Simulation of a quantum phase transition of polaritons with trapped ions

TL;DR

This paper proposes a trapped ion system to simulate quantum phase transitions of polaritons, demonstrating tunable interactions and an experimental protocol for observing phase transition signatures with few ions.

Contribution

It introduces a new trapped ion setup for simulating polariton phase transitions, with tunable parameters and a protocol for experimental detection.

Findings

System exhibits features of polariton phase transitions

Tunable phonon-phonon interactions via laser parameters

Protocol enables detection with few ions

Abstract

We present a novel system for the simulation of quantum phase transitions of collective internal qubit and phononic states with a linear crystal of trapped ions. The laser-ion interaction creates an energy gap in the excitation spectrum, which induces an effective phonon-phonon repulsion and a Jaynes-Cummings-Hubbard interaction. This system shows features equivalent to phase transitions of polaritons in coupled cavity arrays. Trapped ions allow for easy tunabilty of the hopping frequency by adjusting the axial trapping frequency, and the phonon-phonon repulsion via the laser detuning and intensity. We propose an experimental protocol to access all observables of the system, which allows one to obtain signatures of the quantum phase transitions even with a small number of ions.