Ultrastrong Magnon-Photon Coupling

• Ultrastrong magnon–photon coupling is defined when the coherent interaction reaches a significant fraction (typically ≥10%) of the bare mode frequencies, leading to nonperturbative hybridization and breakdown of the rotating-wave approximation.
• Experimental platforms such as 3D cavities, photonic crystals, and superconducting resonators exploit mechanisms like collective spin enhancement and mode-volume reduction to achieve and control this regime.
• Spectroscopic signatures include large avoided crossings, Bloch–Siegert shifts, and clear time-domain Rabi oscillations that reveal the coherent energy exchange between magnons and photons.

Searching arXiv for recent and foundational papers on ultrastrong magnon-photon coupling. Ultrastrong magnon–photon coupling denotes a cavity-magnonic regime in which the coherent interaction between a magnon mode and an electromagnetic mode becomes a substantial fraction of the bare mode frequency, so that hybridization cannot be treated as a small perturbation and counter-rotating terms become relevant (Kostylev et al., 2015, Zhang et al., 2023, Ghirri et al., 2023). In the literature summarized here, the term is used across several architectures—three-dimensional microwave cavities, photonic crystals, superconducting planar resonators, magnetochiral metamolecules, and propagating terahertz media—and is identified through large avoided crossings, normalized coupling ratios such as $g/\omega$ or $J/\omega_P$, and, in some cases, explicit beyond-rotating-wave analyses based on Hopfield-type Hamiltonians (Zhang et al., 2014, Zhang et al., 2023, Mita et al., 2024). Closely related but distinct is the superstrong regime, in which the coupling exceeds not only losses but also the cavity free spectral range, so that a magnon couples to multiple cavity modes within a single intermode spacing (Kostylev et al., 2015).

1. Definitions and regime criteria

The strong-coupling baseline is the regime in which the coherent magnon–photon coupling exceeds the relevant dissipation rates, producing resolvable normal-mode hybridization and avoided level crossings (Zhang et al., 2014, Xu et al., 2022). In the room-temperature three-dimensional cavity experiment of Zhang, Zou, Jiang, and Tang, the effective Hamiltonian is written in rotating-wave form as

$$\frac{\mathcal H}{\hbar} = \omega_a a^\dagger a + \omega_m m^\dagger m + g(a^\dagger m + a m^\dagger),$$

and strong coupling is identified spectroscopically by a normal-mode splitting larger than both cavity and magnon linewidths (Zhang et al., 2014).

Ultrastrong coupling is used in these papers for interaction strengths that are no longer negligible compared with the bare mode frequencies. One explicit criterion is stated in the magnetochiral metamolecule work as: strong coupling requires $g>\kappa$, whereas ultrastrong coupling requires $g>\kappa$ and $g/\omega>0.1$ (Mita et al., 2024). The photonic-crystal cavity-magnonic study similarly adopts the breakdown of the rotating-wave approximation and a normalized coupling efficiency near $10\%$ as the hallmark of the ultrastrong regime (Zhang et al., 2023). The YIG-on-YBCO coplanar-resonator study states the conventional benchmark as $\lambda/\omega_c \ge 0.1$ and reports that its dominant magnon mode exceeds $0.2$ times the cavity frequency (Ghirri et al., 2023).

The superstrong regime is defined more stringently. The multi-post reentrant-cavity paper states the criterion as

$g > \Gamma,\ \delta,\ \omega_{\mathrm{FSR},$

namely that the coupling exceeds the spin loss rate, the cavity loss rate, and the cavity free spectral range (Kostylev et al., 2015). This regime is therefore multimode by construction: neighboring cavity modes cannot be regarded as spectrally isolated.

A recurrent distinction in the literature is that cooperativity and ultrastrong coupling are not interchangeable. The three-dimensional cavity study reaching cooperativity $J/\omega_P$0 at $J/\omega_P$1 GHz explicitly notes that large cooperativity compares coherent coupling to losses, whereas ultrastrong coupling compares coupling to bare frequencies (Zhang et al., 2014). This distinction is central in interpreting claims across platforms.

