The group conducts theoretical research on the dynamics of correlated quantum systems, and more specifically in connection to ultracold atom gases, quantum optics systems, and quantum simulation (see for instance the special issue on Quantum Simulation, coordinated by Prof. Laurent Sanchez-Palencia on the Comptes-Rendus de Physique of the French Academy of Sciences). In regimes where matter and fields are governed by the laws of quantum physics, the interplay of quantum interference and particle interactions gives rise to fascinating phenomena, such as Bose-Einstein condensation, Fermi degeneracy, superfluidity, superconductivity, entanglement, and quantum phase transitions just to name a few examples.

In a nutshell, our work aims at characterizing novel quantum phases of matter and the associated quantum phase transitions, understand transport properties of correlated systems, and develop theoretical approaches to this aim. We develop research lines on quantum disordered systems, quantum quasicrystals, one-dimensional quantum gases, and out-of-equilibrium dynamics of correlated matter (see below). Our work makes use of a wide panel of techniques and, most often, combine analytical approaches (eg. mean field theory, Bethe ansatz, Yang-Yang theory, bosonization, renormalization group analysis, ...) and large-scale numerical simulations for many-body systems (eg. exact diagonalization, path integral quantum Monte Carlo, matrix-product states, ...).

Our main efforts focus on the physics of systems that constitute promising plateforms for concrete realization of quantum technologies. Together with other systems in condensed matter and quantum optics, ultracold atoms have already produced milestone results, which turn quantum technologies from dream to reality. The main part of our work is purely theoretical but we also have long-term collaborations with experimental groups, mainly at

__|Institut d'Optique (France; group of Alain Aspect, David Clément, and Vincent Josse);

__|University of Florence (Italy; group of Massimo Inguscio and Giovanni Modugno).

Moreover, we have collaborations with theory groups worldwide, for instance

__|Institut de Ciences Fotoniques (Spain; group of Maciej Lewenstein and L. Tarruell);

__|University of Barcelona (Spain; group of Luca Tagliacozzo);

__|University of Grenoble (France; groups of Bart van Tiggelen, Markus Holzmann, and Anna Minguzzi);

__|University of Nice (France; group of Patrizia Vignolo);

__|University of Geneva (Switzerland; group of Thierry Giamarchi);

__|College de France (France; group of Antoine Georges).

Disordered quantum systems-- Our activity on the physics of disordered systems started with a theoretical proposal to observe Anderson localization in ultracold-atom systems [Sanchez-Palencia et al., Phys. Rev. Lett. 2007; Piraud et al., Phys. Rev. A (Rapid Comm.) 2011]. It paved the way one year later to the first direct observation of this major effect with ultracold matter waves in one [Billy et al., Nature 2008; Roati et al., Nature 2008] and then in three [Kondov et al., Science 2011; Jendrzejewski et al., Nat. Phys. 2012] dimensions. These milestone results have open unprecedented perpectives, which gave birth to the field of disordered quantum gases [Sanchez-Palencia and Lewenstein, Nat. Phys. 2010]. The main contributions of the group in this field include the demonstration of coexistence of localized and extended states in disordered traps [Pezzé and Sanchez-Palencia, Phys. Rev. Lett. 2011], the analytic computation of the disorder-induced shift of the mobility edge in three-dimensional Anderson localization [Piraud et al., Europhys. Lett. 2012], the non-perturbative treatment of interactions in degenerated Bose gases [Sanchez-Palencia, Phys. Rev. A 2006], the determination of phase diagrams of correlated disordered bosons [Lugan et al., Phys. Rev. Lett. 2007], the analytic theory of collective Anderson localization in disordered Bose superfluids [Lugan et al., Phys. Rev. Lett. 2007; Lellouch and Sanchez-Palencia, Phys. Rev. A (Rapid. Comm.) 2014], and the demonstration of universal Berezinkii-Kosterlitz-Thouless superfluid tansition in two-dimensional disordered Bose gases [Carleo et al., Phys. Rev. Lett. 2013].

Quantum quasicrystals-- We also study the physics of quantum quasicrystals. These systems, intermediate between completely ordered and completely disordered systems, host fascinating properties of localization and fractality. In the group, we particularly focus on the dynamics of strongly correlated bosons in quasicrystal structures, as can be emulated with appropriately engineered laser beams [Sanchez-Palencia and Santos, Phys. Rev. A 2005]. Recent contributions from the group include the demonstration of spectral fractality and localization transition [Yao et al., Phys. Rev. Lett. 2019], the characterization of Bose glass and Mott lobe fractality [Yao et al., Phys. Rev. Lett. 2020], and the phase diagram of strongly correlated bosons in a two-dimensional quasicrystal [Gautier et al., Phys. Rev. Lett. 2021].

One-dimensional quantum gases-- Another part of our activities is devoted the physics of one-dimensional quantum systems, which have a particular flavor. On the one hand, quantum physics in one dimension gives rise to novel effects, such as diverging susceptibilites and unusual superfluid-insulator transitions. On the other hand, it is amenable to exact (Bethe anstaz) or universal hydrodynamic (Luttinger liquid) theories, and efficient numerical approaches (DMRG-like). Recent contributions of the group include the first unbiased determination of the Mott-U and Mott-δ transitions in arbitrary weak periodic potentials using large-scale quantum Monte Carlo calculations [Boéris et al., Phys. Rev. A (Rapid. Comm.) 2016] (collaboration with the experimental group of G. Modugno and M. Inguscio, Florence, Italy), the characterization of the Tan contact and its connection to the crossover to fermionization in trapped Lieb-Liniger gases at arbitrary temperature [Yao et al., Phys. Rev. Lett. 2018], and the determination of critical localization properties and fractality in quasi-periodic models beyond [Yao et al., Phys. Rev. Lett. 2019].

Out-of-equilibrium dynamics of correlated quantum systems-- A significant part of our activities is devoted to the out-of-equilibrium dynamics of correlated quantum systems. We have investigated the propagation of quantum correlations in the 1D and 2D Bose-Hubbard models [Carleo et al., Phys. Rev. A. (Rapid Comm.) 2014; Despres et al., Sci. Rep. (Nature group) 2019] and in the continuous Lieb-Liniger model [Carleo et al., Phys. Rev. X 2017], as well as locality breaking in spin and Bose systems with long-range interactions [Cevolani et al., Phys. Rev. A (Rapid Comm.) 2015; Cevolani et al., New J. Phys. 2016]. Recently, we have also derived a universal scaling form for the spreading of correlations in quantum systems with short- and long-range interactions [Cevolani et al., Phys. Rev. B 2018; Schneider et al., Phys. Rev. Research 2021] and proposed quench spectroscopy as a novel way to probe strongly-correlated quantum matter using quench dynamics [Villa et al., Phys. Rev. A 2019; Villa et al., Phys. Rev. A 2020; Villa et al., Phys. Rev. A 2021].