arXiv subjects

B. Grémaud

Publications and source records attributed to B. Grémaud.

27 records · Page 2Linked to original sources

arXiv2014

Coherent forward scattering in 2D disordered systems

We present a detailed numerical and theoretical analysis of the recently discovered phenomenon of coherent forward scattering. This effect manifests itself as a macroscopic interference peak in the forward direction of the momentum distribution of a matter wave launched with finite velocity in a random potential. Focusing on the two-dimensional case, we show that coherent forward scattering generally arises due the confinement of the wave in a finite region of space, and explain under which conditions it can be seen as a genuine signature of Anderson localization.

cond-mat.dis-nn↗

arXiv2014

Superconducting Transitions in Flat Band Systems

The physics of strongly correlated quantum particles within a flat band was originally explored as a route to itinerant ferromagnetism and, indeed, a celebrated theorem by Lieb rigorously establishes that the ground state of the repulsive Hubbard model on a bipartite lattice with unequal number of sites in each sublattice must have nonzero spin S at half-filling. Recently, there has been interest in Lieb geometries due to the possibility of novel topological insulator, nematic, and Bose-Einstein condensed (BEC) phases. In this paper, we extend the understanding of the attractive Hubbard model on the Lieb lattice by using Determinant Quantum Monte Carlo to study real space charge and pair correlation functions not addressed by the Lieb theorems.

cond-mat.str-el↗

arXiv2014

Competing phases, phase separation and co-existence in the extended one-dimensional bosonic Hubbard model

We study the phase diagram of the one-dimensional bosonic Hubbard model with contact ($U$) and near neighbor ($V$) interactions focusing on the gapped Haldane insulating (HI) phase which is characterized by an exotic nonlocal order parameter. The parameter regime ($U$, $V$ and $μ$) where this phase exists and how it competes with other phases such as the supersolid (SS) phase, is incompletely understood. We use the Stochastic Green Function quantum Monte Carlo algorithm as well as the density matrix renormalization group to map out the phase diagram. Our main conclusions are that the HI exists only at $ρ=1$, the SS phase exists for a very wide range of parameters (including commensurate fillings) and displays power law decay in the one body Green function. In addition, we show that at fixed integer density, the system exhibits phase separation in the $(U,V)$ plane.

cond-mat.quant-gas↗

arXiv2013

Competing Supersolid and Haldane Insulator phases in the extended one-dimensional bosonic Hubbard model

The Haldane Insulator is a gapped phase characterized by an exotic non-local order parameter. The parameter regimes at which it might exist, and how it competes with alternate types of order, such as supersolid order, are still incompletely understood. Using the Stochastic Green Function (SGF) quantum Monte Carlo (QMC) and the Density Matrix Renormalization Group (DMRG), we study numerically the ground state phase diagram of the one-dimensional bosonic Hubbard model (BHM) with contact and near neighbor repulsive interactions. We show that, depending on the ratio of the near neighbor to contact interactions, this model exhibits charge density waves (CDW), superfluid (SF), supersolid (SS) and the recently identified Haldane insulating (HI) phases. We show that the HI exists only at the tip of the unit filling CDW lobe and that there is a stable SS phase over a very wide range of parameters.

cond-mat.quant-gas↗

arXiv2012

Coherent Forward Scattering Peak Induced by Anderson Localization

Numerical simulations show that, at the onset of Anderson localization, the momentum distribution of a coherent wave packet launched inside a random potential exhibits, in the forward direction, a novel interference peak that complements the coherent backscattering peak. An explanation of this phenomenon in terms of maximally crossed diagrams predicts that the signal emerges around the localization time and grows on the scale of the Heisenberg time associated with the localization volume. Together, coherent back and forward scattering provide evidence for the occurrence of Anderson localization.

cond-mat.quant-gas↗

arXiv2012

Pairing in a two-dimensional Fermi gas with population imbalance

Pairing in a population imbalanced Fermi system in a two-dimensional optical lattice is studied using Determinant Quantum Monte Carlo (DQMC) simulations and mean-field calculations. The approximation-free numerical results show a wide range of stability of the Fulde-Ferrell-Larkin-Ovshinnikov (FFLO) phase. Contrary to claims of fragility with increased dimensionality we find that this phase is stable across wide range of values for the polarization, temperature and interaction strength. Both homogeneous and harmonically trapped systems display pairing with finite center of mass momentum, with clear signatures either in momentum space or real space, which could be observed in cold atomic gases loaded in an optical lattice. We also use the harmonic level basis in the confined system and find that pairs can form between particles occupying different levels which can be seen as the analog of the finite center of mass momentum pairing in the translationally invariant case. Finally, we perform mean field calculations for the uniform and confined systems and show the results to be in good agreement with QMC. This leads to a simple picture of the different pairing mechanisms, depending on the filling and confining potential.

cond-mat.quant-gas↗

arXiv2011

Universality of the Anderson transition with the quasiperiodic kicked rotor

We report a numerical analysis of the Anderson transition in a quantum-chaotic system, the quasiperiodic kicked rotor with three incommensurate frequencies. It is shown that this dynamical system exhibits the same critical phenomena as the truly random 3D-Anderson model. By taking proper account of systematic corrections to one-parameter scaling, the universality of the critical exponent is demonstrated. Our result $ν= 1.59 \pm 0.01$ is in perfect agreement with the value found for the Anderson model.

cond-mat.dis-nn↗

arXiv2002

Quantum three body Coulomb problem in two dimensions

We study the three-body Coulomb problem in two dimensions and show how to calculate very accurately its quantum properties. The use of a convenient set of coordinates makes it possible to write the Schrödinger equation only using annihilation and creation operators of four harmonic oscillators, coupled by various terms of degree up to twelve. We analyse in details the discrete symmetry properties of the eigenstates. The energy levels and eigenstates of the two-dimensional helium atom are obtained numerically, by expanding the Schrödinger equation on a convenient basis set, that gives sparse banded matrices, and thus opens up the way to accurate and efficient calculations. We give some very accurate values of the energy levels of the first bound Rydberg series. Using the complex coordinate method, we are also able to calculate energies and widths of doubly excited states, i.e. resonances above the first ionization threshold. For the two-dimensional $H^{-}$ ion, only one bound state is found.

quant-ph↗

arXiv2000

Chaos assisted tunnelling with cold atoms

In the context of quantum chaos, both theory and numerical analysis predict large fluctuations of the tunnelling transition probabilities when irregular dynamics is present at the classical level. We consider here the non-dissipative quantum evolution of cold atoms trapped in a time-dependent modulated periodic potential generated by two laser beams. We give some precise guidelines for the observation of chaos assisted tunnelling between invariant phase space structures paired by time-reversal symmetry.

nlin.CD↗