Long-range Ising interactions mediated by $\lambda\phi^4$ fields: probing the renormalisation of sound in crystals of trapped ions

TL;DR

This paper proposes a quantum sensing protocol using harmonic sources to analyze the renormalisation of sound in trapped-ion crystals, linking quantum field theory dynamics with practical measurements of long-range interactions.

Contribution

It introduces a simplified sensing method that maps quantum field dynamics onto a quantum Ising model, enabling characterization of sound renormalisation without multipartite entanglement.

Findings

Effective real-time dynamics described by a long-range quantum Ising model.

Protocol can characterize renormalisation of sound in trapped-ion crystals.

Simplifies sensing by avoiding the need for multipartite entanglement.

Abstract

The generating functional of a self-interacting scalar quantum field theory (QFT), which contains all the relevant information about real-time dynamics and scattering experiments, can be mapped onto a collection of multipartite-entangled two-level sensors via an interferometric protocol that exploits a specific set of source functions. Although one typically focuses on impulsive delta-like sources, as these give direct access to $n$-point Feynman propagators, we show in this work that using always-on harmonic sources can simplify substantially the sensing protocol. In a specific regime, the effective real-time dynamics of the quantum sensors can be described by a quantum Ising model with long-range couplings, the range and strength of which contains all the relevant information about the renormalisation of the QFT, which can now be extracted in the absence of multi-partite entanglement. We present a detailed analysis of how this sensing protocol can be relevant to characterise the long-wavelength QFT that describes quantised sound waves of trapped-ion crystals in the vicinity of a structural phase transition, opening a new route to characterise the associated renormalisation of sound.