2. Hamiltonian structure and nonperturbative electrodynamics

In ordinary strong coupling, the magnon–photon system is often modeled by a number-conserving bilinear Hamiltonian of Tavis–Cummings type (Zhang et al., 2014, Xu et al., 2022). In ultrastrong coupling, the relevant interaction takes the non-number-conserving form

$J/\omega_P$2

or an equivalent Dicke/Hopfield representation (Zhang et al., 2023, Yoshii et al., 8 Jul 2025, Ghirri et al., 2023). The photonic-crystal defect-mode study writes the interaction as

$J/\omega_P$3

with $J/\omega_P$4, and explicitly states that in the ultrastrong-coupling regime the rotating-wave approximation is no longer valid (Zhang et al., 2023).

A major theoretical theme is the role of diamagnetic or self-interaction terms. In the photonic-crystal cavity-magnonic device the modified Hopfield Hamiltonian includes

$J/\omega_P$5

introduced via the Thomas-Reiche-Kuhn sum rule (Zhang et al., 2023). The YIG-film-on-YBCO resonator study also uses a Hopfield model with a possible diamagnetic contribution $J/\omega_P$6, but finds that $J/\omega_P$7 is essentially negligible compared with the standard electric-dipole expectation, which it identifies as a peculiarity of pure spin systems (Ghirri et al., 2023). By contrast, the on-chip superconducting-resonator/permalloy-stripe platform quantifies a residual diamagnetic term and reports a suppression factor

$J/\omega_P$8

arguing that magnetic-dipole cavity magnonics significantly circumvents the conventional $J/\omega_P$9 constraint (Yoshii et al., 8 Jul 2025).

The theoretical literature has also sharpened the interpretation of nonperturbative spectral shifts. A circuit-based theory of ultrastrong and deep-strong cavity magnonics derives a two-mode Hopfield Hamiltonian from a quantized effective circuit and shows that the positive nontrivial frequency shift arises from competition between a negative Bloch-Siegert contribution and a larger positive self-interaction contribution $$\frac{\mathcal H}{\hbar} = \omega_a a^\dagger a + \omega_m m^\dagger m + g(a^\dagger m + a m^\dagger),$$0 (Chiba et al., 23 Oct 2025). This suggests that measured branch shifts can encode ground-state virtual occupations, squeezing, and entanglement entropy rather than only classical level repulsion.

3. Experimental platforms

The experimental landscape is defined by several distinct architectures, each optimizing a different combination of field confinement, mode volume, spin number, and spectral engineering.

Platform	Representative result	Representative paper
3D copper cavity with YIG sphere	$$\frac{\mathcal H}{\hbar} = \omega_a a^\dagger a + \omega_m m^\dagger m + g(a^\dagger m + a m^\dagger),$$1 GHz at $$\frac{\mathcal H}{\hbar} = \omega_a a^\dagger a + \omega_m m^\dagger m + g(a^\dagger m + a m^\dagger),$$2 GHz, $$\frac{\mathcal H}{\hbar} = \omega_a a^\dagger a + \omega_m m^\dagger m + g(a^\dagger m + a m^\dagger),$$3	(Zhang et al., 2014)
Multi-post reentrant 3D cavity with YIG sphere	$$\frac{\mathcal H}{\hbar} = \omega_a a^\dagger a + \omega_m m^\dagger m + g(a^\dagger m + a m^\dagger),$$4 GHz ultrastrong; $$\frac{\mathcal H}{\hbar} = \omega_a a^\dagger a + \omega_m m^\dagger m + g(a^\dagger m + a m^\dagger),$$5–$$\frac{\mathcal H}{\hbar} = \omega_a a^\dagger a + \omega_m m^\dagger m + g(a^\dagger m + a m^\dagger),$$6 GHz superstrong	(Kostylev et al., 2015)
YIG-defect photonic crystal	$$\frac{\mathcal H}{\hbar} = \omega_a a^\dagger a + \omega_m m^\dagger m + g(a^\dagger m + a m^\dagger),$$7 GHz, $$\frac{\mathcal H}{\hbar} = \omega_a a^\dagger a + \omega_m m^\dagger m + g(a^\dagger m + a m^\dagger),$$8	(Zhang et al., 2023)
YIG film on superconducting YBCO resonator	$$\frac{\mathcal H}{\hbar} = \omega_a a^\dagger a + \omega_m m^\dagger m + g(a^\dagger m + a m^\dagger),$$9 GHz, $g>\kappa$0	(Ghirri et al., 2023)
Magnetochiral metamolecule	$g>\kappa$1 at room temperature	(Mita et al., 2024)
On-chip YBCO resonator with permalloy stripes	$g>\kappa$2 MHz, $g>\kappa$3	(Yoshii et al., 8 Jul 2025)

