Two-photon processes have so far been considered only as resulting from frequency-matched second-order expansions of light-matter interaction, with consequently small coupling strengths. However, a variety of novel physical phenomena arises when such coupling values become comparable with the system characteristic frequencies. Here, we propose a realistic implementation of two-photon quantum Rabi and Dicke models in trapped-ion technologies. In this case, effective two-phonon processes can be explored in all relevant parameter regimes. In particular, we show that an ion chain under bichromatic laser drivings exhibits a rich dynamics and highly counterintuitive spectral features, such as interaction-induced spectral collapse.Comment: Improved versio

We propose the quantum simulation of the quantum Rabi model in all parameter regimes by means of detuned bichromatic sideband excitations of a single trapped ion. We show that current setups can reproduce, in particular, the ultrastrong and deep strong coupling regimes of such a paradigmatic light-matter interaction. Furthermore, associated with these extreme dipolar regimes, we study the controlled generation and detection of their entangled ground states by means of adiabatic methods. Ion traps have arguably performed the first quantum simulation of the Jaynes-Cummings model, a restricted regime of the quantum Rabi model where the rotating-wave approximation holds. We show that one can go beyond and experimentally investigate the quantum simulation of coupling regimes of the quantum Rabi model that are difficult to achieve with natural dipolar interactions.

The quantum Rabi model, involving a two-level system and a bosonic field mode, is arguably the simplest and most fundamental model describing quantum light-matter interactions. Historically, due to the restricted parameter regimes of natural light-matter processes, the richness of this model has been elusive in the lab. Here, we experimentally realize a quantum simulation of the quantum Rabi model in a single trapped ion, where the coupling strength between the simulated light mode and atom can be tuned at will. The versatility of the demonstrated quantum simulator enables us to experimentally explore the quantum Rabi model in detail, including a wide range of otherwise unaccessible phenomena, as those happening in the ultrastrong and deep strong-coupling regimes. In this sense, we are able to adiabatically generate the ground state of the quantum Rabi model in the deep strong-coupling regime, where we are able to detect the nontrivial entanglement between the bosonic field mode and the two-level system. Moreover, we observe the breakdown of the rotating-wave approximation when the coupling strength is increased, and the generation of phonon wave packets that bounce back and forth when the coupling reaches the deep strongcoupling regime. Finally, we also measure the energy spectrum of the quantum Rabi model in the ultrastrong-coupling regime.

We propose the analog-digital quantum simulation of the quantum Rabi and Dicke models using circuit quantum electrodynamics (QED). We find that all physical regimes, in particular those which are impossible to realize in typical cavity QED setups, can be simulated via unitary decomposition into digital steps. Furthermore, we show the emergence of the Dirac equation dynamics from the quantum Rabi model when the mode frequency vanishes. Finally, we analyze the feasibility of this proposal under realistic superconducting circuit scenarios.