Theory of magnon-polaritons in quantum Ising materials

TL;DR

This paper develops a theoretical framework for magnon-polaritons in quantum Ising materials, analyzing how light-matter coupling behaves near quantum critical points and considering real-world damping effects.

Contribution

It introduces a formalism for magnon-photon interactions in quantum Ising systems, including multilevel Hamiltonians and the impact of damping on phase transitions.

Findings

Magnon-photon coupling diverges at the quantum critical point.

Damping and decoherence can prevent superradiant phase transitions.

Application to LiHoF4 matches experimental data.

Abstract

We present a theory of magnon-polaritons in quantum Ising materials, and develop a formalism describing the coupling between light and matter as an Ising system is tuned through its quantum critical point. The theory is applied to Ising materials having multilevel single-site Hamiltonians, in which multiple magnon modes are present, such as the insulating Ising magnet LiHoF$_4$ . We find that the magnon-photon coupling strengths may be tuned by the applied transverse field, with the coupling between the soft mode present in the quantum Ising material and a photonic resonator mode diverging at the quantum critical point of the material. A fixed system of spins will not exhibit the diamagnetic response expected when light is coupled to mobile spins or atoms. Without the diamagnetic response, one expects a divergent magnon-photon coupling strength to lead to a superradiant quantum phase transition. However, this neglects the effects of damping and decoherence present in any real system. We show that damping and decoherence may block the superradiant quantum phase transition, and lead to weak coupling between the soft magnon mode and the resonator mode. The results of the theory are applied to experimental data on the model system LiHoF$_4$ in a microwave resonator.