arXiv subjects

Guillaume Lang

Publications and source records attributed to Guillaume Lang.

12 recordsLinked to original sources

arXiv2023

Hydrogenic Spin-Valley states of the Bromine donor in 2H-MoTe$_2$

In semiconductors, the identification of doping atomic elements allowing to encode a qubit within spin states is of intense interest for quantum technologies. In transition metal dichalcogenides semiconductors, the strong spin-orbit coupling produces locked spin-valley states with expected long coherence time. Here we study the substitutional Bromine Br\textsubscript{Te} dopant in 2H-MoTe$_2$. Electron spin resonance measurements show that this dopant carries a spin with long-lived nanoseconds coherence time. Using scanning tunneling spectroscopy, we find that the hydrogenic wavefunctions associated with the dopant levels have characteristics spatial modulations that result from their hybridization to the \textbf{Q}-valleys of the conduction band. From a Fourier analysis of the conductance maps, we find that the amplitude and phase of the Fourier components change with energy according to the different irreducible representations of the impurity-site point-group symmetry. These results demonstrate that a dopant can inherit the locked spin-valley properties of the semiconductor and so exhibit long spin-coherence time.

cond-mat.mes-hall↗

arXiv2020

Love--Lieb integral equations: applications, theory, approximations, and computation

This paper is concerned mainly with the deceptively simple integral equation \[ u(x) - \frac{1}π\int_{-1}^{1} \frac{α\, u(y)}{α^2+(x-y)^2} \, \rd y = 1, \quad -1 \leq x \leq 1, \] where $α$ is a real non-zero parameter and $u$ is the unknown function. This equation is classified as a Fredholm integral equation of the second kind with a continuous kernel. As such, it falls into a class of equations for which there is a well developed theory. The theory shows that there is exactly one continuous real solution $u$. Although this solution is not known in closed form, it can be computed numerically, using a variety of methods. All this would be a curiosity were it not for the fact that the integral equation arises in several contexts in classical and quantum physics. We review the literature on these applications, survey the main analytical and numerical tools available, and investigate methods for constructing approximate solutions. We also consider the same integral equation when the constant on the right-hand side is replaced by a given function.

math-ph↗

arXiv2019

Conjectures about the structure of strong- and weak-coupling expansions of a few ground-state observables in the Lieb-Liniger and Yang-Gaudin models

In this paper, we apply experimental number theory to two integrable quantum models in one dimension, the Lieb-Liniger Bose gas and the Yang-Gaudin Fermi gas with contact interactions. We identify patterns in weak- and strong-coupling series expansions of the ground-state energy, local correlation functions and pressure. Based on the most accurate data available in the literature, we make a few conjectures about their mathematical structure and extrapolate to higher orders.

cond-mat.quant-gas↗

arXiv2017

Correlations in low-dimensional quantum gases

Ultracold gases are a versatile platform to simulate condensed matter physics, as virtually any parameter is experimentally tunable. In particular, highly anisotropic traps allow the realization of low-dimensional systems, where the role of quantum fluctuations is enhanced. I investigate the paradigmatic model of a one-dimensional Bose gas with contact interactions, a.k.a the Lieb-Liniger model, using powerful analytical tools such as Bethe Ansatz, Conformal Field Theory and the Tomonaga-Luttinger liquid formalism, as well as the Bose-Fermi mapping. The effect of an additional harmonic trap in the longitudinal direction is studied within the Local Density Approximation. These methods allow to investigate with high accuracy its ground-state thermodynamics of the gas, its excitation spectra and correlation functions, from the k-body local correlations to the momentum distribution and the dynamical structure factor. These quantities characterize the coherence and superfluidity of the gas. In particular, I study the drag force exerted by a weak gaussian barrier stirred into the gas within linear response theory. Then, I investigate the appearance of a multimode structure obtained by releasing a transverse trapping, and the dimensional crossover in the limit of an infinite number of transverse modes.

cond-mat.quant-gas↗

arXiv2017

A connection between non-local one-body and local three-body correlations of the Lieb-Liniger model

We derive a connection between the fourth coefficient of the short-distance Taylor expansion of the one-body correlation function, and the local three-body correlation function of the Lieb-Liniger model of $δ$-interacting spinless bosons in one dimension. This connection, valid at arbitrary interaction strength, involves the fourth moment of the density of quasi-momenta. Generalizing recent conjectures, we propose approximate analytical expressions for the fourth coefficient covering the whole range of repulsive interactions, validated by comparison with accurate numerics. In particular, we find that the fourth coefficient changes sign at interaction strength $γ_c\simeq 3.816$, while the first three coefficients of the Taylor expansion of the one-body correlation function retain the same sign throughout the whole range of interaction strengths.

cond-mat.quant-gas↗

arXiv2017

Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution

We study the ground-state properties and excitation spectrum of the Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact interactions. We solve the Bethe-Ansatz equations in the thermodynamic limit by using an analytic method based on a series expansion on orthogonal polynomials developed in \cite{Ristivojevic} and push the expansion to an unprecedented order. By a careful analysis of the mathematical structure of the series expansion, we make a conjecture for the analytic exact result at zero temperature and show that the partially resummed expressions thereby obtained compete with accurate numerical calculations. This allows us to evaluate the density of quasi-momenta, the ground-state energy, the local two-body correlation function and Tan's contact. Then, we study the two branches of the excitation spectrum. Using a general analysis of their properties and symmetries, we obtain novel analytical expressions at arbitrary interaction strength which are found to be extremely accurate in a wide range of intermediate to strong interactions.

