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

The gist: This work establishes a direct and practical protocol for detecting and quantifying quantum squeezing in AFMs, covering both the AM-OM regime and the previously inaccessible RM-LM regime through mapping abstract quadrature operators onto experimentally measurable magnetization dynamics.

Tunable Magnon-Magnon Coupling Channels

The research demonstrates widely tunable ultrastrong magnon-magnon coupling (USC) between chiral (right-/left-handed) and acoustic/optical magnon modes in the van der Waals antiferromagnet CrPS4. Using a full quantum model, the interaction is decomposed into three microscopic interaction channels: the co-rotating term g1 (mode hybridization), the counter-rotating term g2 (two-mode squeezing), and, uniquely in the chiral regime, the self-squared term g3 that mediates single-mode squeezing. The normalized coupling ratio reaches g/fg∼0.41, which enters the USC regime. This comprehensive quantum model bridges the gap between the microscopic Hamiltonian and macroscopic spectroscopic observables in this A-type layered AFM.

Quantum Squeezing Mechanisms

The paper details how USC generates non-classical magnon states through distinct mechanisms depending on the coupling regime. For the AM-OM coupling case, the counter-rotating term g2 accounts for non-energy-conserving processes that create or annihilate magnon pairs, generating two-mode squeezed states. Conversely, in the RM-LM coupling case, the self-squared terms (g3±) replace the two-mode coupling g2, enabling single-mode squeezing through RM-RM and LM-LM pair processes. The net coupling g3 = g3+ + g3− becomes comparable to g1.

Experimental Detection Protocol

The authors establish a general, experimentally actionable protocol to connect USC to quantum squeezing. This involves combining the quantum model with micromagnetic simulations to visualize the chirality and polarization evolution of the hybrid modes and extract quadrature fluctuations with a squeezing factor up to ~9.7 dB from simulated magnetization dynamics. The mapping between abstract quadrature operators and physical observables is achieved using Holstein-Primakoff transformations, where quadratures X1 and X2 can be mapped onto linear combinations of the transverse magnetization components of the two sublattices.

Quantification via Micromagnetic Simulations

To bridge the gap between theory and experiment, stochastic, thermally-driven micromagnetic simulations are used to extract quantum-level fluctuations from simulated classical magnetization dynamics. The variance of the quantum operator X1 is proportional to the expectation value of ⟨deltaX̂12⟩ in the ground state. This correspondence is validated by showing that the time-averaged mean-square fluctuation of the corresponding classical observable X1(t) is proportional to ⟨0H, 0LdeltaX̂12⟩. The degree of noise suppression is quantified by the squeezing factor Ssq, defined as Ssq = −10log10 (⟨deltaX̂12⟩/0.25).

Tunability and Control

The coupling strength, chirality, polarization, and the resulting quantum states are tunable by temperature and magnetic field. The orientation of the external magnetic field provides an additional dimension for controlling magnon-magnon coupling in CrPS4. This angular dependence allows for selective activation or suppression of different interaction channels through symmetry control. The system reaches the USC regime with a normalized coupling ratio g/fg~0.41, where these terms collectively reshape the quantum ground state, generating a strongly squeezed magnon vacuum with a squeezing factor up to ~9.7 dB.

Material Properties and Damping

CrPS4 is characterized as a low-damping van der Waals magnetic material. The cryogenic-temperature ferromagnetic resonance (FMR) spectra show that the coupled-LM mode exhibits low magnetic damping, with αLM = 0.002. This framework provides a complete theoretical protocol for detecting and quantifying magnon squeezing, which is validated against the micromagnetic simulation results in the main text.

This work establishes a direct and practical protocol for detecting and quantifying quantum squeezing in AFMs, covering both the AM-OM regime and the previously inaccessible RM-LM regime through mapping abstract quadrature operators onto experimentally measurable magnetization dynamics. The research provides a material-specific quantum framework for USC and a practical pathway to detect and exploit non-classical magnon states in low-damping two-dimensional magnets, opening a route toward quantum-enhanced spintronics and hybrid quantum information platforms.

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Tunable Ultrastrong Magnon-Magnon Coupling and Squeezed States in a Triaxial Van der Waals Antiferromagnet Xiao Xiao1, Zishuang Li1, Zui Tao1, Lina Chen2,3, Ping Liu2, Shuai Zhang1, Haozhe Wang1,, Yong Pu2 and Ronghua Liu1,, National Key Laboratory of Spintronics and School of Physics, Nanjing University,, Nanjing 210093, China 2 School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China 3 Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093,, State Key Laboratory of Spintronics, Nanjing University, Suzhou 215163, Corresponding Email: rhliu@nju.edu.cn Abstract: Achieving and quantifying ultrastrong magnon-magnon coupling (USC) remains a key challenge for quantum magnonics. Here, we demonstrate widely tunable USC between chiral (right-/left-handed) and acoustic/optical magnon modes in the van der Waals antiferromagnet CrPS4. Using a full quantum model, we decompose the interaction into three microscopic interaction channels: the co-rotating term g1 (mode hybridization), the counter-rotating term g2 (two-mode squeezing), and, uniquely in the chiral regime, the self-squared term g3 that mediates single-mode squeezing. The normalized coupling ratio reaches g/fg∼0.41, entering the USC regime. Most significantly, we establish a complete protocol linking these USC parameters to a measurable quantum phenomenon: a squeezed magnon vacuum state. Our simulations not only visualize the chirality and polarization evolution of the hybrid modes but also demonstrate how to directly extract quadrature fluctuations and a substantial squeezing factor (up to ∼9.7 dB) from thermal noise-driven magnetization dynamics. This work provides a material-specific quantum framework for USC and a practical pathway to detect and exploit non-classical magnon states in low-damping two-dimensional magnets, opening a route toward quantum-enhanced spintronics and hybrid quantum information platforms.

