arXiv subjects

Laurent Sanchez-Palencia

Publications and source records attributed to Laurent Sanchez-Palencia.

At least 37 records · Page 2Linked to original sources

arXiv2019

Quantum simulation of the Hubbard model with ultracold fermions in optical lattices

Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly-correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi-Hubbard model with ultracold atoms. After introducing the Fermi-Hubbard model in the context of condensed matter, its implementation in ultracold atom systems, and its phase diagram, we review landmark experimental achievements, from the early observation of the onset of quantum degeneracy and superfluidity to demonstration of the Mott insulator regime and the emergence of long-range anti-ferromagnetic order. We conclude by discussing future challenges, including the possible observation of high-Tc superconductivity, transport properties, and the interplay of strong correlations and disorder or topology.

cond-mat.quant-gas↗

arXiv2018

Quantum simulation: From basic principles to applications

Envisioned by Richard Feynman in the early 1980s, quantum simulation has received dramatic impetus thanks to the development of a variety of plateforms able to emulate a wide class of quantum Hamiltonians. During the past decade, most of the quantum simulators have implemented rather well-known models, hence permitting a direct comparison with theoretical calculations and a precise benchmarking of their reliability. The field has now reached a maturity such that one can address difficult problems, which cannot be solved efficiently using classical algorithms. These advances provide unprecedented opportunities to explore previously unreachable fields, test theoretical predictions, and inspire novel approaches. This contribution is an introduction to quantum simulation. It is published as a forward to the special issue on Quantum Simulation of the Comptes-Rendus de Physique of the French Academy of Sciences.

cond-mat.quant-gas↗

arXiv2018

Tan's Contact for Trapped Lieb-Liniger Bosons at Finite Temperature

The universal Tan relations connect a variety of microscopic features of many-body quantum systems with two-body contact interactions to a single quantity, called the contact. The latter has become pivotal in the description of quantum gases.We provide a complete characterization of the Tan contact of the harmonically trapped Lieb-Liniger gas for arbitrary interactions and temperature.Combining thermal Bethe ansatz, local-density approximation, and exact quantum Monte Carlo calculations,we show that the contact is a universal function of only two scaling parameters, and determine the scaling function.We find that the temperature dependence of the contact, or equivalently the interaction dependence of the entropy, displays a maximum. The presence of this maximum provides an unequivocal signature of the crossover to the fermionized regime and it is accessible in current experiments.

cond-mat.quant-gas↗

arXiv2018

Universal Scaling Laws for Correlation Spreading in Quantum Systems with Short- and Long-Range Interactions

We study the spreading of information in a wide class of quantum systems, with variable-range interactions. We show that, after a quench, it generally features a double structure, whose scaling laws are related to a set of universal microscopic exponents that we determine. When the system supports excitations with a finite maximum velocity, the spreading shows a twofold ballistic behavior. While the correlation edge spreads with a velocity equal to twice the maximum group velocity, the dominant correlation maxima propagate with a different velocity that we derive. When the maximum group velocity diverges, as realizable with long-range interactions, the correlation edge features a slower-than-ballistic motion. The motion of the maxima is, instead, either faster-than-ballistic, for gapless systems, or ballistic, for gapped systems. The phenomenology that we unveil here provides a unified framework, which encompasses existing experimental observations with ultracold atoms and ions. It also paves the way to simple extensions of those experiments to observe the structures we describe in their full generality.

cond-mat.stat-mech↗

arXiv2017

Unitary dynamics of strongly-interacting Bose gases with time-dependent variational Monte Carlo in continuous space

We introduce time-dependent variational Monte Carlo for continuous-space Bose gases. Our approach is based on the systematic expansion of the many-body wave-function in terms of multi-body correlations and is essentially exact up to adaptive truncation. The method is benchmarked by comparison to exact Bethe-ansatz or existing numerical results for the integrable Lieb-Liniger model. We first show that the many-body wave-function achieves high precision for ground-state properties, including energy and first-order as well as second-order correlation functions. Then, we study the out-of-equilibrium, unitary dynamics induced by a quantum quench in the interaction strength. Our time-dependent variational Monte Carlo results are benchmarked by comparison to exact Bethe ansatz results available for a small number of particles, and also compared to quench action results available for non-interacting initial states. Moreover, our approach allows us to study large particle numbers and general quench protocols, previously inaccessible beyond the mean-field level. Our results suggest that it is possible to find correlated initial states for which the long-term dynamics of local density fluctuations is close to the predictions of a simple Boltzmann ensemble.

cond-mat.quant-gas↗

arXiv2017

Effect of a bias field on disordered waveguides: Universal scaling of conductance and application to ultracold atoms

