Louis VILLA

 

PhD Student

Resarch activities at CPHT: Condensed Matter

Thesis: Far-from-equilibrium dynamics of ultracold quantum systems
Advisor: Laurent Sanchez-Palencia

Abstract : Some unidimensional quantum systems said integrable are analytically exactly solvable: it becomes possible to write down the wavefunction and the eigenenergies of the ground state by using a powerful analytical method called the Bethe Ansatz. The wavefunction is chosen to be a sum of plane waves whose coefficients are unknown and obey some constraints called Bethe's equations. These equations include all the thermodynamical information about the system at equilibrium and zero temperature. However solving these equations to extract the physical information is not a trivial task. I'm interested in the conditions where the Bethe Ansatz method can be applied, for an exactly integrable system (Lieb-Liniger model) or a system close to be integrable (Bose-Hubbard for strong interactions). I'm also interested in fermionic systems and some generalisations at non zero temperature (Yang-yang equations). 

The previous paragraph focused on the study at equilibrium. However, understanding how a strongly-correlated quantum system evolves when driven out of equilibrium is presently a central challenge to quantum physics. It would deeply impact our fundamental understanding of quantum matter and promise fascinating application to quantum communications.  In practice, I focus on ultracold gases where the gas is prepared in some initial state, then one abruptly change Hamiltonian parameters (quench), and observe the subsequent dynamics. Whether the system will evolve towards thermal equilibrium or a more complicated stationary state remains largely an open question. One dimensional systems are particularly fascinating when they are integrable and are thus enable to reach thermal equilibrium. Fortunately, the peculiarities of one dimensional systems make them amenable to a variety of powerful analytical [1] and numerical techniques [2,3]. The aim of the thesis is to develop a new approach based on the Bethe ansatz, which has been proposed recently and pave the way to exact solutions of far-from-equilibrium problems. It will be applied to the dynamics of one-dimensional bosons with arbitrary strong interactions, for instance release from a trap and relaxation towards equilibrium. Possible extensions with enormous potential include generalizations to Fermi systems and long-range interactions. A part of the project may be developed in direct collaborations with experiments.

1] T.Giamarchi, Quantum Physics in One Dimension (Carendon Press, Oxford, 2004).

[2] F.Verstraete & J.Cirac, Phys.Rev.Lett.104,190405 (2010).

[3] G.Carleo, L.Cevolani, L.Sanchez-Palencia & M.Holzmann, Phys.Rev.X 7,031026 (2017).

Publications :

Villa L, Despres J, Thomson SJ, Sanchez-Palencia L.
Local quench spectroscopy of many-body quantum systems
DOI: 10.1103/PhysRevA.102.033337
Physical Review A. 2020;102(3):033337.

Villa L, Despres J, Sanchez-Palencia L.
Unraveling the excitation spectrum of many-body systems from quantum quenches.
Physical Review A. 2019;100(6):063632.
DOI: 10.1103/PhysRevA.100.063632.

Despres J, Villa L, Sanchez-Palencia L.
Twofold correlation spreading in a strongly correlated lattice Bose gas.
Scientific Reports. 2019;9:4135.
DOI: 10.1038/s41598-019-40679-3.

 

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