The early three-dimensional cavity platform uses a polished YIG sphere in a rectangular copper cavity and exploits collective enhancement of the Kittel mode through placement at the magnetic-field antinode (Zhang et al., 2014). The multi-post reentrant architecture instead uses a 3D lumped-element cavity machined from oxygen-free copper, with the electric field localized in small post gaps and the magnetic field circulating around the posts, enabling unusually high magnetic filling factors and direct engineering of the cavity spectrum (Kostylev et al., 2015).

Planar superconducting platforms pursue a different route: they shrink the photon mode volume and place magnetic films or patterned magnetic elements directly in the region of strongest microwave magnetic field. The YIG-on-YBCO coplanar resonator achieves ultrastrong coupling by direct contact of a $g>\kappa$4m YIG film with a superconducting coplanar waveguide, thereby approximately doubling the local vacuum field compared with a lifted geometry (Ghirri et al., 2023). The YBCO/permalloy-stripe platform uses a notch-type meander-inductor/interdigital-capacitor resonator, with multiple $g>\kappa$5 nm Py stripes on top of the inductor and separated by a $g>\kappa$6 nm $g>\kappa$7 buffer, combining strong magnetic confinement with Dicke-type collective enhancement across remote elements (Yoshii et al., 8 Jul 2025).

Photonic-crystal and metamaterial realizations emphasize confinement by electromagnetic structuring rather than conventional cavities. The photonic-crystal defect device replaces a copper defect cylinder with a YIG cylinder, so that the defect-localized microwave mode and the FMR mode occupy the same physical region (Zhang et al., 2023). The magnetochiral metamolecule embeds a YIG cylinder inside a right-handed copper helix, using the helix itself as the resonator and thereby achieving direct near-field overlap between confined microwave photons and magnons (Mita et al., 2024).

A distinct terahertz route appears in the polar antiferromagnet Fe$g>\kappa$8Mo$g>\kappa$9O$g>\kappa$0, where no cavity is used. There the hybridization occurs between a propagating THz electromagnetic wave and an electric-active antiferromagnetic magnon at $g>\kappa$1 THz, detected only in time-domain spectroscopy through beating and split modes at $g>\kappa$2 THz and $g>\kappa$3 THz (Shi et al., 2020). This suggests that ultrastrong magnon–photon coupling is not restricted to microwave cavity geometries.

4. Spectroscopic and dynamical signatures

The most universal experimental signature is the avoided crossing between a field-tunable magnon resonance and a photonic mode. In the canonical three-dimensional cavity system, tuning the YIG Kittel mode through the cavity TE101 resonance at $g>\kappa$4 mT produces a splitting fitted as

$g>\kappa$5

thereby establishing textbook strong coupling (Zhang et al., 2014). When the same approach is pushed to a $g>\kappa$6 GHz cavity with a $g>\kappa$7 mm YIG sphere, the coupling rises to $g>\kappa$8 GHz and the cooperativity to $g>\kappa$9, while the normalized ratio reaches $g/\omega>0.1$0 (Zhang et al., 2014).

The four-post reentrant cavity offers a sharper mode-selective example. There, a split whispering-gallery-like doublet couples asymmetrically to a central YIG sphere, and fitting yields

$g/\omega>0.1$1

with cavity linewidths $g/\omega>0.1$2 MHz and $g/\omega>0.1$3 MHz and magnon linewidth about $g/\omega>0.1$4 MHz (Kostylev et al., 2015). One doublet member remains nearly dark by symmetry, making the mode selectivity itself part of the spectroscopic evidence. In the eight-post version, the first two cavity modes lie at $g/\omega>0.1$5 GHz and $g/\omega>0.1$6 GHz, so the free spectral range is $g/\omega>0.1$7 GHz, while couplings of $g/\omega>0.1$8 GHz and $g/\omega>0.1$9 GHz exceed that spacing, placing the system in the superstrong regime (Kostylev et al., 2015).

