Quantum phase transitions and non-linear dynamics in systems of trapped cold ions

The aim of this project is to investigate various aspects of quantum phase transitions (QPTs) [1], excited-state quantum phase transitions (ESQPTs) [2] and other similar phenomena (eigenstate [3] and dynamical [4] quantum phase transitions) in non-equilibrium quantum thermodynamics, observable in systems of cold ions in radio-frequency Paul traps [5, 6].

The PhD candidate will derive relevant simplified Hamiltonians (a’la the Jaynes-Cummings and Rabi models), showing the QPTs and ESQPTs, from a general quantum electrodynamics Hamiltonian involving the 40 Ca+ ion in the Paul trap with additional laser fields. Particular attention will be paid to the specific details of the experimental apparatus at ISI Brno [7] in an attempt for the first experimental observation of ESQPTs in trapped cold ion systems. The candidate will also consider relevance of the quantum states prepared by critical quantum quench protocols for applications in quantum computing and quantum sensing.

References:

[1] L. D. Carr, Understanding Quantum Phase Transitions, CRC Press, (2011).
[2] P. Cejnar, P. Stránský, M. Macek, M. Kloc, Excited-state quantum phase transitions, J. Phys. A: Math. Theor. 54, 133001 (2021).
[3] S. A. Parameswaran, A. C. Potter, R. Vasseur, Eigenstate phase transitions and the emergence of universal dynamics in highly excited states, Ann. Phys. (Berlin) 529, 1600302 (2017).
[4] M. Heyl, Dynamical quantum phase transitions: a review, Rep. Prog. Phys. 81, 054001 (2018).
[5] D. Liebfried, R. Blatt, C. Monroe, D. Wineland, Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281 (2003).
[6] 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).
[7] P. Obšil et al., A room-temperature ion trapping apparatus with hydrogen partial pressure below 10^–11 mbar, Rev. Sci. Instrum. 90, 083201 (2019).