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arXiv:2603.28509 · Physical Review Research

Probing excited-state quantum phase transitions with trapped cold ions

Marek Kuchař, Michal Macek

quant-phcond-mat.stat-mechnucl-thSubmitted Mar 30, 2026• Announced Mar 31, 2026• 0 citations• Revised Aug 28, 2026 (v3)

v1 · Mar 30, 2026 v2 · Apr 3, 2026 v3 · Aug 28, 2026

Abstract

We propose concrete protocols to realize quantum criticality due to excited-state quantum phase transitions (ESQPTs) experimentally in presumably the simplest and most resilient system involving a single trapped ion oscillating in a radio-frequency Paul trap. We identify a specific class of excited states of the Extended Rabi Model (ERM) Hamiltonian, which occur between two critical ESQPT energies of the model in its (anti)Jaynes-Cummings superradiant phase. Properties of these states motivate the definition of several ESQPT witness observables. We study their critical scaling behaviors as well as various distinct state evolutions by driving the system across the quantum criticalities by changing the qubit-phonon coupling strength linearly in time at different finite rates. A mapping of the theoretical control parameters of the ERM to the experimental parameters of a trapped ion setup is provided, and simulations are performed for values referencing existing state-of-the-art setups, addressing both unitary state evolutions as well as relevant open-system corrections.

Journal reference: Physical Review Research, 8, 033241 (2026)
DOI: 10.1103/cb7c-8df3
Comments: 15 pages, 11 figures (published version)

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