Time-domain measurements provide stronger evidence than static spectroscopy alone. The room-temperature 3D cavity study observes classical Rabi oscillation with period $10\%$0 ns and extinction ratio greater than $10\%$1 dB at exact resonance, in agreement with $10\%$2 ns inferred from the spectral splitting (Zhang et al., 2014). This demonstrates coherent energy exchange rather than mere line repulsion.

The terahertz antiferromagnetic experiment offers a different signature. Below $10\%$3 K, the transmitted THz waveform develops a long-lived oscillatory tail with clear beating, and Fourier transforming only the $10\%$4–$10\%$5 ps time window reveals two peaks at $10\%$6 THz and $10\%$7 THz around the bare $10\%$8 THz magnon (Shi et al., 2020). Frequency-domain FTIR, by contrast, shows only a single absorption line. This establishes that coherent time-domain excitation can reveal ultrastrong magnon-polaritonic splitting that is washed out in incoherent spectroscopy.

In on-chip ultrastrong devices, beyond-RWA signatures become accessible directly. The superconducting-resonator/permalloy platform reports a pronounced Bloch-Siegert shift of about $10\%$9 MHz and shows that it scales with $\lambda/\omega_c \ge 0.1$0, providing direct evidence of counter-rotating processes (Yoshii et al., 8 Jul 2025). The YIG-film-on-YBCO resonator, while not emphasizing a Bloch-Siegert shift, requires a Hopfield fit and extracts $\lambda/\omega_c \ge 0.1$1 GHz at $\lambda/\omega_c \ge 0.1$2 GHz, demonstrating that the rotating-wave approximation is not adequate for the dominant cavity-coupled mode (Ghirri et al., 2023).

5. Mechanisms that produce large coupling

Across the literature, four mechanisms recur.

Collective spin enhancement: The basic scaling $\lambda/\omega_c \ge 0.1$3 is explicit in the three-dimensional cavity work, where the coupling strength depends on the total number of spins $\lambda/\omega_c \ge 0.1$4 in the YIG sphere and the overlap factor $\lambda/\omega_c \ge 0.1$5 (Zhang et al., 2014). The same collective law reappears in on-chip devices: the permalloy-stripe platform reports

$\lambda/\omega_c \ge 0.1$6

for $\lambda/\omega_c \ge 0.1$7 remote stripes coupled to the same photon mode (Yoshii et al., 8 Jul 2025).

Magnetic filling factor and field overlap: The multi-post reentrant cavities emphasize that the posts concentrate microwave magnetic field in a compact region around the YIG sphere while localizing electric field in the small gaps, yielding filling factors $\lambda/\omega_c \ge 0.1$8 and $\lambda/\omega_c \ge 0.1$9 in the four-post and eight-post devices (Kostylev et al., 2015). The YIG-on-YBCO study similarly argues that only an effective thickness $0.2$0 nm near the interface contributes strongly, underscoring that overlap, not total volume alone, controls the collective coupling (Ghirri et al., 2023).

Mode-volume reduction and low-impedance electrodynamics: Superconducting planar structures obtain large couplings by shrinking the photon mode volume. The on-chip ultrastrong magnon-polariton experiment uses a YBCO meander resonator with bare $0.2$1, exploiting the small magnetic mode volume to raise the single-Bohr-magneton coupling into the tens of hertz range (Yoshii et al., 8 Jul 2025). The YIG/YBCO coplanar study attributes its $0.2$2 primarily to the strong local field at direct contact with the superconducting center conductor (Ghirri et al., 2023). Closely related multilayer superconductor/ferromagnet/insulator structures achieve radical suppression of photon phase velocity through Swihart electrodynamics; one such study reports $0.2$3 GHz with $0.2$4, explicitly attributing the enhancement to the compressed electromagnetic mode volume of a thin-film superconducting resonator (Golovchanskiy et al., 2021). A plausible implication is that superconducting slow-wave confinement and magnetic-dipole coupling together form one of the most effective routes toward deep-strong cavity magnonics.

Electromagnetic confinement by superconductors and Meissner currents: In superconductor/ferromagnet nanostructures, the confined Swihart mode and Meissner-current-mediated field enhancement are central. The theory of S/FI/S and S/FM/I/S nanostructures derives hybridized magnon-polaritons from Maxwell electrodynamics and finds that the coupling can become comparable to the bare mode frequencies, with an upper bound $0.2$5 at $0.2$6 (Silaev, 2022). In S/F/I/F/S multilayers, the same Meissner mechanism mediates ultrastrong magnon–magnon coupling while retaining the previously established ultrastrong magnon–photon channel, strongest for $0.2$7 and vanishing in the Damon–Eshbach geometry (Gordeeva et al., 28 Jan 2025).

