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Enhanced Friedel oscillations in attractively interacting 1D Fermi gases

J. R. McKenney, C. R. Shill, William J. Porter, Joaquín E. Drut

Published Oct 28, 2015• 0 citations
OpenAlex

Abstract

Many-fermion systems bound by hard walls display non-trivial density profiles characterized by so-called Friedel oscillations. In non-interacting systems, the characteristic scale of the oscillations is $2 k^{}_F$, where $k^{}_F$ is the Fermi momentum, while repulsive interactions tend to generate Wigner-crystal oscillations at $4 k^{}_F$. We take a closer look at interacting systems in the presence of strong pairing correlations, such as those realized experimentally with ultracold atoms. We use ab initio lattice Monte Carlo methods to study the density profiles of few- to many-fermion systems in 1D, in the presence of hard-wall boundary conditions and attractive interactions. Additionally, we compute the ground-state energy and the momentum distribution.

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Many-fermion systems bound by hard walls display non-trivial density profiles characterized by so-called Friedel oscillations. In non-interacting systems, the characteristic scale of the oscillations is 2kF2 k^{}_F2kF​, where kFk^{}_FkF​ is the Fermi momentum, while repulsive interactions tend to generate Wigner-crystal oscillations at 4kF4 k^{}_F4kF​. We take a closer look at interacting systems in the presence of strong pairing correlations, such as those realized experimentally with ultracold atoms. We use ab initio lattice Monte Carlo methods to study the density profiles of few- to many-fermion systems in 1D, in the presence of hard-wall boundary conditions and attractive interactions. Additionally, we compute the ground-state energy and the momentum distribution.
Motivated by the realization of hard-wall boundary conditions in experiments with ultracold atoms, we investigate the ground-state properties of spin-1/2 fermions with attractive interactions in a one-dimensional box.We use lattice Monte Carlo methods to determine essential quantities like the energy, which we compute as a function of coupling strength and particle number in the regime from few to many particles.Many-fermion systems bound by hard walls display non-trivial density profiles characterized by so-called Friedel oscillations (which are similar to those observed in harmonic traps).In non-interacting systems, the characteristic length scale of the oscillations is set by (2k F ) -1 , where k F is the Fermi momentum, while repulsive interactions tend to generate Wignercrystal oscillations of period (4k F ) -1 .Based on the non-interacting result, we find a remarkably simple parametrization of the density profiles of the attractively interacting case, which we generalize to the one-body density matrix.While the total momentum is not a conserved quantity in the presence of hard walls, the magnitude of the momentum does provide a good quantum number.We are therefore able to provide a detailed characterization of the (quasi-)momentum distribution, which displays rather robust discontinuity at the Fermi surface.In addition, we determine the spatially varying on-site density-density correlation, which in turn yields Tan's contact density and, upon integration, Tan's contact.As is well known, the latter fully determines the short-range correlations and plays a crucial role in a multitude of equilibrium and non-equilibrium sum rules.
Abstract Motivated by the realization of hard-wall boundary conditions in experiments with ultracold atoms, we investigate the ground-state properties of spin-1/2 fermions with attractive interactions in a one-dimensional box. We use lattice Monte Carlo methods to determine essential quantities like the energy, which we compute as a function of coupling strength and particle number in the regime from few to many particles. Many-fermion systems bound by hard walls display non-trivial density profiles characterized by so-called Friedel oscillations (which are similar to those observed in harmonic traps). In non-interacting systems, the characteristic length scale of the oscillations is set by ( 2 k F ) − 1 , where k F is the Fermi momentum, while repulsive interactions tend to generate Wigner-crystal oscillations of period ( 4 k F ) − 1 . Based on the non-interacting result, we find a remarkably simple parametrization of the density profiles of the attractively interacting case, which we generalize to the one-body density matrix. While the total momentum is not a conserved quantity in the presence of hard walls, the magnitude of the momentum does provide a good quantum number. We are therefore able to provide a detailed characterization of the (quasi-)momentum distribution, which displays rather robust discontinuity at the Fermi surface. In addition, we determine the spatially varying on-site density–density correlation, which in turn yields Tan’s contact density and, upon integration, Tan’s contact. As is well known, the latter fully determines the short-range correlations and plays a crucial role in a multitude of equilibrium and non-equilibrium sum rules.
A model of interacting one-dimensional fermions confined to a harmonic trap is proposed. The model is treated analytically to all orders of the coupling constant by a method analogous to that used for the Luttinger model. As a first application, the particle density is evaluated and the behavior of Friedel oscillations under the influence of interactions is studied. It is found that attractive interactions tend to suppress the Friedel oscillations, while strong repulsive interactions enhance the Friedel oscillations significantly. The momentum distribution function and the relation of the model interaction to realistic pair interactions are also discussed.
This work examines a mobile impurity interacting with a bath of a few spin- ↑ and spin- ↓ fermions in a small one-dimensional open lattice system. We study ground-state properties using the exact diagonalization method, where the system is modeled by a three-component Fermi Hubbard Hamiltonian. We find that in addition to the standard phase separation between a strongly repulsive impurity and the bath, a strongly attractive impurity also phase separates with the fermionic holes due to the particle-hole symmetry. Furthermore, we find that the impurity can show an oscillatory pattern in its density for intermediate attractive and repulsive bath-impurity interactions, which are induced by Friedel oscillations in the finite-size fermionic bath. This rich behavior of the impurity could be probed with fermionic ultracold mixtures in optical lattices.
Understanding the effect of correlations in interacting many-body systems is one of the main challenges in quantum mechanics. While the general problem can only be addressed by approximate methods and numerical simulations, in some limiting cases, it is amenable to exact solutions. I will present a family of exact solutions for strongly interacting 1D quantum gases in arbitrary external potential, valid for bosons, multicomponent fermions and mixtures. It allows us to obtain experimental observables such as the density profiles and momentum distribution at all momentum scales, beyond the Luttinger liquid approach. It also predicts the exact quantum dynamics at all the times, including the small oscillation regime yielding the collective modes of the system and the large quench regime where the system parameters are changed considerably. The solution can be extended to describe finite-temperature conditions, spin, and magnetization effects. In particular I will present large-size calculations of the frequency- and momentum-resolved spectral function of strongly repulsive lattice bosons and a symmetry-breaking exact solution for a Bose-Bose mixture. Our approach directly describes the experiments with trapped ultracold atoms where the strongly correlated regime in one dimension has been achieved.
Using exact continuous quantum Monte Carlo techniques, we study the zero- and finite-temperature properties of a system of harmonically trapped one-dimensional spin-12\frac{1}{2}21​ fermions with short-range interactions. Motivated by experimental searches for modulated Fulde-Ferrel-Larkin-Ovchinikov states, we systematically examine the impact of a spin imbalance on the density profiles. We quantify the accuracy of the Thomas-Fermi approximation, finding that for sufficiently large particle numbers $(N\ensuremath{\gtrsim}100)$ it quantitatively reproduces most features of the exact density profile. The Thomas-Fermi approximation fails to capture small Friedel-like spin and density oscillations and overestimates the size of the fully paired region in the outer shell of the trap. Based on our results, we suggest a range of experimentally tunable parameters to maximize the visibility of the double-shell structure of the system and the Fulde-Ferrel-Larkin-Ovchinikov state in the one-dimensional harmonic trap. Furthermore, we analyze the fingerprints of the attractive contact interactions in the features of the momentum and pair momentum distributions.