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arXiv · 2105.06886

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

G. Martín-Vázquez·G. Aarts·M. Müller·A. Bermudez
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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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G. Martín-Vázquez, G. Aarts, M. Müller, A. Bermudez. 2021-06-02. Long-range Ising interactions mediated by $λϕ^4$ fields: probing the renormalisation of sound in crystals of trapped ions. https://doi.org/10.1103/prxquantum.3.020352

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