6. Regime-specific phenomena, controversies, and outlook

A recurring ambiguity is terminological. The 2014 three-dimensional cavity work calls $0.2$8 ultrastrong coupling, whereas later papers more often reserve the term for values at or above $0.2$9 (Zhang et al., 2014, Zhang et al., 2023, Mita et al., 2024). This is not a contradiction of data but a difference in convention. A careful reading suggests three broad categories: very-high-cooperativity strong coupling, threshold ultrastrong coupling, and more deeply nonperturbative ultrastrong or deep-strong coupling.

Another recurrent issue is the role of diamagnetic terms. The photonic-crystal device retains a Thomas-Reiche-Kuhn-derived diamagnetic term and explicitly states that the system is only at the threshold of ultrastrong coupling and not in a superradiant phase (Zhang et al., 2023). The YIG/YBCO coplanar-resonator work instead finds a vanishing diamagnetic contribution within fitting uncertainty and identifies this as a peculiarity of pure spin systems (Ghirri et al., 2023). The superconducting-resonator/permalloy-stripe platform reports a small but finite diamagnetic term, about $g > \Gamma,\ \delta,\ \omega_{\mathrm{FSR},$0 of the electric-dipole TRK value (Yoshii et al., 8 Jul 2025). This suggests that “the” diamagnetic constraint in cavity magnonics is platform dependent rather than universal.

The quantum consequences of ultrastrong coupling are increasingly explicit in the theory literature. Superconductor/ferromagnet nanostructures are predicted to host squeezed magnon and photon vacuum states, large virtual populations, and bipartite magnon–photon entanglement, all tunable by external magnetic field (Silaev, 2022). A theory of second-order photon correlation beyond the rotating-wave approximation shows that counter-rotating magnon–photon interactions alone can generate cavity-photon squeezing and sub-Poissonian $g > \Gamma,\ \delta,\ \omega_{\mathrm{FSR},$1 without intrinsic Kerr nonlinearity, especially in ferromagnetic cavities with anisotropic rotating and counter-rotating couplings (Falch et al., 2024). Circuit-based Hopfield theories further relate observable frequency shifts directly to virtual ground-state populations and entanglement entropy (Chiba et al., 23 Oct 2025). These developments indicate that ultrastrong magnon–photon coupling is no longer treated merely as a spectroscopy problem.

At the device level, scalability is becoming a central theme. The planar organic ferrimagnet V[TCNE]$g > \Gamma,\ \delta,\ \omega_{\mathrm{FSR},$2 coupled to a superconducting lumped resonator reaches very large cooperativity, $g > \Gamma,\ \delta,\ \omega_{\mathrm{FSR},$3, but remains in ordinary strong coupling with $g > \Gamma,\ \delta,\ \omega_{\mathrm{FSR},$4 for the main device (Xu et al., 2022). This suggests that lithographic compatibility and ultrastrong normalized coupling have not yet been simultaneously optimized in all materials platforms. By contrast, the YBCO/permalloy and YBCO/YIG platforms show that ultrastrong coupling is already feasible on chip (Yoshii et al., 8 Jul 2025, Ghirri et al., 2023).

The current frontier therefore appears to consist of three partially convergent directions. One is multimode spectral engineering, exemplified by reentrant cavities reaching superstrong coupling (Kostylev et al., 2015). Another is genuinely nonperturbative on-chip ultrastrong coupling with observable Bloch-Siegert shifts and suppressed diamagnetic terms (Yoshii et al., 8 Jul 2025, Ghirri et al., 2023, Golovchanskiy et al., 2021). A third is quantum-optical exploitation of the dressed ground state, including squeezing, entanglement, and gain-driven nonlinear dynamics in the ultrastrong regime (Silaev, 2022, Falch et al., 2024, Suzuki et al., 11 Sep 2025). Taken together, these works establish ultrastrong magnon–photon coupling as a mature hybrid regime spanning microwave, terahertz, cavity, photonic-crystal, superconducting, and metamaterial implementations rather than a single materials-specific phenomenon.