# Terahertz Strong-Field Physics without a Strong External Terahertz Field

## TL;DR

This paper explores how matter can exhibit strong-field phenomena through quantum vacuum interactions in cavity systems, especially in the ultrastrong coupling regime, without the need for external terahertz fields.

## Contribution

It discusses two condensed matter systems demonstrating cooperative ultrastrong interactions in the terahertz range, expanding understanding of vacuum-field coupled systems.

## Key findings

- Observation of vacuum Rabi splitting in systems without external fields
- Identification of systems reaching the ultrastrong coupling regime
- Potential for quantum phase transitions in matter-vacuum interactions

## Abstract

Traditionally, strong-field physics explores phenomena in matter (atoms, molecules, and solids) driven by an extremely strong laser field nonperturbatively. However, even in the complete absence of an external electromagnetic field, strong-field phenomena can arise when matter strongly couples with the zero-point field of the quantum vacuum state, i.e., fluctuating electromagnetic waves whose expectation value is zero. Some of the most striking examples of this occur in a cavity setting, in which an ensemble of two-level atoms resonantly interacts with a single photonic mode of vacuum fields, producing vacuum Rabi splitting. In particular, the nature of the matter-vacuum-field coupled system fundamentally changes when the coupling rate (equal to one half of the vacuum Rabi splitting) becomes comparable to, or larger than, the resonance frequency. In this so-called ultrastrong coupling regime, a non-negligible number of photons exist in the ground state of the coupled system. Furthermore, the coupling rate can be cooperatively enhanced (via so-called Dicke cooperativity) when the matter is comprised of a large number of identical two-level particles, and a quantum phase transition is predicted to occur as the coupling rate reaches a critical value. Low-energy electronic or magnetic transitions in many-body condensed matter systems with large dipole moments are ideally suited for searching for these predicted phenomena. Here, we discuss two condensed matter systems that have shown cooperative ultrastrong interactions in the terahertz frequency range: a Landau-quantized two-dimensional electron gas interacting with high-quality-factor cavity photons, and an Er$^{3+}$ spin ensemble interacting with Fe$^{3+}$ magnons in ErFeO$_3$.