Molecular branch of a small highly elongated Fermi gas with an impurity: Full three-dimensional versus effective one-dimensional description

Gharashi, Seyed Ebrahim; Yin, X. Y.; Blume, D.

doi:10.1103/physreva.89.023603

Cited by 7 publications

(6 citation statements)

References 33 publications

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“…For the molecular branch, it has been shown theoretically that the strictly one-dimensional energies for the system without tunneling agree quite well with the full three-dimensional energies provided the one-dimensional scattering length a 1D is larger than the harmonic oscillator length a ρ [32]. Correspondingly, we restrict our molecular branch calculations to this regime (i.e., the smallest a 1D considered in Sec.…”

Section: Two-body Hamiltonian and Simulation Of Two-particle Tunnelin...mentioning

confidence: 88%

Tunneling dynamics of two interacting one-dimensional particles

Gharashi¹,

Blume²

2015

Phys. Rev. A

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We present one-dimensional simulation results for the cold atom tunneling experiments by the Heidelberg group [G. Zürn et al., Phys. Rev. Lett. 108, 075303 (2012) and G. Zürn et al., Phys. Rev. Lett. 111, 175302 (2013)] on one or two 6 Li atoms confined by a potential that consists of an approximately harmonic optical trap plus a linear magnetic field gradient. At the non-interacting particle level, we find that the WKB (Wentzel-Kramers-Brillouin) approximation may not be used as a reliable tool to extract the trapping potential parameters from the experimentally measured tunneling data. We use our numerical calculations along with the experimental tunneling rates for the non-interacting system to reparameterize the trapping potential. The reparameterized trapping potentials serve as input for our simulations of two interacting particles. For two interacting (distinguishable) atoms on the upper branch, we reproduce the experimentally measured tunneling rates, which vary over several orders of magnitude, fairly well. For infinitely strong interaction strength, we compare the time dynamics with that of two identical fermions and discuss the implications of fermionization on the dynamics. For two attractively-interacting atoms on the molecular branch, we find that single-particle tunneling dominates for weakly-attractive interactions while pair tunneling dominates for strongly-attractive interactions. Our first set of calculations yields qualitative but not quantitative agreement with the experimentally measured tunneling rates. We obtain quantitative agreement with the experimentally measured tunneling rates if we allow for a weakened radial confinement.

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Section: Two-body Hamiltonian and Simulation Of Two-particle Tunnelin...mentioning

confidence: 88%

Tunneling dynamics of two interacting one-dimensional particles

Gharashi¹,

Blume²

2015

Phys. Rev. A

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“…Remarkably, also in the latter case strong correlations occur (again, consistent with quasi long-range order) for interaction strengths γ ≫ 1, where multiband effects are important. While previous theoretical studies on confined onedimensional fermions addressed the case of (typically small) harmonic traps [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65], in this Rapid Communication we considered a commensurate periodic potential, using sufficiently large system sizes to inspect the thermodynamic limit. On the one hand, this study provides new unbiased predictions for a paradigmatic model of strongly-correlated Fermi systems, which interpolates between Yang theory of the homogeneous Fermi gas and Lieb-Wu theory of the Hubbard model; on the other hand, it serves as a guide for possible new cold-atoms experiments aiming at observing antiferromagnetism beyond the tight-binding regime [30,66].…”

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confidence: 99%

One-dimensional repulsive Fermi gas in a tunable periodic potential

Pilati

Barbiero²,

Fazio

et al. 2017

Phys. Rev. A

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By using unbiased continuos-space quantum Monte Carlo simulations, we investigate the ground state properties of a one-dimensional repulsive Fermi gas subjected to a commensurate periodic optical lattice (OL) of arbitrary intensity. The equation of state and the magnetic structure factor are determined as a function of the interaction strength and of the OL intensity. In the weak OL limit, Yang's theory for the energy of a homogeneous Fermi gas is recovered. In the opposite limit (deep OL), we analyze the convergence to the Lieb-Wu theory for the Hubbard model, comparing two approaches to map the continuous-space to the discrete-lattice model: the first is based on (noninteracting) Wannier functions, the second effectively takes into account strong-interaction effects within a parabolic approximation of the OL wells. We find that strong antiferromagnetic correlations emerge in deep OLs, and also in very shallow OLs if the interaction strength approaches the TonksGirardeau limit. In deep OLs we find quantitative agreement with density matrix renormalization group calculations for the Hubbard model. The spatial decay of the antiferromagnetic correlations is consistent with quasi long-range order even in shallow OLs, in agreement with previous theories for the half-filled Hubbard model.Making unbiased predictions for the properties of strongly correlated Fermi systems is one of the major challenges in quantum physics research. One dimensional systems play a central role in this context since, on the one hand, correlations effects are more pronounced in low dimensions and, on the other hand, exact results have been derived in a few relevant cases [1]. Two such cases are the homogeneous Fermi gas, whose exact ground-state energy was first determined by Yang [2] via the Bethe Anstatz technique, and the single-band Hubbard model, whose solution was provided by Lieb and Wu [3]. These two paradigmatic models describe two opposite limits of realistic physical systems, which in general are neither perfectly homogeneous nor devoid of interband couplings. In the absence of exact analytical theories for the more realistic intermediate regime, developing unbiased computational techniques is of outmost importance. The experiments performed with ultracold atoms trapped in optical lattices (OLs) have emerged as the ideal playground to investigate quantum many-body phenomena in periodic potentials [4]. The intensity of the external periodic field can be easily varied by tuning a laser power, and also the interaction strength can by tuned exploiting Feshbach resonances [5]. This has recently allowed the remarkable observation of antiferromagnetic correlations in a controlled experimental setup, both in two and in one dimension [6][7][8][9][10][11][12]. The bulk of early research activity on OL systems focussed on deep OLs and weak interactions, where single-band tight-binding models are adequate [13]. Away from this regime multi-band processes come into play, and the effect of the independent tuning of the OL intensity and the in...

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“…The experimental progress has generated great interest for few-body problems in one-dimensional geometries for both bosonic [21][22][23][24][25][26][27][28], fermionic [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46], and mixed systems [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61]. Recently, it has been shown that for strong short-range repulsive interactions a 1D two-component Fermi system in a harmonic trap exhibits strong magnetic correlations already at the three-body level [37,40].…”

Section: Introductionmentioning

confidence: 99%

A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap

et al. 2015

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We study a three-body system with zero-range interactions in a one-dimensional harmonic trap. The system consists of two spin-polarized fermions and a third particle which is distinct from two others (2+1 system). First we assume that the particles have equal masses. For this case the system in the strongly and weakly interacting limits can be accurately described using wave function factorized in hypercylindrical coordinates. Inspired by this result we propose an interpolation ansatz for the wave function for arbitrary repulsive zero-range interactions. By comparison to numerical calculations, we show that this interpolation scheme yields an extremely good approximation to the numerically exact solution both in terms of the energies and also in the spin-resolved densities. As an outlook, we discuss the case of mass imbalanced systems in the strongly interacting limit. Here we find spectra that demonstrate that the triply degenerate spectrum at infinite coupling strength of the equal mass case is in some sense a singular case as this degeneracy will be broken down to a doubly degenerate or non-degenerate ground state by any small mass imbalance.

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Molecular branch of a small highly elongated Fermi gas with an impurity: Full three-dimensional versus effective one-dimensional description

Cited by 7 publications

References 33 publications

Tunneling dynamics of two interacting one-dimensional particles

Tunneling dynamics of two interacting one-dimensional particles

One-dimensional repulsive Fermi gas in a tunable periodic potential

A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap

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