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

• URL: http://arxiv.org/abs/2105.06886v2
• Date: Wed, 2 Jun 2021 15:20:10 GMT
• Title: Long-range Ising interactions mediated by $\lambda\phi^4$ fields: probing the renormalisation of sound in crystals of trapped ions
• Authors: G. Mart\'in-V\'azquez, G. Aarts, M. M\"uller and A. Bermudez
• Abstract summary: Self-interacting scalar quantum field theory can be mapped onto a collection of multipartite-entangled two-level sensors. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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