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The Dicke model describes the cooperative interaction of an ensemble of two-level atoms with a single-mode photonic field and exhibits a quantum phase transition as a function of light–matter coupling strength. Extending this model by incorporating short-range atom–atom interactions makes the problem intractable but is expected to produce new physical phenomena and phases. Here, we simulate such an extended Dicke model using a crystal of ErFeO₃, where the role of atoms (photons) is played by Er³⁺spins (Fe³⁺magnons). Through terahertz spectroscopy and magnetocaloric effect measurements as a function of temperature and magnetic field, we demonstrated the existence of a novel atomically ordered phase in addition to the superradiant and normal phases that are expected from the standard Dicke model. Further, we elucidated the nature of the phase boundaries in the temperature–magnetic-field phase diagram, identifying both first-order and second-order phase transitions. These results lay the foundation for studying multiatomic quantum optics models using well-characterized many-body solid-state systems.

Terahertz (THz) magnetoresistance effects have been extensively investigated and have shown promising results for applications in magnetic modulations of the amplitude of THz waves. However, THz magnetocapacitance in dielectric systems, which is essential for phase modulations of THz radiation, remains largely unexplored. Here, we study the THz response of a bulk single crystal of La_0.875Sr_0.125MnO₃at around its Curie temperature, observing significant magnetic-field-induced changes in the THz resistance and capacitance extracted from the optical conductivity. We discuss possible mechanisms for the observed coexistence of colossal THz magnetoresistance and magnetocapacitance in a perovskite manganite that is not multiferroic. This work enhances our understanding of colossal magnetoresistance in a complex system with THz spectroscopy and demonstrates potential use of perovskite manganites in THz technology.

Some of the most exotic properties of the quantum vacuum are predicted in ultrastrongly coupled photon–atom systems; one such property is quantum squeezing leading to suppressed quantum fluctuations of photons and atoms. This squeezing is unique because (1) it is realized in the ground state of the system and does not require external driving, and (2) the squeezing can be perfect in the sense that quantum fluctuations of certain observables are completely suppressed. Specifically, we investigate the ground state of the Dicke model, which describes atoms collectively coupled to a single photonic mode, and we found that the photon–atom fluctuation vanishes at the onset of the superradiant phase transition in the thermodynamic limit of an infinite number of atoms. Moreover, when a finite number of atoms is considered, the variance of the fluctuation around the critical point asymptotically converges to zero, as the number of atoms is increased. In contrast to the squeezed states of flying photons obtained using standard generation protocols with external driving, the squeezing obtained in the ground state of the ultrastrongly coupled photon–atom systems is resilient against unpredictable noise.

In the superradiant phase transition (SRPT), coherent light and matter fields are expected to appear spontaneously in a coupled light–matter system in thermal equilibrium. However, such an equilibrium SRPT is forbidden in the case of charge-based light–matter coupling, known as no-go theorems. Here, we show that the low-temperature phase transition of ErFeO₃at a critical temperature of approximately 4 K is an equilibrium SRPT achieved through coupling between Fe³⁺magnons and Er³⁺spins. By verifying the efficacy of our spin model using realistic parameters evaluated via terahertz magnetospectroscopy and magnetization experiments, we demonstrate that the cooperative, ultrastrong magnon–spin coupling causes the phase transition. In contrast to prior studies on laser-driven non-equilibrium SRPTs in atomic systems, the magnonic SRPT in ErFeO₃occurs in thermal equilibrium in accordance with the originally envisioned SRPT, thereby yielding a unique ground state of a hybrid system in the ultrastrong coupling regime.

Exotic quantum vacuum phenomena are predicted in cavity quantum electrodynamics systems with ultrastrong light-matter interactions. Their ground states are predicted to be vacuum squeezed states with suppressed quantum fluctuations owing to antiresonant terms in the Hamiltonian. However, such predictions have not been realized because antiresonant interactions are typically negligible compared to resonant interactions in light-matter systems. Here we report an unusual, ultrastrongly coupled matter-matter system of magnons that is analytically described by a unique Hamiltonian in which the relative importance of resonant and antiresonant interactions can be easily tuned and the latter can be made vastly dominant. We found a regime where vacuum Bloch-Siegert shifts, the hallmark of antiresonant interactions, greatly exceed analogous frequency shifts from resonant interactions. Further, we theoretically explored the system’s ground state and calculated up to 5.9 dB of quantum fluctuation suppression. These observations demonstrate that magnonic systems provide an ideal platform for exploring exotic quantum vacuum phenomena predicted in ultrastrongly coupled light-matter systems.