🔬 mesoscale physics

Tunable Ultrastrong Magnon-Magnon Coupling and Squeezed States in a Triaxial Van der Waals Antiferromagnet

This paper demonstrates widely tunable ultrastrong magnon-magnon coupling in the van der Waals antiferromagnet $CrPS_4$ , establishing a protocol to detect and quantify the resulting squeezed magnon vacuum states with up to 9.7 dB of squeezing through a complete quantum model of chiral and acoustic/optical mode interactions.

Original authors: Xiao Xiao, Zishuang Li, Zui Tao, Lina Chen, Ping Liu, Shuai Zhang, Haozhe Wang, Yong Pu, Ronghua Liu

Published 2026-10-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Xiao Xiao, Zishuang Li, Zui Tao, Lina Chen, Ping Liu, Shuai Zhang, Haozhe Wang, Yong Pu, Ronghua Liu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the quiet world of quantum physics, there is a constant struggle to make the smallest possible things talk to each other. Scientists have long known that particles of light, called photons, can be made to interact with particles of sound, called phonons, or with magnetic waves, called magnons. When these interactions become strong enough, they enter a special regime where the energy of the connection is so intense that the two things effectively become a single, hybrid entity. This is known as strong coupling, and when it reaches an even more extreme level called ultrastrong coupling, the rules of the game change. In this extreme state, the usual ways of describing how things interact break down. Instead of simply swapping energy back and forth, the system begins to create and destroy pairs of particles simultaneously, a process that generates a strange, non-classical state known as a squeezed state. In this state, the natural jitter or noise of the system is reduced in one direction while increasing in another, a phenomenon that could revolutionize how we build sensitive sensors and quantum computers. However, proving that these exotic states exist in real, solid materials has been a major hurdle, as the signals are often too faint or too complex to measure directly.

A team of researchers at Nanjing University has now taken a significant step forward by demonstrating this ultrastrong coupling in a specific, two-dimensional magnetic material called CrPS4. This material is a van der Waals antiferromagnet, which means it is made of thin layers held together by weak forces, and its internal magnetic spins are arranged in a way that they point in opposite directions, canceling each other out. The researchers focused on the magnetic waves, or magnons, that travel through this material. By carefully adjusting the temperature and the direction of an external magnetic field, they were able to force two different types of magnetic waves to interact so intensely that they entered the ultrastrong coupling regime. They found that the strength of this interaction reached a level where it was nearly half the frequency of the waves themselves, a ratio that confirms the system has crossed the threshold into this extreme quantum territory.

To understand what was happening inside the material, the team moved beyond the standard mathematical tools that scientists usually use. These traditional tools assume that energy is always conserved in a simple exchange, ignoring the more chaotic processes that happen when interactions are this strong. The researchers instead built a new, more complete quantum model that accounted for three distinct ways the magnetic waves could interact. One type of interaction caused the waves to mix and hybridize, much like two musical notes blending into a new chord. A second type allowed the system to create or destroy pairs of waves at the same time, a process that generates a two-mode squeezed state. Most uniquely, they discovered a third type of interaction specific to the chiral, or handed, nature of the waves in this material, which allowed a single wave to squeeze itself, creating a single-mode squeezed state. This third mechanism had not been reported before in this context, and its discovery was crucial for explaining the full behavior of the system.

The team did not stop at theory; they designed a practical method to see these invisible quantum effects in the real world. They linked the abstract numbers from their quantum model to the actual movement of the magnetic spins inside the material. By running detailed computer simulations that included the natural thermal noise present in any material, they were able to watch how the magnetic waves fluctuated over time. These simulations showed that the noise in the system was indeed being squeezed. In one direction of measurement, the fluctuations were suppressed well below the standard limit of uncertainty, while in the perpendicular direction, they were amplified. The amount of noise reduction they observed was substantial, reaching a level of about 9.7 decibels. This is a significant degree of squeezing, comparable to what is achieved in specialized microwave devices, but here it was found naturally within a solid magnetic crystal.

The researchers also explored how the orientation of the magnetic field could be used as a control knob to turn these interactions on and off. Because the crystal structure of CrPS4 is not perfectly symmetrical, changing the angle of the magnetic field relative to the crystal axes could switch the system between different types of magnetic behavior. At certain angles, the waves would remain separate and uncoupled, while at others, they would mix intensely. This ability to tune the coupling strength and the type of quantum state simply by rotating the magnet offers a powerful level of control that was previously difficult to achieve. The study confirms that this material is a promising platform for generating and manipulating non-classical states of matter, providing a clear path for future experiments to detect these squeezed states directly using advanced magnetic sensing techniques. By bridging the gap between complex quantum theory and measurable physical dynamics, this work opens a new route toward using magnetic materials for quantum-enhanced technologies.

