The group conducts fundamental theoretical research on correlated quantum matter, and more specifically in connection to ultracold quantum gases, quantum optics, and quantum simulation. In regimes where matter and fields are governed by the laws of quantum physics, the interplay of quantum interference, entanglement, and particle interactions foster a plethora of intriguing phenomena. Quantum simulation has established itself as a powerful tool, complementary to traditional theoretical and experimental approaches, to gain fundamental insights on this fascinating physics.

Our work aims at investigating open questions to impact our understanding of complex quantum matter, move towards unexplored fields, and developing new theoretical approaches to this aim. We develop research lines on quantum quasicrystals, quantum information and dynamics of many-body systems, one-dimensional quantum systems, and disordered quantum systems (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 quantum systems (eg. exact diagonalization, path integral quantum Monte Carlo, matrix-product states, ...).

The main part of our work is 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, including
__|University of Geneva (Switzerland; group of Thierry Giamarchi);
__|Institut de Ciences Fotoniques (Spain; group of Maciej Lewenstein and Leticia Tarruell);
__|University of Barcelona (Spain; group of Luca Tagliacozzo);
__|College de France (group of Antoine Georges).
__|University of Grenoble (groups of Bart van Tiggelen, Markus Holzmann, and Anna Minguzzi);
__|University of Nice (group of Patrizia Vignolo);

Bosonic quasicrystals-- Since 2019, we started a research program on quantum simulation of quantum quasicrystals. We specifically explore the new frontier opened by synthetic bosonic matter, which offer unprecedented perspectives compared to its fermionic counterpart. Quasicrystals are fascinating systems, intermediate between completely ordered and completely disordered materials. As such they host intriguing properties of localization, fractality, anomalous criticality, and exotic excitations. In the group, we particularly focus on the physics of strongly correlated bosons in quasicrystal structures, as can be emulated with engineered laser beams in ultracold atomic gases [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 in a quasiperiodic Lieb-Liniger gas [Yao et al., Phys. Rev. Lett. 2020], and the discovery of anomalous mobility edges in one-dimensional quasiperiodic models [Liu et al., SciPost 2022]. In the very recent years, we have pioneered theoretical work on 2D bosonic quasicrystals. We determined the first quantum phase diagrams of strongly-correlated bosons in such structures [Gautier et al., Phys. Rev. Lett. 2021] as well as the impact of thermal fluctuations [Zhu et al., Phys. Rev. Lett. 2023]. We also considered twisted potentials and unveiled the role of commensurability on the onset of weak superfluids [Johnstone et al. (2024)].

Quantum information and dynamics of many-body systems-- A significant part of our activity is devoted to the connection between quantum information theory and many-body physics, in particular in out-of-equilibrium systems. We have characterised 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]. An important contribution is the derivation of a universal scaling form for the spreading of correlations and entanglement in quantum systems with short- and long-range interactions [Cevolani et al., Phys. Rev. B 2018; Schneider et al., Phys. Rev. Research 2021]. We also devised quench spectroscopy as a general approach 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]. Recently, we turned our attention towards entanglement Hamiltonians in long-range systems [Schneider et al., Phys. Rev. B 2022]

One-dimensional quantum systems-- Another part of our activities is devoted to the physics of one-dimensional systems, where quantum correlations are enhanced. On the one hand, quantum physics in one dimension gives rise to spectacular 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 (tensor-netwok 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 in 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].

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]. Further contributions of the group in this field include one-dimensional Anderson localization in speckle potentials [Lugan et al., Phys. Rev. A 2009], the demonstration of coexistence of localized and extended states in disordered traps [Pezzé and Sanchez-Palencia, Phys. Rev. Lett. 2011], and the analytic computation of the disorder-induced shift of the mobility edge in three-dimensional Anderson localization [Piraud et al., Europhys. Lett. 2012]. We also studied localization in interacting Bose gases. Our main contributions include 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].