Tutelle du CNRSQuantum Matter group
led by Laurent Sanchez-Palencia



Publications / Theses and habilitations

Strongly-correlated one-dimensional bosons in continuous and quasiperiodic potentials

Hepeng YAO

Ph-D thesis; October 20, 2020

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Abstract (click on text): In this thesis, we investigate the properties of one-dimensional bosons in various types of systems, focusing on the phase transitions or crossovers between different quantum degeneracy regimes. Combining quantum Monte Carlo with other standard techniques such as exact diagonalization and thermal Bethe ansatz, we can compute the behavior of 1D bosons in different cases where the results are still lacking. Firstly, in the case of harmonically trapped continuous bosons, we provide a full characterization of a quantity called Tan's contact. By computing the universal scaling function of it, we identify the behavior of the contact in various regimes of degeneracy for 1D bosons. We show that the contact exhibits a maximum versus temperature and that it is a signature of the crossover to fermionization in the strongly-interacting regime. Secondly, we study the localization and fractal properties of 1D ideal gases in shallow quasiperiodic potentials. The quasiperiodic system provides an appealing intermediate between long-range ordered and genuine disordered systems with unusual critical properties. While the tight-binding Aubry-Andre (AA) model has been widely studied, the shallow lattice case behaves differently. We determine the critical localization properties of the system, the critical potential, mobility edges and critical exponents which are universal. Moreover, we calculate the fractal dimension of the energy spectrum and find it is nonuniversal but always smaller than unity, which shows the spectrum is nowhere dense. Finally, we move to the study of the interacting case. With the quantum Monte Carlo calculations, we compute the phase diagram of Lieb-Liniger bosons in shallow quasiperiodic potentials. A Bose glass, surrounded by superfluid and Mott phases, is found. At finite temperature, we show that the melting of the Mott lobes is characteristic of a fractal structure and find that the Bose glass is robust against thermal fluctuations up to temperatures accessible in experiments.

Correlation spreading in quantum lattice models with variable-range interactions


Ph-D thesis; December 17, 2019

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Abstract (click on text): In this thesis, we have investigated the spreading of quantum correlations in isolated lattice models with short- or long-range interactions driven far from equilibrium via sudden global quenches. A main motivation for this research topic was to shed new light on the conflicting results in the literature concerning the scaling law of the correlation edge, its lack of universality and the incompleteness of the existing physical pictures to fully characterize the propagation of quantum correlations. To do so, we have presented a general theoretical approach relying on a quasi-particle theory. The latter has permitted to unveil a generic expression for the equal-time connected correlation functions valid both for short-range and long-range interacting particle and spin lattice models on a hypercubic lattice. Relying on stationary phase arguments, we have shown that its causality cone displays a universal twofold structure consisting of a correlation edge and a series of local extrema defining the outer and inner structures of the space-time correlations. For short-range interactions, the motion of each structure is ballistic and the associated spreading velocities are related to the group and phase velocites of the quasi-particle dispersion relation of the post-quench Hamiltonian. For long-range interactions,the correlation spreading is substantially different due to a possible divergence of group velocity when tuning the interaction range. For a divergent group velocity, ie. the quasi-local regime, we have presented evidence of a universal algebraic structure for the causality cone. While, the correlation edge motion has been found to be always slower than ballistic, the local extrema propagate faster than ballistically and ballistically for gapless and gapped quantum systems respectively. For the local regime implying a well-defined group velocity, we have recovered similar scaling laws and spreading velocities than the short-range case for the causality cone of correlations. The previous theoretical predictions have been verified numerically using tensor network techniques within the case study of the short-range Bose-Hubbard chain and the long-range S= 1/2 XY and transverse Ising chains.

