STAGE Offre de stage : Far-from-Equilibrium Dynamics in Utracold Quantum Systems

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 applications to quantum communications.
At the moment, we lack a universal picture and many questions remain open.
In this context, ultracold atoms are particularly interesting for it is now possible to investigate a
variety of far-from-equilibrium properties of these systems thanks to accurate time-dependent
control of the physical parameters [1,2]. In practice, one can prepare the gas in some initial state,
then abruptly change Hamiltonian parameters, 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 unable to reach thermal equilibrium. Fortunately, the peculiarities of onedimensional (1D) systems make them amenable to a variety of powerful analytical [3] and
numerical techniques [4,5].
The aim of the internship and thesis will be to theoretically investigate the propagation of
information in 1D quantum system. We will study the behavior of correlations and entanglement in
the limit of strong interactions, relevant to the modern experiments on ultracold atoms. Following
previous studies of us [6-8], we will focus on novel situations where known theorems break down,
for instance in the presence of long-range interactions, which are relevant to experiments on
molecular condensates or ion systems for instance. These fundamental issues will be addressed
from a theoretical point of view, using the most modern N-body approaches, both analytical and
numerical, for instance using Matrix Product States approaches.
[1] J. Eisert, M. Friesdorf & C. Gogolin, Nature Phys. 11, 124-130 (2015).
[2] S. Trotzky et al., Nat. Phys. 8, 325–330 (2012).
[3] T. Giamarchi. Quantum Physics in One Dimension (Carendon press, Oxford, 2004).
[4] F. Verstraete & J. I. Cirac, Phys. Rev. Lett. 104, 190405 (2010).
[5] G. Carleo, L. Cevolani, L. Sanchez-Palencia & M. Holzmann, Phys. Rev. X 7, 031016 (2017).
[6] L. Cevolani, G. Carleo, and L. Sanchez-Palencia, Phys. Rev. A 92, 041603(R) (2015).
[7] L. Cevolani, G. Carleo, and L. Sanchez-Palencia, New J. Phys. 18, 093002 (2016)
[8] L. Cevolani et al., Phys. Rev. B 98, 024302 (2018)