrometer volumes.
• The system acts as a quantum transducer, potentially connecting superconducting qubits to spin-based devices or optical networks.
• Scaling to multiple addressable magnon modes and reducing surface-induced damping remain the main technical obstacles.