Conductance and expansion of a quantum wave in a one-dimensional guide : Effect of a force


Ph-D thesis; November 7, 2017

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Abstract (click on text): Dans un milieu désordonné, une onde peut être localisée exponentiellement par des effets d'interférence. Ce phénomène de localisation d'Anderson conduit notamment à une annulation de la conductance d'un fluide quantique unidimensionnel. Des travaux théoriques ont cependant montré que l'application d'un champ électrique pouvait réduire, voire supprimer, cette localisation. Nous étudions ici l'effet d'une force sur la localisation d'une onde quantique de matière dans un système unidimensionnel. En lien direct avec les expériences d'atomes ultrafroids, qui permettent d'observer la localisation d'Anderson d'un paquet d'onde en étalement, ou bien l'effet du désordre sur le transport entre deux réservoirs, nous nous intéressons à deux systèmes : la diffusion et la transmission d'une particule. Afin d'étudier la transmission à travers un guide, nous étendons un formalisme de matrices de transfert à la présence d'une force, éventuellement inhomogène. Deux approches analytiques complémentaires nous permettent d'étendre les résultats au cas d'un désordre de tavelures tel que celui utilisé dans les expériences d'atomes ultrafroids. Nous montrons que la force peut être entièrement prise en compte à l'aide d'une renormalisation de la longueur du guide par un libre parcours moyen local de la particule. Pour un désordre blanc, la force conduit alors une localisation plus faible, algébrique, tandis qu'une délocalisation apparaît pour un désordre corrélé. Nous nous intéressons ensuite à la diffusion d'une particule, à l'aide d'une approche numérique. Nous mettons en évidence une délocalisation de la position à grande force sous la forme d'une croissance temporelle algébrique, dont l'exposant augmente avec la force. Nous montrons de plus que la localisation est systématiquement détruite dans un désordre corrélé.

Out-of-equilibrium and locality in long-range interacting many-body quantum systems


Ph-D thesis; December 2nd, 2016

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Abstract (click on text): In this thesis we present our results on the propagation of correlations in long-range interacting quantum systems. The dynamics of local observables in these systems cannot be described with the standard methods used in equilibrium statistical physics and completely new methods have to be developed. Several bounds on the time evolution of correlations have been derived for these systems. However the propagation found in experimental and numerical results is completely different and several regimes are present depending on the long-range character of the interactions. Here we present analytical expressions to describe the time evolution of generic observables in systems where the Hamiltonian takes a quadratic form with long- and short-range interactions. These expressions describe the spreading of local observables as the spreading of the fundamental excitations of the system. We apply these expressions to a spin model finding three different propagation regimes. They can be described qualitatively et quantitatively by the divergences in the energy spectrum. The most important result is that the propagation is at most ballistic, but it can be also significantly slower, where the general bounds predict a propagation faster than ballistic. This points out that the bounds are not able to describe properly the propagation, but a more specific approach is needed. We then move to a system of lattice bosons interacting via long-range interactions. In this case we study two different observables finding completely different results for the same interactions: the spreading of two-body correlations is always ballistic while the one of the one-body correlations ranges from faster-than-ballistic to ballistic. Using our general analytic expressions we find that different parts of the spectrum contribute differently to different observables determining the previous differences. This points out that an observable-dependent notion of locality, missing in the general bounds, have to be developed to correctly describe the time evolution.

Collective localization transitions in interacting disordered and quasiperiodic Bose superfluids


Ph-D thesis; December 12th, 2014

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Abstract (click on text): In this thesis, we theoretically investigate the collective localization properties of weakly-Interacting Bose superfluids subjected to disordered or quasiperiodic potentials. While disorder has been recognized since Anderson to induce single-Particle localization, the interplay between disorder and interactions in quantum systems is today among the most challenging questions in the field, and underlies fascinating phase transitions and non-Trivial localization effetcs. Focusing on Bose gases in the weakly-Interacting regime for which the Bogoliubov theory proves a successful tool, we study the localization transitions of collective excitations in several contexts. First, in the case of a continuous true disorder, we develop a strong-Disorder formalism going beyond previous studies, providing us with a complete description of the localization behaviour of collective excitations in arbitrary dimension. A generic localization diagram is obtained and the transport of excitations in the disorder is microscopically interpreted. Secondly, we consider the case of one-Dimensional quasiperiodic potentials, which are known to display intermediate properties between periodic and disordered ones. We perform a numerical and analytical treatment of the localization problem of collective excitations, allowing us to quantitatively characterize and interpret the localization transition in terms of an effective multiharmonic problem. Finally, we set up the general inhomogeneous formalism to address such issues in multicomponent Bose gases, and enlighten the basic physic of such systems, which are known to exhibit their own specific features.

