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arXiv:2603.22416

Dicke materials as a resource for quantum squeezing

Vaibhav Sharma, Shung-An Koh, Jonathan Stepp, Dasom Kim, Takumu Obata, Yuki Saito, Motoaki Bamba, Han Pu, Hanyu Zhu, Junichiro Kono, Kaden R. A. Hazzard

quant-phcond-mat.mtrl-scicond-mat.quant-gascond-mat.str-elSubmitted Mar 23, 2026• Announced Mar 25, 2026• 0 citations
v1 · Mar 23, 2026v2 · Apr 3, 2026
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Abstract

We study magnetic materials whose low energy physics can be effectively described by a Dicke model, which we term Dicke materials. We show how a Dicke model emerges in such materials due to a coexistence of fast-dispersing and slow-dispersing spins, which are strongly coupled. Analogous to the paradigmatic Dicke model describing light-matter interactions, these materials also exhibit signatures of a superradiant phase transition. The ground state near the superradiant phase transition is expected to be squeezed, making Dicke materials a resource for quantum metrology and witnessing entanglement in solid-state systems. However, as an entanglement measure, squeezing can be sensitive to perturbations that are otherwise irrelevant for usual correlation functions and order parameters. Motivated by the prospect of observing squeezing in such Dicke materials, we study the robustness of ground state squeezing under ubiquitous imperfections such as finite temperature, disorder, and local interactions. Using analytical and numerical techniques, we show that the squeezing obtained is perturbatively stable against these imperfections and quantitatively evaluate regimes promising for experimental observation.

Comments
18 pages, 7 figures

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We study magnetic materials whose low energy physics can be effectively described by a Dicke model, which we term Dicke materials. We show how a Dicke model emerges in such materials due to a coexistence of fast-dispersing and slow-dispersing spins, which are strongly coupled. Analogous to the paradigmatic Dicke model describing light-matter interactions, these materials also exhibit signatures of a superradiant phase transition. The ground state near the superradiant phase transition is expected to be squeezed, making Dicke materials a resource for quantum metrology and witnessing entanglement in solid-state systems. However, as an entanglement measure, squeezing can be sensitive to perturbations that are otherwise irrelevant for usual correlation functions and order parameters. Motivated by the prospect of observing squeezing in such Dicke materials, we study the robustness of ground state squeezing under ubiquitous imperfections such as finite temperature, disorder, and local interactions. Using analytical and numerical techniques, we show that the squeezing obtained is perturbatively stable against these imperfections and quantitatively evaluate regimes promising for experimental observation.
In this study, the energy spectrum and thermal equilibrium states of the finite-size Dicke-Stark model were numerically obtained within the extended coherent state space by solving the dressed master equation for strongly coupled light-atom systems. The critical point of the superradiant phase transition in the infinite-size Dicke-Stark model was analytically derived using the mean-field approach and confirmed with numerical calculation. Under thermal equilibrium conditions, analyses of the negativity, zero-time-delay two-photon correlation function, and atom-spin squeezing parameters in the finite-size Dicke-Stark model reveal that as the coupling strength increases, the light field undergoes a transition from photon bunching to anti-bunching and then back to bunching. The Stark field can modulate both the maximum and minimum values of the two-photon correlation function and their corresponding coupling strengths. At low temperatures, the system exhibits entanglement and spin squeezing. As temperature rises, entanglement gradually diminishes, while strong coupling facilitates the preservation of entanglement in the system state. Atom-spin squeezing spin squeezing is highly sensitive to temperature and vanishes rapidly with increasing temperature. This work contributes to the fundamental understanding of quantum phenomena in Dicke-Stark systems.
In view of recent proposals for the realization of anisotropic light-matter interaction in such platforms as (i) nonstationary or inductively and capacitively coupled superconducting qubits, (ii) atoms in crossed fields, and (iii) semiconductor heterostructures with spin-orbital interaction, the concept of a generalized Dicke model, where coupling strengths of rotating wave and counter-rotating wave terms are unequal, has attracted great interest. For this model we study photon fluctuations in the critical region of normal-to-superradiant phase transition when both the temperatures and numbers of two-level systems are finite. In this case, the superradiant quantum phase transition is changed to a fluctuational region in the phase diagram that reveals two types of critical behaviors. These are regimes of Dicke model (with discrete Z2{\mathbb{Z}}_{2}Z2​ symmetry), and that of anti-Tavis-Cummings and Tavis-Cummings U(1)U(1)U(1) models. We show that squeezing parameters of photon condensate in these regimes show distinct temperature scalings. Besides, relative fluctuations of a photon number take universal values. We also find a temperature scale below which one approaches a zero-temperature quantum phase transition where quantum fluctuations dominate. Our effective theory is provided by a non-Goldstone functional for condensate mode and by Majorana representation of Pauli operators. We also discuss the Bethe ansatz solution for integrable U(1)U(1)U(1) limits.
The superradiant phenomenon, usually described by the Dicke model, is a hallmark of strong light-matter interaction. We explore how matter-matter interactions influence this phenomenon by performing ground-state simulations of Dicke-like models with both isotropic and anisotropic interactions. We find that Ising-type interactions produce two qualitatively distinct phase boundaries, one of which gives rise to an antiferromagnetic-normal phase connected to the superradiant regime via a first-order phase transition. Under anisotropic couplings, we uncover a strongly correlated phase where in-plane spin order coexists with superradiance, exhibiting sublinear scaling of the photon occupation per site and power-law decay of spin correlations. Furthermore, superradiance is strengthened by tuning either isotropic or anisotropic interactions, highlighting the role of intrinsic many-body correlations in shaping light-matter quantum phases.
We gain quantitative insights on effects of light-matter interactions on correlated quantum matter by quantum Monte Carlo simulations. We introduce a wormhole algorithm for the paradigmatic Dicke-Ising model which combines the light-matter interaction of the Dicke model with Ising interactions. The quantum phase diagrams for ferro- and antiferromagnetic interactions on the chain and the square lattice are determined. The occurring superradiant phase transitions are in the same universality class as the Dicke model, leading to a well-known peculiar finite-size scaling that we elucidate in terms of scaling above the upper critical dimension. For the ferromagnetic case, the transition between the normal and the superradiant phase is of second order with Dicke criticality (first order) for large (small) longitudinal fields separated by a multicritical point. For antiferromagnetic interactions, we establish the light-matter analog of a lattice supersolid with off-diagonal superradiant and diagonal magnetic order and determine the nature of all transition lines. Our achievements allow to quantitatively enter the domain of mesoscopic light-matter systems, which is an increasingly prominent topic at the interface of quantum optics and condensed matter physics.
High precision macroscopic quantum control in interacting light–matter systems remains a significant goal toward novel information processing and ultra-precise metrology. We show that the out-of-equilibrium behavior of a paradigmatic light–matter system (Dicke model) reveals two successive stages of enhanced quantum correlations beyond the traditional schemes of near-adiabatic and sudden quenches. The first stage features magnification of matter-only and light-only entanglement and squeezing due to effective nonlinear self-interactions. The second stage results from a highly entangled light–matter state, with enhanced superradiance and signatures of chaotic and highly quantum states. We show that these new effects scale up consistently with matter system size, and are reliable even in dissipative environments.
Abstract 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 ErFeO 3 , where the role of atoms (photons) is played by Er 3+ spins (Fe 3+ 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.