We study the transmission of a disordered waveguide subjected to a finite bias field. The statisticaldistribution of transmission is analytically shown to take a universal form. It depends on a singleparameter, the system length expressed in a rescaled metrics, which encapsulates all the microscopicfeatures of the medium and the bias field. Excellent agreement with numerics is found for variousmodels of disorder and bias field. For white-noise disorder and a linear bias field, we demonstratethe algebraic nature of the decay of the transmission with distance, irrespective of the value ofthe bias field. It contrasts with the expansion of a wave packet, which features a delocalizationtransition for large bias field. The difference is attributed to the different boundary conditionsfor the transmission and expansion schemes. The observability of these effects in conductancemeasurements for electrons or ultracold atoms is discussed, taking into account key features, suchas finite-range disorder correlations, nonlinear bias fields, and finite temperatures.

cond-mat.quant-gas↗

arXiv2016

Spreading of correlations in exactly-solvable quantum models with long-range interactions in arbitrary dimensions

We study the out-of-equilibrium dynamics induced by quantum quenches in quadratic Hamiltonians featuring both short- and long-range interactions. The spreading of correlations in the presence of algebraic decaying interactions, $1/R^α$, is studied for lattice Bose models in arbitrary dimension $D$. These models are exactly solvable and provide useful insight in the universal description of more complex systems as well as comparisons to the known universal upper bounds for the spreading of correlations. Using analytical calculations of the dominant terms and full numerical integration of all quasi-particle contributions, we identify three distinct dynamical regimes. For strong decay of nteractions, $α>D+1$, we find a causal regime, qualitatively similar to what previously found for short-range interactions. This regime is characterized by ballistic (linear cone) spreading of the correlations with a cone velocity equal to twice the maximum group velocity of the quasi-particles. For weak decay of interactions, $α<D$, we find instantaneous activation of correlations at arbitrary distance. This signals the breaking of causality, which can be associated with the divergence of the quasi-particle energy spectrum. Finite-size scaling of the activation time precisely confirms this interpretation. For intermediate decay of interactions, $D<α<D+1$, we find a sub-ballistic, algebraic (bent cone) spreading and determine the corresponding exponent as a function of $α$. These outcomes generalize existing results for one-dimensional systems to arbitrary dimension. We precisely relate the three regimes to the first- and second-order divergences of the quasi-particle energy spectrum for any dimension.

cond-mat.stat-mech↗

arXiv2015

Protected quasi-locality in quantum systems with long-range interactions

We study the out-of-equilibrium dynamics of quantum systems with long-range interactions. Two different models describing, respectively, interacting lattice bosons and spins are considered. Our study relies on a combined approach based on accurate many-body numerical calculations as well as on a quasiparticle microscopic theory. For sufficiently fast decaying long-range potentials, we find that the quantum speed limit set by the long-range Lieb-Robinson bounds is never attained and a purely ballistic behavior is found. For slowly decaying potentials, a radically different scenario is observed. In the bosonic case, a remarkable local spreading of correlations is still observed, despite the existence of infinitely fast traveling excitations in the system. This is in marked contrast to the spin case, where locality is broken. We finally provide a microscopic justification of the different regimes observed and of the origin of the protected locality in the bosonic model.

cond-mat.quant-gas↗

arXiv2015

Propagation of collective pair excitations in disordered Bose superfluids

We study the effect of disorder on the propagation of collective excitations in a disordered Bose superfluid. We incorporate local density depletion induced by strong disorder at the meanfield level, and formulate the transport of the excitations in terms of a screened scattering problem. We show that the competition of disorder, screening, and density depletion induces a strongly non-monotonic energy dependence of the disorder parameter. In three dimensions, it results in a rich localization diagram with four different classes of mobility spectra, characterized by either no or up to three mobility edges. Implications on experiments with disordered ultracold atoms are discussed.

cond-mat.quant-gas↗

arXiv2015

Anderson Localization of Matter Waves in 3D Anisotropic Disordered Potentials

Using a cutoff-free formulation of the coherent transport theory, we show that the interference terms at the origin of localization strongly affect the transport anisotropy. In contrast to the common hypothesis, we then find that the anisotropies of incoherent and coherent diffusion are significantly different, in particular at criticality. There, we show that the coherent transport anisotropy is mainly determined by the properties of the disorder-averaged effective scattering medium while the incoherent transport contributions become irrelevant.

cond-mat.dis-nn↗

arXiv2015

Localization transition in weakly-interacting Bose superfluids in one-dimensional quasiperdiodic lattices

We study the localization of collective pair excitations in weakly-interacting Bose superfluids in one-dimensional quasiperiodic lattices. The localization diagram is first determined numerically. For intermediate interaction and quasiperiodic amplitude we find a sharp localization transition, with extended low-energy states and localized high-energy states. We then develop an analytical treatment, which allows us to quantitatively map the localization transition into that of an effective multiharmonic quasiperiodic system.

