Quantum correlations and entanglement in generalized Dicke-Ising models

Geoffrey R. Grimmett, Tobias J. Osborne, Petra F. Scudo

Santiago F. Caballero-Benitez

Quantum systems inside high-Q cavities offer an excellent testbed for the control of emergent symmetries induced by light and their interplay with quantum matter. Recently several developments in cavity experiments with neutral atoms and other quantum objects such as ions motivate the study of their quantum correlated properties and their entanglement to tailor and control the behavior of the system. Using the enhanced coupling between light and interacting matter we explore the properties of emergent superradiant modes using our newly developed Light-Matter DMRG algorithm with strongly interacting spin chains. We explore a experimentally viable generalization of the transverse Ising chain coupled to the cavity light where it is possible to induce multimode structures tailored by the light pumped into the system. We find a plethora of scenarios can be explored with clear and accesible measurable signatures. This allows to study the physics of emergent orders and strong quantum correlations with quantum spins where the local and long range coupling can be efficiently simulated. We find that quantum spin nematic states with long range order and magnon pairs emerge as the transitions to superradiant phases take place. Notably, we show the cavity field allows the optimization of entanglement between spins for different light induced modes which can be used for quantum state engineering of quantum correlated states. Our methods can be used to model other hybrid quantum systems efficiently.

Max Hörmann, Anja Langheld, Jonas Leibig +2 more

Recently, Mendonça et al. [arXiv:2503.04961] investigated the Dicke-XXZ model and the Dicke-Ising model. For the latter model, their calculated quantum phase diagram contradicts claims about the existence of an intermediate phase with superradiant and antiferromagnetic order and the change in order of some phase transition lines, observed in other studies. In this comment we demonstrate that both features are indeed present in the Dicke-Ising model for the investigated parameter range in [arXiv:2503.04961].

Anja Langheld, Max Hörmann, Kai Phillip Schmidt

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.

Michal Kloc, Pavel Stránský, Pavel Cejnar

Xiaoqian Wang, Wei Zhong, Xiaoguang Wang