Laboratoire de Physique Théorique
Toulouse - UMR 5152

Rydberg atom arrays provide an ideal platform for quantum analog simulations and computations [Browaeys2020]. These are individual neutral atoms with large dipole moments trapped in microscopic dipole trap arrays, which can be optically moved at will. Each atom can be excited to its Rydberg state, and a pair of excited states interact via a long-range interaction. In a certain regime, a Rydberg blockage occurs, where two atoms cannot be excited simultaneously to their Rydberg states [Lukin2001]. The enormous experimental progress in recent years has made it possible to implement almost arbitrary geometries for the atomic lattice (including frustrated lattices, the presence or absence of defects, local fields, etc.) as well as to control and measure individual "spins" with local pulses - something that is impossible in condensed matter. Such Rydberg atom arrays are probably the systems that have seen the greatest increase in experimental precision, control and number of qubits in recent years in all quantum simulation platforms.

This thesis proposes to use large-scale numerical simulations to determine the phase diagrams and physical properties of these systems on different geometries. On the one hand, it is possible to simulate by stochastic methods (quantum Monte-Carlo). On the other hand, at low energy, blocking allows to use constrained effective models, such as quantum loop or dimer models, which have a long history in condensed matter theory [Rokhsar1988]. Recently, a new algorithm has made it possible to handle exactly this type of constraint in a path integral approach [Yan2019, Dabholkar2022].

Using methodological developments, we will study the phase diagrams of these models on different networks and characterize their properties, e.g. by measuring the quantum entanglement for topological phases or by determining the excitations in the dynamic spectral functions [Shao2017].

References :

[Browaeys2020] A. Browaeys, T. Lahaye, Nat. Phys. 16, 132 (2020)

[Lukin2001] M. D. Lukin et al, Phys. Rev. Lett. 87, 037901 (2001)


[Merali2021] E. Merali, I. J. S. De Vlugt, R. G. Melko, preprint arXiv:2107.00766

[Rokhsar1988] D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988)

[Yan2019] Z. Yan, Y. Wu, C. Liu, O. F. Syljuåsen, J. Lou, Y. Chen, Phys. Rev. B 99, 165135 (2019)

[Shao2017] H. Shao, Y. Q. Qin, S. Capponi, S. Chesi, Z. Y. Meng, A. W. Sandvik, Phys. Rev. X 7, 041072 (2017)

[Dabholkar2022] B. Dabholkar, G. J. Sreejith, and F. Alet, Phys. Rev. B 106, 205121 (2022)

Contacts : Sylvain Capponi , Professor, University of Toulouse

capponi@irsamc.ups-tlse.fr https://www.lpt.ups-tlse.fr/capponi

Fabien Alet, Director of Research, CNRS

fabien.alet@cnrs.fr https://www.lpt.ups-tlse.fr/alet