cond-mat.quant-gas↗

arXiv2014

Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids

We study the spreading of density-density correlations in Bose-Hubbard models after a quench of the interaction strength, using time-dependent variational Monte Carlo simulations. It gives access to unprecedented long propagation times and to dimensions higher than one. In both one and two dimensions, we find ballistic light-cone spreading of correlations and extract accurate values of the light-cone velocity in the superfluid regime. We show that the spreading of correlations is generally supersonic, with a light-cone propagating faster than sound modes but slower than the maximum group velocity of density excitations, except at the Mott transition, where all the characteristic velocities are equal. Further, we show that in two dimensions the correlation spreading is highly anisotropic and presents nontrivial interference effects.

cond-mat.quant-gas↗

arXiv2014

Two-component Bose gases with one-body and two-body couplings

We study the competition between one-body and two-body couplings in weakly-interacting two-component Bose gases, in particular as regards field correlations. We derive the meanfield theory for both ground state and low-energy pair excitations in the general case where both one-body and two-body couplings are position-dependent and the fluid is subjected to a state-dependent trapping potential. General formulas for phase and density correlations are also derived. Focusing on the case of homogeneous systems, we discuss the pair-excitation spectrum and the corresponding excitation modes, and use them to calculate correlation functions, including both quantum and thermal fluctuation terms. We show that the relative phase of the two components is imposed by that of the one-body coupling, while its fluctuations are determined by the modulus of the one-body coupling and by the two-body coupling. One-body coupling and repulsive two-body coupling cooperate to suppress relative-phase fluctuations, while attractive two-body coupling tends to enhance them. Further applications of the formalism presented here and extensions of our work are also discussed.

cond-mat.quant-gas↗

arXiv2013

Universal Superfluid Transition and Transport Properties of Two-Dimensional Dirty Bosons

We study the phase diagram of two-dimensional, interacting bosons in the presence of a correlated disorder in continuous space, using large-scale finite temperature quantum Monte Carlo simulations. We show that the superfluid transition is strongly protected against disorder. It remains of the Berezinskii-Kosterlitz-Thouless type up to disorder strengths comparable to the chemical potential. Moreover, we study the transport properties in the strong disorder regime where a zero-temperature Bose-glass phase is expected. We show that the conductance exhibits a thermally activated behavior vanishing only at zero temperature. Our results point towards the existence of Bose bad-metal phase as a precursor of the Bose-glass phase.

cond-mat.quant-gas↗

arXiv2013

Quantum transport of atomic matterwaves in anisotropic 2D and 3D disorder

The macroscopic transport properties in a disordered potential, namely diffusion and weak/strong localization, closely depend on the microscopic and statistical properties of the disorder itself. This dependence is rich of counter-intuitive consequences. It can be particularly exploited in matter wave experiments, where the disordered potential can be tailored and controlled, and anisotropies are naturally present. In this work, we apply a perturbative microscopic transport theory and the self-consistent theory of Anderson localization to study the transport properties of ultracold atoms in anisotropic 2D and 3D speckle potentials. In particular, we discuss the anisotropy of single-scattering, diffusion and localization. We also calculate a disorder-induced shift of the energy states and propose a method to include it, which amounts to renormalize energies in the standard on-shell approximation. We show that the renormalization of energies strongly affects the prediction for the 3D localization threshold (mobility edge). We illustrate the theoretical findings with examples which are revelant for current matter wave experiments, where the disorder is created with a laser speckle. This paper provides a guideline for future experiments aiming at the precise location of the 3D mobility edge and study of anisotropic diffusion and localization effects in 2D and 3D.

cond-mat.dis-nn↗

arXiv2013

Tailoring Anderson localization by disorder correlations in 1D speckle potentials

We study Anderson localization of single particles in continuous, correlated, one-dimensional disordered potentials. We show that tailored correlations can completely change the energy-dependence of the localization length. By considering two suitable models of disorder, we explicitly show that disorder correlations can lead to a nonmonotonic behavior of the localization length versus energy. Numerical calculations performed within the transfer-matrix approach and analytical calculations performed within the phase formalism up to order three show excellent agreement and demonstrate the effect. We finally show how the nonmonotonic behavior of the localization length with energy can be observed using expanding ultracold-atom gases.

cond-mat.dis-nn↗

arXiv2012

Matter Wave Transport and Anderson Localization in Anisotropic 3D Disorder

We study quantum transport in anisotropic 3D disorder and show that non rotation invariant correlations can induce rich diffusion and localization properties. For instance, structured finite-range correlations can lead to the inversion of the transport anisotropy. Moreover, working beyond the self-consistent theory of localization, we include the disorder-induced shift of the energy states and show that it strongly affects the mobility edge. Implications to recent experiments are discussed.

cond-mat.dis-nn↗

arXiv2012

Anderson localization of matter waves in tailored disordered potentials

We show that, in contrast to immediate intuition, Anderson localization of noninteracting particles induced by a disordered potential in free space can increase (i.e., the localization length can decrease) when the particle energy increases, for appropriately tailored disorder correlations. We predict the effect in one, two, and three dimensions, and propose a simple method to observe it using ultracold atoms placed in optical disorder. The increase of localization with the particle energy can serve to discriminate quantum versus classical localization.

cond-mat.quant-gas↗