cond-mat.quant-gas↗

arXiv2017

Tan's contact of a harmonically trapped one-dimensional Bose gas: strong-coupling expansion and conjectural approach at arbitrary interactions

We study Tan's contact, i.e. the coefficient of the high-momentum tails of the momentum distribution at leading order, for an interacting one-dimensional Bose gas subjected to a harmonic confinement. Using a strong-coupling systematic expansion of the ground-state energy of the homogeneous system stemming from the Bethe-Ansatz solution, together with the local-density approximation, we obtain the strong-coupling expansion for Tan's contact of the harmonically trapped gas. Also, we use a very accurate conjecture for the ground-state energy of the homogeneous system to obtain an approximate expression for Tan's contact for arbitrary interaction strength, thus estimating the accuracy of the strong-coupling expansion. Our results are relevant for ongoing experiments with ultracold atomic gases.

cond-mat.quant-gas↗

arXiv2016

Dimensional crossover in a Fermi gas from one to effective six dimensions and a cross-dimensional Tomonaga-Luttinger model

We describe the dimensional crossover in a noninteracting Fermi gas in an anisotropic trap, obtained by populating various transverse modes of the trap. We study the dynamical structure factor and drag force. Starting from a dimension $d$, the $(\!d\!+\!1\!)$-dimensional case is obtained to a good approximation with relatively few modes. We show that the dynamical structure factor of a gas in a $d$-dimensional harmonic trap simulates an effective $2d$-dimensional box trap. We focus then on the experimentally relevant situation when only a portion of the gas in harmonic confinement is probed and give a condition to obtain the behavior of a $d$-dimensional gas in a box. Finally, we propose a generalized Tomonaga-Luttinger model for the multimode configuration and compare the dynamical structure factor in the 2D limit with the exact result, finding that it is accurate in the backscattering region and at low energy.

cond-mat.quant-gas↗

arXiv2015

Dynamic structure factor and drag force in a one-dimensional strongly-interacting Bose gas at finite temperature

We study the effect of thermal and quantum fluctuations on the dynamical response of a one-dimensional strongly-interacting Bose gas in a tight atomic waveguide. We combine the Luttinger liquid theory at arbitrary interactions and the exact Bose-Fermi mapping in the Tonks-Girardeau-impenetrable-boson limit to obtain the dynamic structure factor of the strongly-interacting fluid at finite temperature. Then, we determine the drag force felt by a potential barrier moving along the fluid in the experimentally realistic situation of finite barrier width and temperature.

cond-mat.quant-gas↗

arXiv2015

Thermodynamics of a spin-1 Bose gas with fixed magnetization

We investigate the thermodynamics of a spin-1 Bose gas with fixed magnetization including the quadratic Zeeman energy shift. Our calculations are based on the grand canonical description for the ideal gas and the classical fields approximation for atoms with ferromagnetic and antiferromagnetic interactions. We confirm the occurence of a double phase transition in the system that takes place due to two global constraints. We show analytically for the ideal gas how critical temperatures and condensed fractions are changed by a non-zero magnetic field. The interaction strongly affects the condensate scenario below the second critical temperature. The effect imposed by interaction energies becomes diminished in high magnetic fields where condensation, of both ferromagnetic and antiferromagnetic atoms, agree with the ideal gas results.

cond-mat.quant-gas↗

arXiv2012

Structural and electronic phase diagrams of CeFeAsO1-xFx and SmFeAsO1-xFx

We have studied the structural and electronic phase diagrams of CeFeAsO1-xFx and SmFeAsO1-xFx by a detailed analysis of muon spin relaxation experiments, synchrotron X-ray diffraction, Mössbauer spectroscopy, electrical resistivity, specific heat, and magnetic susceptibility measurements (Full abstract in the main document).

cond-mat.supr-con↗

arXiv2011

As-vacancies, local moments, and Pauli limiting in LaO_0.9F_0.1FeAs_(1-delta) superconductors

We report magnetization measurements of As-deficient LaO_0.9F_0.1FeAs_1-delta (delta about 0.06) samples with improved superconducting properties as compared with As-stoichiometric optimally doped La-1111 samples. In this As-deficient system with almost homogeneously distributed As-vacancies (AV), as suggested by the (75)As-nuclear quadrupole resonance (NQR) measurements,we observe a strong enhancement of the spin-susceptibility by a factor of 3-7. This observation is attributed to the presence of an electronically localized state around each AV, carrying a magnetic moment of about 3.2 mu_Bohr per AV or 0.8 mu_Bohr/Fe atom. From theoretical considerations we find that the formation of a local moment on neighboring iron sites of an AV sets in when the local Coulomb interaction exceeds a critical value of about 1.0 eV in the dilute limit. Its estimated value amounts to ~ 2.5 eV and implies an upper bound of ~ 2 eV for the Coulomb repulsion at Fe sites beyond the first neighbor-shell of an AV. Electronic correlations are thus moderate/weak in doped La-1111. The strongly enhanced spin susceptibility is responsible for the Pauli limiting behavior of the superconductivity that we observe in As-deficient LaO_0.9F_0.1FeAs_1-delta. In contrast, no Pauli limiting behavior is found for the optimally doped, As-stoichiometric LaO_0.9F_0.1FeAs superconductor in accord with its low spin susceptibility.

cond-mat.supr-con↗