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Quantum magnonics, which explores coherent magnon-matter interactions for low-power quantum information processing and storage, has attracted significant interest in recent years [1–4]. Within hybrid magnonic systems, magnon-magnon coupling represents a fundamental interaction in magnetic materials and plays a crucial role in spintronics and quantum information science [4–7]. Tunable magnon-magnon coupling has been experimentally demonstrated in a variety of magnetic systems, including magnetic multilayers [8,9], synthetic antiferromagnets (SAFs) [4,6,10–17], and two-dimensional (2D) van der Waals (vdW) antiferromagnets (AFMs), such as CrCl3 [7,18], CrSBr [19,20], MnPS3 [21], CrPS4 [22–24]. A key challenge arises when the coupling strength g becomes comparable to the magnon resonance frequencies fg, entering the strong and ultrastrong coupling (USC) regimes. In this regime, conventional methods for quantifying coupling, such as the minimal frequency splitting (direct gap) or field-dependent frequency difference (indirect gap) [7,13,24], break down. These approaches typically rely on the rotating-wave approximation (RWA) [25], which neglects counter-rotating terms responsible for non-energy-conserving processes like simultaneous magnon pair creation/annihilation [4,28–31]. The RWA is valid only when g ≪ fg; as g/fg approaches or exceeds 0.1, counter-rotating interactions induce significant spectral shifts (e.g., the vacuum Bloch-Siegert shift) and reshape the quantum ground state. These interactions also generate squeezed magnon states, where quantum fluctuations in one quadrature are suppressed below the standard quantum limit (SQL) [32,33]. Such entangled, non-classical states are a direct resource for quantum-enhanced sensing and information processing. However, the experimental identification of these squeezed states and their quantitative linkage to USC parameters through directly measurable spin dynamics in a real magnetic material, particularly in 2D vdW magnets, remains an outstanding challenge. The A-type vdW AFM CrPS4 presents a uniquely promising platform to address this challenge.

1. Improved AI for Quantum Magnonics Simulation: The system can now perform micromagnetic simulations that well reproduce the FMR experimental results at 7 K and extract quadrature fluctuations directly from simulated magnetization trajectories via stochastic, thermally-driven micromagnetic simulations.

2. Improved AI for Non-Classical State Characterization: The system can quantify noise suppression by calculating the squeezing factor Ssq, defined as Ssq = −10log10 (⟨deltaX̂12⟩/0.25), to directly confirm quadrature squeezing and demonstrate that a value above 0 dB indicates quadrature squeezing.

3. Improved AI for Tunable Coupling Control: The system can utilize the established protocol to control coupling channels, as it can demonstrate how the coupling strength, chirality, polarization, and the resulting quantum states are tunable by temperature and magnetic field, enabling the switchable manipulation of g2/g3 enabling tunable nonclassical spin states.

4. Improved AI for Material-Specific Framework Development: The system provides a material-specific quantum framework for USC by linking microscopic interaction channels (the co-rotating term g1 (mode hybridization), the counter-rotating term g2 (two-mode squeezing), and, uniquely in the chiral regime, the self-squared term g3) to measurable outcomes.

Achieving and quantifying ultrastrong magnon-magnon coupling (USC) remains a key challenge for quantum magnonics. Here, we demonstrate widely tunable USC between chiral (right- and left-handed) and acoustic or optical magnon modes in the van der Waals antiferromagnet CrPS 4. Using a full quantum model, we decompose the interaction into three microscopic interaction channels: the co-rotating term g 1 (mode hybridization), the counter-rotating term g 2 (two-mode squeezing), and, uniquely in the chiral regime, the self-squared term g 3 that mediates single-mode squeezing. The normalized coupling ratio reaches g/f g about 0.41, entering the USC regime. Most significantly, we establish a complete protocol linking these USC parameters to a measurable quantum phenomenon: a squeezed magnon vacuum state. Our simulations not only visualize the chirality and polarization evolution of the hybrid modes but also demonstrate how to directly extract quadrature fluctuations and a substantial squeezing factor (up to about 9.7 dB) from thermal noise-driven magnetization dynamics. This work provides a material-specific quantum framework for USC and a practical pathway to detect and exploit non-classical magnon states in low-damping two-dimensional magnets, opening a route toward quantum-enhanced spintronics and hybrid quantum information platforms.