Technical Summary: Tunable Ultrastrong Magnon-Magnon Coupling and Squeezed States in a Triaxial Van der Waals Antiferromagnet

Problem Statement
Quantum magnonics aims to utilize coherent magnon-matter interactions for low-power quantum information processing. A central challenge in this field is achieving and quantifying ultrastrong magnon-magnon coupling (USC), where the coupling strength $g$ becomes comparable to the magnon resonance frequencies $f_g$ ( $g/f_g \gtrsim 0.1$ ). In this regime, conventional quantification methods relying on the rotating-wave approximation (RWA) fail because they neglect counter-rotating terms responsible for non-energy-conserving processes, such as simultaneous magnon pair creation/annihilation. These neglected terms are critical as they induce spectral shifts (e.g., vacuum Bloch-Siegert shift) and generate non-classical squeezed states. While tunable magnon-magnon coupling has been demonstrated in various systems, including 2D van der Waals (vdW) antiferromagnets (AFMs), the experimental identification of squeezed magnon states and their quantitative linkage to USC parameters in real materials remains an outstanding challenge. Prior studies on the A-type vdW AFM CrPS4 were confined to classical models within the RWA, leaving its quantum USC physics unexplored.

Methodology
The authors employ a multi-faceted approach combining experimental spectroscopy, microscopic quantum modeling, and micromagnetic simulations:

Experimental Characterization: Differential antiferromagnetic resonance (AFMR) measurements were performed on a CrPS4 single crystal using a coplanar waveguide (CPW) setup. The study utilized temperature control (4–40 K) and magnetic field orientation ( $H \parallel z$ , $H \parallel b$ , $H \parallel a$ , and angular variations) to access distinct magnetic phases (AFM $_b$ and AFM $_c$ ) and coupling regimes.
Quantum Modeling Beyond RWA: To quantify coupling in the USC regime, the authors developed a full quantum Hamiltonian model that decomposes interactions into three microscopic channels:
- Co-rotating term ( $g_1$ ): Responsible for mode hybridization.
- Counter-rotating term ( $g_2$ ): Responsible for two-mode squeezing (in the acoustic-optical regime).
- Self-squared term ( $g_3$ ): Uniquely identified in the chiral (right/left-handed) regime, mediating single-mode squeezing.
  The model utilizes the Holstein-Primakoff transformation and Bogoliubov transformation to diagonalize the Hamiltonian and extract coupling strengths from experimental spectra.
Micromagnetic Simulations: To bridge the gap between abstract quantum operators and measurable observables, the authors performed micromagnetic simulations (using Mumax3) incorporating classical thermal noise. These simulations mapped the theoretical quadrature operators onto time-dependent magnetization dynamics, allowing for the extraction of quadrature fluctuations and squeezing factors from simulated thermal noise.

Key Contributions and Results

Demonstration of Tunable USC: The study experimentally demonstrates widely tunable USC in CrPS4, achieving a normalized coupling ratio $g/f_g \approx 0.41$ . This value firmly places the system in the USC regime, where quantum fluctuation terms ( $g_2, g_3$ ) are comparable to the coherent hybridization term ( $g_1$ ).
Decomposition of Interaction Channels: The work uniquely identifies and quantifies three distinct interaction channels. In the acoustic-optical (AM-OM) regime, the counter-rotating term $g_2$ dominates, leading to two-mode squeezing. In the chiral right-handed/left-handed (RM-LM) regime, the self-squared term $g_3$ is significant, enabling single-mode squeezing.
Protocol for Detecting Squeezed States: The authors establish a complete protocol linking USC parameters to measurable quantum phenomena. By mapping quadrature operators to magnetization components ( $X_1$ and $X_2$ ), they demonstrate how to extract quadrature fluctuations from thermal noise-driven magnetization dynamics.
Quantification of Squeezing: Simulations based on the experimental parameters reveal a substantial squeezing factor of up to $\sim 9.7$ dB. This indicates a significant suppression of quantum noise in one quadrature below the standard quantum limit (SQL), confirming the generation of a squeezed magnon vacuum state.
Control via Symmetry and Field: The study shows that magnetic field orientation acts as a continuous tuning knob. By breaking or restoring specific symmetries (e.g., aligning $H$ along the $b$ -axis vs. the $c$ -axis), the system can switch between RM-LM and AM-OM coupling regimes, or even decouple modes entirely.

Significance
The paper claims to provide a material-specific quantum framework for ultrastrong magnon-magnon coupling in low-damping 2D magnets. Its primary significance lies in establishing a practical pathway to detect and exploit non-classical magnon states. By validating a protocol that connects microscopic Hamiltonian parameters to macroscopic, measurable magnetization dynamics, the work bridges quantum-optical metrology and spintronics. The authors posit that this approach opens a route toward quantum-enhanced spintronics and hybrid quantum information platforms, offering a solid-state platform for generating squeezed states complementary to existing microwave squeezing technologies. The ability to tune coupling strength, chirality, and polarization via temperature and magnetic field highlights the unique control afforded by low-symmetry vdW magnets for future functional quantum devices.

More like this