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  • Open Access

Probing excited-state quantum phase transitions with trapped cold ions

Marek Kuchař*

Michal Macek†

  • Institute of Scientific Instruments, Czech Academy of Sciences,  Královopolská 147, 61264 Brno, Czech Republic and Institute of Theorertical Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 2, 12000 Prague, Czech Republic

  • *Contact author: marek.kuchar@isibrno.cz
  • †Contact author: michal.macek@isibrno.cz
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Phys. Rev. Research 8, 033241 – Published 28 August, 2026

DOI: https://doi.org/10.1103/cb7c-8df3

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 and relevant open-system corrections.

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Phys. Rev. Research 8, 033241– Published 28 August, 2026
  • Received 30 March 2026
  • Accepted 27 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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