Three interacting atoms in a one-dimensional trap: a benchmark system for computational approaches

D'Amico, Pino; Rontani, Massimo

doi:10.1088/0953-4075/47/6/065303

Cited by 24 publications

(14 citation statements)

References 98 publications

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“…We verified that for ω y /ω x = 100 (strictly-1D single trap), our CI calculations agree with the results of Table 2 of Ref. [30].…”

Section: Many-body Hamiltoniansupporting

confidence: 89%

“…Note that the TCO single-particle states automatically adjust to the separation d as it varies from the limit of the unified atom d=0 to that of the two fully separated traps (for sufficiently large d). We verified that for w w = 100 y x (strictly 1D single trap), our CI calculations agree with the results of table 2 of [30]. The matrix elements of  MB between the CI determinants are calculated using the Slater rules.…”

Section: Many-body Hamiltoniansupporting

confidence: 80%

“…[27,28] and [29], respectively. Similarly, states of ultracold fermions in a single strictly-1D trap, away from the fermionization limit, using an exact diagonalization of the many-body Hamiltonian have been reported [30].…”

Section: Introductionmentioning

confidence: 80%

“…We remark that the physics of ultracold atoms in 1D and 3D single traps has been investigated also away from the fermionization point using a Lippman-Schwinger equation approach, see [27][28][29], respectively. Similarly, states of ultracold fermions in a single strictly 1D trap, away from the fermionization limit, using an exact diagonalization of the many-body Hamiltonian have been reported [30].…”

Section: Introductionmentioning

confidence: 80%

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Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg andt–Jmodels

2016

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Advances with trapped ultracold atoms intensified interest in simulating complex physical phenomena, including quantum magnetism and transitions from itinerant to non-itinerant behavior.Here we show formation of antiferromagnetic ground states of few ultracold fermionic atoms in single and double well (DW) traps, through microscopic Hamiltonian exact diagonalization for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells, and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D, nature. The spectra and spin-resolved conditional probabilities reveal for both cases, under strong repulsion, atomic spatial localization at extemporaneously created sites, forming quantum molecular magnetic structures with non-itinerant character. These findings usher future theoretical and experimental explorations into the highly correlated behavior of ultracold strongly repelling fermionic atoms in higher dimensions, beyond the fermionization physics that is strictly applicable only in the 1D case. The results for four atoms are well described with finite Heisenberg spin-chain and cluster models. The numerical simulations of three fermionic atoms in symmetric DWs reveal the emergent appearance of coupled resonating 2D Heisenberg clusters, whose emulation requires the use of a t-J-like model, akin to that used in investigations of high T c superconductivity. The highly entangled states discovered in the microscopic and model calculations of controllably detuned, asymmetric, DWs suggest three-cold-atom DW quantum computing qubits. New J. Phys. 18 (2016) 073018 C Yannouleas et al New J. Phys. 18 (2016) 073018 C Yannouleas et al ⎟ ⎟ ⎟ 18 J J J t t t J J J J t t t J J J J t t t t t t J J J t t t J J J J t t t J J J J Figure B1. Schematics indicating the four-site numbering convention in the Heisenberg Hamiltonian. (a) The case of formation of a rectangular parallelogram (ring topology). The Heisenberg exchange parameters = = J J s 14 23 and = = J J r 12 34 . (b) The linear arrangement of the four sites which results from (a) by opening the ring through setting = J 0 34 , = J r 12 , = = J J s 14 23 . ( )  Due to the reflection symmetry in x and y,  H RP,gen has only two different exchange constants = = J J s 14 23 and = = J J r 12 34

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“…We verified that for ω y /ω x = 100 (strictly-1D single trap), our CI calculations agree with the results of Table 2 of Ref. [30].…”

Section: Many-body Hamiltoniansupporting

confidence: 89%

Section: Many-body Hamiltoniansupporting

confidence: 80%

Section: Introductionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 80%

See 2 more Smart Citations

Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg andt–Jmodels

2016

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“…In this work we focus on mixtures where the number of atoms is small. The recent successful experimental trapping of ensembles of a few atoms [48][49][50][51][52] has inspired an intense theoretical effort [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67], and very recently even systems with SU(N) symmetry and > N 2 have been experimentally realized [68]. For mixtures of a few atoms, direct diagonalization methods [31,42,45] can be used together with other numerical methods efficient for larger numbers of atoms, like multiconfigurational Hartree-Fock methods (MCTDH) [70], density functional theory (DFT) [44], or quantum diffusion Monte Carlo (DMC) [69].…”

Section: Introductionmentioning

confidence: 99%

Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures

et al. 2014

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We present the complete phase diagram for one-dimensional binary mixtures of bosonic ultracold atomic gases in a harmonic trap. We obtain exact results with direct numerical diagonalization for a small number of atoms, which permits us to quantify quantum many-body correlations. The quantum Monte Carlo method is used to calculate energies and density profiles for larger system sizes. We study the system properties for a wide range of interaction parameters. For the extreme values of these parameters, different correlation limits can be identified, where the correlations are either weak or strong. We investigate in detail how the correlations evolve between the limits. For balanced mixtures in the number of atoms in each species, the transition between the different limits involves sophisticated changes in the one-and two-body correlations. Particularly, we quantify the entanglement between the two components by means of the von Neumann entropy. We show that the limits equally exist when the number of atoms is increased for balanced mixtures. Also, the changes in the correlations along the transitions among these limits are qualitatively similar. We also show that, for imbalanced mixtures, the same limits with similar transitions exist. Finally, for strongly imbalanced systems, only two limits survive, i.e., a miscible Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. limit and a phase-separated one, resembling those expected with a mean-field approach.

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One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: I. One, Two, and Three Particles

Harshman

2015

Few-Body Syst

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This is the first in a pair of articles that classify the configuration space and kinematic symmetry groups for N identical particles in one-dimensional traps experiencing Galilean-invariant two-body interactions. These symmetries explain degeneracies in the few-body spectrum and demonstrate how tuning the trap shape and the particle interactions can manipulate these degeneracies.The additional symmetries that emerge in the non-interacting limit and in the unitary limit of an infinitely strong contact interaction are sufficient to algebraically solve for the spectrum and degeneracy in terms of the one-particle observables. Symmetry also determines the degree to which the algebraic expressions for energy level shifts by weak interactions or nearly-unitary interactions are universal, i.e. independent of trap shape and details of the interaction. Identical fermions and bosons with and without spin are considered. This article sequentially analyzes the symmetries of one, two and three particles in asymmetric, symmetric, and harmonic traps; the sequel article treats the N particle case.

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Three interacting atoms in a one-dimensional trap: a benchmark system for computational approaches

Cited by 24 publications

References 98 publications

Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg andt–Jmodels

Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg andt–Jmodels

Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures

One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: I. One, Two, and Three Particles

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