In the first part of the talk, we briefly overview quantum phase transitions [1, 2] in diverse physical settngs, ranging from condensed mater physics, nuclear physics, molecular physics, to quantum optics. We pay particular atention to Excited State Quantum Phase Transitions (ESPQTs), which were first identified in the context of collective dynamics of atomic nuclei and later systematically classified in a broad range of physical settings, using different Hamiltonians showing both regular as well as chaotic dynamics [3]. In the second part of the talk, we propose concrete protocols to realize quantum criticality due to ESQPTs [4] experimentally in presumably the simplest system involving a single trapped ion oscillating in a radio-frequency Paul trap [5-7]. 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 distrnct 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 [8], addressing both unitary state evolutions as well as relevant open-system corrections. The work is supported by OPJAK project No. CZ.02.01.01/00/22_008/0004649 “QUEENTEC “ by Ministry of Education, Youth and Sports of the Czech Republic.

References:

[1] L. D. Carr (Ed.), "Understanding Quantum Phase Transitions", London: Taylor and Francis, (2010).
[2] S. Sachdev, "Quantum Phase Transitions", Cambridge: Cambridge University Press, (1999).
[3] P. Cejnar, P. Stránský, M. Macek, M. Kloc, Journal of Physics A: Mathematical and Theoretical 54, 133001 (2021).
[4] M. Kuchař and M. Macek, htps://arxiv.org/abs/2603.28509, submited
[5] D. Leibfried, R. Blat, C. Monroe, D. Wineland, Rev. Mod. Phys. 75, 281 (2003).
[6] M.-J. Hwang, R. Puebla and M. B. Plenio, Phys. Rev. Let. 115 180404 (2015).
[7] M.-L. Cai et al., "Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion", Nat. Comm. 12, 1126 (2021).
[8] P. Obšil et al., Rev. Sci. Instrum. 90, 083201 (2019)