Anderson localization of matter waves in correlated disorder: From 1D to 3D


Ph-D thesis; December 18th, 2012

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Abstract (click on text): In this thesis we investigate quantum transport and Anderson localization of non- interacting matterwaves in anisotropic disorder. Using microscopic approaches, we study the effect of disorder correlations, which are shown to significantly modify quantum transport properties in 1D, 2D and 3D. We develop general theoretical tools and apply them to particular models of continuous disorder, which are relevant to ultracold atom experiments : speckle potentials. First, in the one-dimensional case we extend previous models for the localization process of ultracold atoms expanding in a standard speckle potential and show that taking into account new ingredients could permit to understand deviations between experiments and theory observed previously. We then study quantum transport and Anderson localization in dimensions higher than one, with special emphasis on anisotropic correlations, which are naturally present in most speckle potentials. We compute quantum transport properties and propose a new method to estimate the 3D localization threshold (mobility edge). Our theoretical findings are compared with the results of two recent experiments which report evidence of 3D localization of matterwaves. Eventually, we further study effects of disorder correlations, which can induce inversion of localization anisotropies and enhancement of Anderson localization with the particle energy, when appropriately tailored.

Disordered, ultracold quantum gases: Theoretical studies and experimental perspectives


Habilitation; February 3rd, 2011

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Abstract (click on text): Disorder plays a fundamental role in many fields of physics such as condensed-matter physics, optics, acoustics, or atomic physics. It is responsible for a number of surprizing effects, such as Anderson localization, metal-insulator transitions and intriguing glass phases. The inherent complexity of disordered systems poses outstanding challenges to the full understanding of these phenomena. In the last years, disorder has emerged as a major line of research in the field of ultracold quantum gases. The latter offer fascinating perspectives to better understand the effects of disorder in quantum systems, thanks not only to an unprecedented control of parameters, but also to their original properties. This Habilitation thesis reviews our recent contributions to the theory of disordered quantum gases along three main lines: - Anderson localization in disordered quantum gases; - Disorder in interacting Bose gases; - Simulating extended Hubbard and spin models with ultracold gases. On the one hand, we propose and analyze experiments aiming at realizing quantum simulators to address open questions of fundamental importance for the field of disordered systems. In this respect, we show that quantum gases offer promising perspectives. On the other hand, we lead prospective works, which in particular show that quantum gases have original properties. They hence shed new light on issues of broad interest in the field of disordered systems.

Ultracold Bose gases in random potentials: collective excitations and localization effects

Pierre LUGAN

Ph-D thesis; January 25th, 2010

| on-line version (tel-00468888)
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Abstract (click on text): In this thesis, we theoretically investigate the localization properties of weakly-interacting Bose gases in the presence of one-dimensional disorder. We focus on three aspects of those disordered systems. First, we study the case of a non-interacting gas. According to general results, all single-particle states are localized in one dimension. We show that for certain classes of correlated disorder, the dependence of the localization length of the atoms on their energy undergoes sharp crossovers for weak disorder. These findings allow for the interpretation of recent experiments beyond previous analyses. Then, we examine the ground state of an interacting gas, and establish a diagram of the quantum states as a function of the strength of disorder and interactions. We analyze the density modulations imposed on the gas by the disorder, in order to describe the crossover from the regime of delocalized Bose-Einstein condensate to the regime of fragmented condensate. For the regime of very weak interactions, we develop a microscopic description of the system on the basis of the eigenstates of the single-particle Hamiltonian. These results contribute to characterizing the Bose-glass phase at weak interactions, which has yet to be explored thoroughly. Finally, we study the localization of the elementary excitations of the Bose gas in the (quasi-) condensate regime. We show that the suppressed localization of the excitations of lowest energy is due to an efficient screening by the (quasi-) condensate of the long-wavelength variations of the external potential.